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Your data matches 13 different statistics following compositions of up to 3 maps.
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Matching statistic: St000079
(load all 9 compositions to match this statistic)
(load all 9 compositions to match this statistic)
St000079: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> 1
[1,0,1,0]
=> 1
[1,1,0,0]
=> 1
[1,0,1,0,1,0]
=> 1
[1,0,1,1,0,0]
=> 1
[1,1,0,0,1,0]
=> 1
[1,1,0,1,0,0]
=> 2
[1,1,1,0,0,0]
=> 2
[1,0,1,0,1,0,1,0]
=> 1
[1,0,1,0,1,1,0,0]
=> 1
[1,0,1,1,0,0,1,0]
=> 1
[1,0,1,1,0,1,0,0]
=> 2
[1,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,0,1,0]
=> 1
[1,1,0,0,1,1,0,0]
=> 1
[1,1,0,1,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,0]
=> 5
[1,1,0,1,1,0,0,0]
=> 5
[1,1,1,0,0,0,1,0]
=> 2
[1,1,1,0,0,1,0,0]
=> 5
[1,1,1,0,1,0,0,0]
=> 7
[1,1,1,1,0,0,0,0]
=> 7
[1,0,1,0,1,0,1,0,1,0]
=> 1
[1,0,1,0,1,0,1,1,0,0]
=> 1
[1,0,1,0,1,1,0,0,1,0]
=> 1
[1,0,1,0,1,1,0,1,0,0]
=> 2
[1,0,1,0,1,1,1,0,0,0]
=> 2
[1,0,1,1,0,0,1,0,1,0]
=> 1
[1,0,1,1,0,0,1,1,0,0]
=> 1
[1,0,1,1,0,1,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,1,0,0]
=> 5
[1,0,1,1,0,1,1,0,0,0]
=> 5
[1,0,1,1,1,0,0,0,1,0]
=> 2
[1,0,1,1,1,0,0,1,0,0]
=> 5
[1,0,1,1,1,0,1,0,0,0]
=> 7
[1,0,1,1,1,1,0,0,0,0]
=> 7
[1,1,0,0,1,0,1,0,1,0]
=> 1
[1,1,0,0,1,0,1,1,0,0]
=> 1
[1,1,0,0,1,1,0,0,1,0]
=> 1
[1,1,0,0,1,1,0,1,0,0]
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> 2
[1,1,0,1,0,0,1,0,1,0]
=> 2
[1,1,0,1,0,0,1,1,0,0]
=> 2
[1,1,0,1,0,1,0,0,1,0]
=> 5
[1,1,0,1,0,1,0,1,0,0]
=> 14
[1,1,0,1,0,1,1,0,0,0]
=> 14
[1,1,0,1,1,0,0,0,1,0]
=> 5
[1,1,0,1,1,0,0,1,0,0]
=> 14
[1,1,0,1,1,0,1,0,0,0]
=> 21
[1,1,0,1,1,1,0,0,0,0]
=> 21
Description
The number of alternating sign matrices for a given Dyck path.
The Dyck path is given by the last diagonal of the monotone triangle corresponding to an alternating sign matrix.
Matching statistic: St001934
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St001934: Integer partitions ⟶ ℤResult quality: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 29%
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St001934: Integer partitions ⟶ ℤResult quality: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 29%
Values
[1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> [1]
=> 1
[1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,1,0,1,0,0]
=> [1]
=> 1
[1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> [2,1]
=> 1
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1]
=> 1
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,1,0,1,0,0,1,0]
=> [3,1]
=> 2
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0]
=> [2,1,1]
=> 1
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> [2,1]
=> 1
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 2
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1]
=> 1
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> [4,1]
=> 5
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [3,1,1]
=> 2
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [3,1]
=> 2
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> ? ∊ {1,5,7,7}
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> 1
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> ? ∊ {1,5,7,7}
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [2,1,1]
=> 1
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [2,1]
=> 1
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> 5
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> ? ∊ {1,5,7,7}
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> 2
[1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> 2
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> ? ∊ {1,5,7,7}
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1]
=> 1
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [5,1]
=> 14
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [4,1,1]
=> 5
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [4,1]
=> 5
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0,1,0]
=> [5,4,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [3,1,1,1]
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [3,1,1]
=> 2
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [3,1]
=> 2
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> [5,3,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [4,3,1,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [4,3,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,1,1,1,1]
=> 1
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0,1,0]
=> [5,2,1,1,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,1,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [2,1,1,1]
=> 1
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0]
=> [5,2,1,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [2,1,1]
=> 1
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [2,1]
=> 1
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0,1,0]
=> [5,2,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [4,2,1,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [4,2,1]
=> 5
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [3,2,2,2,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> [3,2,2,1,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [3,2,1,1,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [3,2,2,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [3,2,1,1]
=> 2
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [3,2,1]
=> 2
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,2,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1]
=> ? ∊ {1,1,1,2,2,2,2,2,5,5,5,7,7,7,7,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> [1]
=> 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> [6,1]
=> 42
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,1,0,0]
=> [5,1,1]
=> 14
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,1,0,0]
=> [5,1]
=> 14
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
=> [6,5,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429}
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=> [1,1,1,0,1,1,1,0,0,0,1,0,0,0]
=> [4,1,1,1]
=> 5
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0,1,0]
=> [6,4,1,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429}
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,1,0,0,0,1,0,0,0]
=> [4,1,1]
=> 5
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,1,0,0,0]
=> [4,1]
=> 5
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
=> [6,4,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429}
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,0,1,1,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,1,0,1,0,0]
=> [5,4,4,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429}
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,1,0,1,0,0]
=> [5,4,1,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429}
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
=> [5,4,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429}
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
=> [6,5,4,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429}
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> [3,1,1,1,1]
=> 2
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,0,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=> [6,3,1,1,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429}
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [5,3,3,1,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429}
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=> [5,3,1,1,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429}
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0,1,0]
=> [6,5,3,1,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429}
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,1,0,1,1,1,0,0,1,0,0,0,0]
=> [3,1,1,1]
=> 2
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0,1,0]
=> [6,3,1,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429}
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,1,0,0,1,0,0,0,0]
=> [3,1,1]
=> 2
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,1,0,0,0,0]
=> [3,1]
=> 2
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0,1,0]
=> [6,3,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429}
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,1,0,0]
=> [5,3,3,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429}
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,1,0,0]
=> [5,3,1,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429}
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,1,0,0]
=> [5,3,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429}
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
=> [6,5,3,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429}
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,1,0,1,0,0,0]
=> [4,3,3,3,1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429}
[1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [2,1,1,1,1,1]
=> 1
[1,1,0,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> [2,1,1,1,1]
=> 1
[1,1,0,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,1,1,0,1,1,1,0,1,0,0,0,0,0]
=> [2,1,1,1]
=> 1
[1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> [2,1,1]
=> 1
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [2,1]
=> 1
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,1,0,0,0]
=> [4,2,1]
=> 5
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,0,1,0,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=> [3,2,1,1]
=> 2
Description
The number of monotone factorisations of genus zero of a permutation of given cycle type.
A monotone factorisation of genus zero of a permutation $\pi\in\mathfrak S_n$ with $\ell$ cycles, including fixed points, is a tuple of $r = n - \ell$ transpositions
$$
(a_1, b_1),\dots,(a_r, b_r)
$$
with $b_1 \leq \dots \leq b_r$ and $a_i < b_i$ for all $i$, whose product, in this order, is $\pi$.
For example, the cycle $(2,3,1)$ has the two factorizations $(2,3)(1,3)$ and $(1,2)(2,3)$.
Matching statistic: St001630
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 6% ●values known / values provided: 14%●distinct values known / distinct values provided: 6%
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 6% ●values known / values provided: 14%●distinct values known / distinct values provided: 6%
Values
[1,0]
=> [1] => ([(0,1)],2)
=> ([(0,1)],2)
=> ? = 1 + 1
[1,0,1,0]
=> [1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,1,0,0]
=> [2,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,0,1,0]
=> [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,0,0]
=> [1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2} + 1
[1,1,0,0,1,0]
=> [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2} + 1
[1,1,0,1,0,0]
=> [2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2} + 1
[1,1,1,0,0,0]
=> [3,1,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2} + 1
[1,0,1,0,1,0,1,0]
=> [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,0,1,1,0,0]
=> [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,0,1,1,0,0,1,0]
=> [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,0,1,0,0]
=> [1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,0,1,1,1,0,0,0]
=> [1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,1,0,0,1,0,1,0]
=> [2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,1,0,0,1,1,0,0]
=> [2,1,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,1,0,1,0,0,1,0]
=> [2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,1,0,1,0,1,0,0]
=> [2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,1,0,1,1,0,0,0]
=> [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 1 + 1
[1,1,1,0,0,0,1,0]
=> [3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,1,1,0,0,1,0,0]
=> [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 1 + 1
[1,1,1,0,1,0,0,0]
=> [3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,1,1,1,0,0,0,0]
=> [4,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,2,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,3,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,0,1,1,0,1,1,0,0,0]
=> [1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,0,1,1,1,0,1,0,0,0]
=> [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(1,9),(2,7),(3,7),(4,6),(5,6),(6,9),(7,8),(8,10),(9,10)],11)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,1,1,0,0,1,0,0]
=> [2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [2,4,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,1,1,1,0,0,0,0]
=> [2,5,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,0,0,0,1,0,1,0]
=> [3,1,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,0,0,0,1,1,0,0]
=> [3,1,2,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,0,0,1,0,0,1,0]
=> [3,1,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,0,0,1,0,1,0,0]
=> [3,1,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,0,0,1,1,0,0,0]
=> [3,1,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
[1,1,1,0,1,0,0,0,1,0]
=> [3,4,1,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,0,1,0,0,1,0,0]
=> [3,4,1,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,0,1,0,1,0,0,0]
=> [3,4,5,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,0,1,1,0,0,0,0]
=> [3,5,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,1,0,0,0,0,1,0]
=> [4,1,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,1,0,0,0,1,0,0]
=> [4,1,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,1,0,0,1,0,0,0]
=> [4,1,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,1,0,1,0,0,0,0]
=> [4,5,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,1,1,0,0,0,0,0]
=> [5,1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,2,3,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,2,4,3,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(2,17),(3,13),(4,12),(5,12),(5,15),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,14),(16,9),(16,14),(17,15),(17,16)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,2,4,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,2,5,3,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,3,2,4,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,3,2,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,13),(5,14),(6,14),(8,7),(9,7),(10,8),(11,9),(12,8),(12,9),(13,10),(13,12),(14,11),(14,12)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,3,4,2,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,3,4,5,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,3,5,2,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,9),(8,9),(10,7),(10,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,4,2,3,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,9),(8,9),(10,7),(10,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,4,5,2,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,8),(4,8),(5,7),(6,7),(7,11),(8,11),(9,12),(10,12),(11,9),(11,10)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,5,2,3,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
Description
The global dimension of the incidence algebra of the lattice over the rational numbers.
Matching statistic: St001878
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
St001878: Lattices ⟶ ℤResult quality: 6% ●values known / values provided: 14%●distinct values known / distinct values provided: 6%
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
St001878: Lattices ⟶ ℤResult quality: 6% ●values known / values provided: 14%●distinct values known / distinct values provided: 6%
Values
[1,0]
=> [1] => ([(0,1)],2)
=> ([(0,1)],2)
=> ? = 1 + 1
[1,0,1,0]
=> [1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,1,0,0]
=> [2,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,0,1,0]
=> [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,0,0]
=> [1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2} + 1
[1,1,0,0,1,0]
=> [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2} + 1
[1,1,0,1,0,0]
=> [2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2} + 1
[1,1,1,0,0,0]
=> [3,1,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2} + 1
[1,0,1,0,1,0,1,0]
=> [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,0,1,1,0,0]
=> [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,0,1,1,0,0,1,0]
=> [1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,0,1,0,0]
=> [1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,0,1,1,1,0,0,0]
=> [1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,1,0,0,1,0,1,0]
=> [2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,1,0,0,1,1,0,0]
=> [2,1,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,1,0,1,0,0,1,0]
=> [2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,1,0,1,0,1,0,0]
=> [2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,1,0,1,1,0,0,0]
=> [2,4,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 1 + 1
[1,1,1,0,0,0,1,0]
=> [3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,1,1,0,0,1,0,0]
=> [3,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
=> 2 = 1 + 1
[1,1,1,0,1,0,0,0]
=> [3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,1,1,1,0,0,0,0]
=> [4,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,5,5,5,7,7} + 1
[1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,2,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,3,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,0,1,1,0,1,1,0,0,0]
=> [1,3,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [1,4,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,0,1,1,1,0,1,0,0,0]
=> [1,4,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,5,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(1,9),(2,7),(3,7),(4,6),(5,6),(6,9),(7,8),(8,10),(9,10)],11)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,1,1,0,0,0,1,0]
=> [2,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,1,1,0,0,1,0,0]
=> [2,4,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [2,4,5,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,0,1,1,1,0,0,0,0]
=> [2,5,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,0,0,0,1,0,1,0]
=> [3,1,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,0,0,0,1,1,0,0]
=> [3,1,2,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,0,0,1,0,0,1,0]
=> [3,1,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,0,0,1,0,1,0,0]
=> [3,1,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,0,0,1,1,0,0,0]
=> [3,1,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 2 = 1 + 1
[1,1,1,0,1,0,0,0,1,0]
=> [3,4,1,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,0,1,0,0,1,0,0]
=> [3,4,1,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,0,1,0,1,0,0,0]
=> [3,4,5,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,0,1,1,0,0,0,0]
=> [3,5,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,1,0,0,0,0,1,0]
=> [4,1,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,1,0,0,0,1,0,0]
=> [4,1,2,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,1,0,0,1,0,0,0]
=> [4,1,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,1,0,1,0,0,0,0]
=> [4,5,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([],1)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,1,1,1,1,0,0,0,0,0]
=> [5,1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,2,3,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,2,4,3,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(2,17),(3,13),(4,12),(5,12),(5,15),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,14),(16,9),(16,14),(17,15),(17,16)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,2,4,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,2,5,3,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,3,2,4,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,3,2,5,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,13),(5,14),(6,14),(8,7),(9,7),(10,8),(11,9),(12,8),(12,9),(13,10),(13,12),(14,11),(14,12)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,3,4,2,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,3,4,5,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,3,5,2,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,9),(8,9),(10,7),(10,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,4,2,3,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,4,2,5,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,9),(8,9),(10,7),(10,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,4,5,2,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,8),(4,8),(5,7),(6,7),(7,11),(8,11),(9,12),(10,12),(11,9),(11,10)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,5,2,3,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
Description
The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.
Matching statistic: St001876
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
St001876: Lattices ⟶ ℤResult quality: 6% ●values known / values provided: 13%●distinct values known / distinct values provided: 6%
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
St001876: Lattices ⟶ ℤResult quality: 6% ●values known / values provided: 13%●distinct values known / distinct values provided: 6%
Values
[1,0]
=> [1] => ([(0,1)],2)
=> ([(0,1)],2)
=> ? = 1
[1,0,1,0]
=> [2,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,0]
=> [1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,0]
=> [3,2,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,0]
=> [2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,2,2}
[1,1,0,0,1,0]
=> [3,1,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,2,2}
[1,1,0,1,0,0]
=> [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,2,2}
[1,1,1,0,0,0]
=> [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(1,9),(2,7),(3,7),(4,6),(5,6),(6,9),(7,8),(8,10),(9,10)],11)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,0,1,1,0,0,0]
=> [3,4,1,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,1,0,0,0,1,0]
=> [5,2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,1,0,1,0,0,0]
=> [3,2,1,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,1,1,0,0,0,0]
=> [2,3,1,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,1,0,0,0,0,1,0]
=> [5,1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,1,0,0,0,1,0,0]
=> [4,1,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,1,0,0,1,0,0,0]
=> [3,1,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,5,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(2,17),(3,13),(4,12),(5,12),(5,15),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,14),(16,9),(16,14),(17,15),(17,16)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [6,4,3,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [6,3,4,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,5,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,13),(5,14),(6,14),(8,7),(9,7),(10,8),(11,9),(12,8),(12,9),(13,10),(13,12),(14,11),(14,12)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [6,3,4,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [6,5,2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [6,4,2,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [6,3,2,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [6,2,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,12),(5,12),(5,15),(6,13),(6,15),(8,14),(9,14),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
Description
The number of 2-regular simple modules in the incidence algebra of the lattice.
Matching statistic: St001877
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
St001877: Lattices ⟶ ℤResult quality: 6% ●values known / values provided: 13%●distinct values known / distinct values provided: 6%
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
St001877: Lattices ⟶ ℤResult quality: 6% ●values known / values provided: 13%●distinct values known / distinct values provided: 6%
Values
[1,0]
=> [1] => ([(0,1)],2)
=> ([(0,1)],2)
=> ? = 1
[1,0,1,0]
=> [2,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,1,0,0]
=> [1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,0]
=> [3,2,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,0]
=> [2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,2,2}
[1,1,0,0,1,0]
=> [3,1,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,2,2}
[1,1,0,1,0,0]
=> [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,2,2}
[1,1,1,0,0,0]
=> [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7}
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(1,9),(2,7),(3,7),(4,6),(5,6),(6,9),(7,8),(8,10),(9,10)],11)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,0,1,1,0,0,0]
=> [3,4,1,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,1,0,0,0,1,0]
=> [5,2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,1,0,1,0,0,0]
=> [3,2,1,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,1,1,0,0,0,0]
=> [2,3,1,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,1,0,0,0,0,1,0]
=> [5,1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,1,0,0,0,1,0,0]
=> [4,1,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,1,0,0,1,0,0,0]
=> [3,1,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,5,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(2,17),(3,13),(4,12),(5,12),(5,15),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,14),(16,9),(16,14),(17,15),(17,16)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [6,4,3,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [6,3,4,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,5,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,13),(5,14),(6,14),(8,7),(9,7),(10,8),(11,9),(12,8),(12,9),(13,10),(13,12),(14,11),(14,12)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [6,3,4,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [6,5,2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [6,4,2,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [6,3,2,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [6,2,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,12),(5,12),(5,15),(6,13),(6,15),(8,14),(9,14),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
Description
Number of indecomposable injective modules with projective dimension 2.
Matching statistic: St001846
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
St001846: Lattices ⟶ ℤResult quality: 12% ●values known / values provided: 13%●distinct values known / distinct values provided: 12%
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
St001846: Lattices ⟶ ℤResult quality: 12% ●values known / values provided: 13%●distinct values known / distinct values provided: 12%
Values
[1,0]
=> [2,1] => [2,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 0 = 1 - 1
[1,0,1,0]
=> [3,1,2] => [2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 1 - 1
[1,1,0,0]
=> [2,3,1] => [1,3,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 1 - 1
[1,0,1,0,1,0]
=> [4,1,2,3] => [2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> 0 = 1 - 1
[1,0,1,1,0,0]
=> [3,1,4,2] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> 0 = 1 - 1
[1,1,0,0,1,0]
=> [2,4,1,3] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> 0 = 1 - 1
[1,1,0,1,0,0]
=> [4,3,1,2] => [3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> 1 = 2 - 1
[1,1,1,0,0,0]
=> [2,3,4,1] => [1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> 1 = 2 - 1
[1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => [2,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} - 1
[1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => [5,2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} - 1
[1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => [4,1,5,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> 0 = 1 - 1
[1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => [4,5,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} - 1
[1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => [3,1,5,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 0 = 1 - 1
[1,1,0,0,1,0,1,0]
=> [2,5,1,3,4] => [1,3,4,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} - 1
[1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => [5,1,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} - 1
[1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => [3,4,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} - 1
[1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => [3,4,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} - 1
[1,1,0,1,1,0,0,0]
=> [4,3,1,5,2] => [5,3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} - 1
[1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => [1,2,4,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} - 1
[1,1,1,0,0,1,0,0]
=> [2,5,4,1,3] => [4,5,1,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} - 1
[1,1,1,0,1,0,0,0]
=> [5,3,4,1,2] => [4,2,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
=> 0 = 1 - 1
[1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [1,2,3,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} - 1
[1,0,1,0,1,0,1,0,1,0]
=> [6,1,2,3,4,5] => [2,3,4,5,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(2,13),(3,7),(4,13),(4,16),(5,14),(5,17),(6,16),(6,17),(8,12),(9,12),(10,8),(11,9),(12,7),(13,10),(14,11),(15,8),(15,9),(16,10),(16,15),(17,11),(17,15)],18)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,0,1,0,1,1,0,0]
=> [5,1,2,3,6,4] => [6,2,3,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(3,8),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,0,1,1,0,0,1,0]
=> [4,1,2,6,3,5] => [5,6,2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,9),(5,9),(6,7),(6,10),(7,12),(8,11),(9,10),(10,12),(12,11)],13)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,0,1,1,0,1,0,0]
=> [6,1,2,5,3,4] => [5,6,2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,9),(4,12),(5,12),(6,10),(6,11),(8,7),(9,7),(10,13),(11,13),(12,8),(13,8),(13,9)],14)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,0,1,1,1,0,0,0]
=> [4,1,2,5,6,3] => [4,6,2,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,9),(3,9),(4,9),(5,7),(6,7),(7,8),(8,9)],10)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,1,0,0,1,0,1,0]
=> [3,1,6,2,4,5] => [4,1,5,6,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,1,0,0,1,1,0,0]
=> [3,1,5,2,6,4] => [1,6,4,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,10),(5,11),(6,8),(7,11),(9,10),(10,8),(11,9)],12)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,1,0,1,0,0,1,0]
=> [6,1,4,2,3,5] => [4,5,2,3,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,8),(4,8),(5,7),(6,7),(7,11),(8,11),(9,10),(11,9)],12)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,1,0,1,0,1,0,0]
=> [6,1,5,2,3,4] => [4,5,6,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(2,11),(3,10),(4,13),(5,13),(6,11),(6,12),(8,9),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,1,0,1,1,0,0,0]
=> [5,1,4,2,6,3] => [6,4,2,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,10),(4,9),(5,8),(6,11),(7,9),(7,10),(9,12),(10,12),(11,8),(12,11)],13)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,1,1,0,0,0,1,0]
=> [3,1,4,6,2,5] => [3,1,5,6,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 0 = 1 - 1
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,6,5,2,4] => [1,5,6,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,9),(6,10),(6,11),(7,11),(8,10),(10,12),(11,12),(12,9)],13)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,1,1,0,1,0,0,0]
=> [6,1,4,5,2,3] => [5,3,6,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,8),(6,7),(8,7)],9)
=> 0 = 1 - 1
[1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => [3,1,4,6,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,1,0,0,1,0,1,0,1,0]
=> [2,6,1,3,4,5] => [1,3,4,5,6,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,13),(3,12),(4,7),(5,12),(5,14),(6,13),(6,14),(8,11),(9,8),(10,8),(11,7),(12,9),(13,10),(14,9),(14,10)],15)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,5,1,3,6,4] => [6,1,3,4,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,10),(6,11),(7,11),(8,12),(9,12),(11,8),(11,9),(12,10)],13)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,0,1,1,0,0,1,0]
=> [2,4,1,6,3,5] => [5,1,2,6,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,0,1,1,0,1,0,0]
=> [2,6,1,5,3,4] => [5,6,1,3,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,7),(4,7),(5,8),(6,8),(7,11),(8,9),(9,10),(10,11)],12)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,0,1,1,1,0,0,0]
=> [2,4,1,5,6,3] => [4,1,2,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 0 = 1 - 1
[1,1,0,1,0,0,1,0,1,0]
=> [6,3,1,2,4,5] => [3,4,2,5,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,10),(5,11),(6,7),(6,9),(7,12),(8,11),(9,12),(11,9),(12,10)],13)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,1,0,0,1,1,0,0]
=> [5,3,1,2,6,4] => [6,3,2,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,10),(5,11),(6,8),(7,11),(9,10),(10,8),(11,9)],12)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,1,0,1,0,0,1,0]
=> [6,4,1,2,3,5] => [3,4,5,2,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(3,8),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,1,0,1,0,1,0,0]
=> [5,6,1,2,3,4] => [3,4,5,1,6,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,8),(5,7),(6,7),(6,8),(7,9),(8,9),(9,10)],11)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,1,0,1,1,0,0,0]
=> [5,4,1,2,6,3] => [6,3,4,2,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,9),(5,11),(6,7),(6,10),(7,12),(8,10),(10,12),(11,9),(12,11)],13)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,1,1,0,0,0,1,0]
=> [4,3,1,6,2,5] => [5,2,1,6,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,8),(4,8),(5,7),(6,7),(7,9),(8,9)],10)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,1,1,0,0,1,0,0]
=> [6,3,1,5,2,4] => [5,2,6,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,9),(4,7),(5,7),(6,8),(7,9),(9,8)],10)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,1,1,0,1,0,0,0]
=> [6,4,1,5,2,3] => [5,6,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,7),(4,7),(5,8),(6,8),(7,12),(8,9),(9,10),(9,12),(10,11),(12,11)],13)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,1,1,1,0,0,0,0]
=> [4,3,1,5,6,2] => [4,2,1,6,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 0 = 1 - 1
[1,1,1,0,0,0,1,0,1,0]
=> [2,3,6,1,4,5] => [1,2,4,5,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(2,11),(3,13),(4,10),(5,11),(5,12),(6,9),(6,13),(8,10),(9,7),(10,9),(11,8),(12,8),(13,7)],14)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,1,0,0,0,1,1,0,0]
=> [2,3,5,1,6,4] => [6,1,2,4,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(2,14),(3,14),(4,11),(5,7),(6,12),(6,13),(8,10),(9,10),(10,7),(11,9),(12,8),(13,8),(13,9),(14,11),(14,13)],15)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,1,0,0,1,0,0,1,0]
=> [2,6,4,1,3,5] => [4,5,1,3,6,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 0 = 1 - 1
[1,1,1,0,0,1,0,1,0,0]
=> [2,6,5,1,3,4] => [4,5,6,1,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,8),(3,7),(4,9),(5,9),(6,7),(6,8),(7,11),(8,11),(9,10),(10,12),(11,12)],13)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,1,0,0,1,1,0,0,0]
=> [2,5,4,1,6,3] => [6,4,1,3,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,10),(5,11),(6,8),(7,11),(9,10),(10,8),(11,9)],12)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,1,0,1,0,0,0,1,0]
=> [6,3,4,1,2,5] => [4,2,5,3,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(9,7)],10)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,1,0,1,0,0,1,0,0]
=> [6,3,5,1,2,4] => [4,2,5,6,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,9),(4,7),(5,7),(6,8),(7,9),(9,8)],10)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,1,0,1,0,1,0,0,0]
=> [6,5,4,1,2,3] => [4,5,6,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(2,13),(3,12),(4,13),(4,14),(5,11),(5,15),(6,12),(6,15),(8,11),(9,7),(10,7),(11,9),(12,10),(13,8),(14,8),(15,9),(15,10)],16)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,1,0,1,1,0,0,0,0]
=> [5,3,4,1,6,2] => [2,6,4,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
=> 0 = 1 - 1
[1,1,1,1,0,0,0,0,1,0]
=> [2,3,4,6,1,5] => [1,2,3,5,6,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(2,13),(3,13),(4,11),(5,12),(5,14),(6,10),(6,14),(8,7),(9,7),(10,9),(11,10),(12,8),(13,11),(14,8),(14,9)],15)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,1,1,0,0,0,1,0,0]
=> [2,3,6,5,1,4] => [5,6,1,2,4,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,8),(3,8),(4,9),(5,9),(6,7),(6,10),(7,12),(8,11),(9,10),(10,12),(12,11)],13)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,1,1,0,0,1,0,0,0]
=> [2,6,4,5,1,3] => [5,3,6,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> 0 = 1 - 1
[1,1,1,1,0,1,0,0,0,0]
=> [6,3,4,5,1,2] => [2,5,3,6,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(9,7)],10)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,6,1] => [1,2,3,4,6,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,14),(2,14),(3,13),(4,12),(4,16),(5,13),(5,17),(6,16),(6,17),(8,10),(9,11),(10,7),(11,7),(12,8),(13,9),(14,12),(15,10),(15,11),(16,8),(16,15),(17,9),(17,15)],18)
=> ? ∊ {2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => ?
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429} - 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [6,1,2,3,4,7,5] => [7,2,3,4,5,1,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,12),(2,13),(3,15),(4,14),(5,8),(6,14),(6,16),(7,15),(7,16),(9,12),(10,9),(11,9),(12,13),(13,8),(14,10),(15,11),(16,10),(16,11)],17)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429} - 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,1,2,3,7,4,6] => [6,7,2,3,1,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,11),(2,8),(3,8),(4,9),(5,10),(6,10),(7,9),(7,12),(8,14),(9,13),(10,11),(11,12),(12,13),(13,14)],15)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429} - 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [7,1,2,3,6,4,5] => [6,7,2,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,12),(2,15),(3,15),(4,14),(5,13),(6,13),(6,17),(7,14),(7,17),(9,16),(10,16),(11,8),(12,8),(13,9),(14,10),(15,11),(16,11),(16,12),(17,9),(17,10)],18)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429} - 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [5,1,2,3,6,7,4] => [5,7,2,3,1,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,11),(4,11),(5,11),(6,9),(7,10),(8,10),(9,11),(10,9)],12)
=> ? ∊ {1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429} - 1
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [6,1,4,5,2,7,3] => [3,7,5,2,4,1,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0 = 1 - 1
[1,1,0,0,1,1,1,0,1,0,0,0]
=> [2,7,1,5,6,3,4] => [6,4,7,1,3,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0 = 1 - 1
[1,1,0,1,0,0,1,1,1,0,0,0]
=> [5,3,1,2,6,7,4] => [5,2,7,3,1,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0 = 1 - 1
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [5,3,4,1,6,7,2] => [2,5,3,1,7,4,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0 = 1 - 1
[1,1,1,1,0,0,1,0,0,0,1,0]
=> [2,7,4,5,1,3,6] => [5,3,6,1,4,7,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0 = 1 - 1
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [2,6,4,5,1,7,3] => [3,7,5,1,4,2,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0 = 1 - 1
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [2,7,4,5,6,1,3] => [3,6,4,7,1,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
=> 0 = 1 - 1
Description
The number of elements which do not have a complement in the lattice.
A complement of an element $x$ in a lattice is an element $y$ such that the meet of $x$ and $y$ is the bottom element and their join is the top element.
Matching statistic: St001875
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
St001875: Lattices ⟶ ℤResult quality: 6% ●values known / values provided: 13%●distinct values known / distinct values provided: 6%
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
St001875: Lattices ⟶ ℤResult quality: 6% ●values known / values provided: 13%●distinct values known / distinct values provided: 6%
Values
[1,0]
=> [1] => ([(0,1)],2)
=> ([(0,1)],2)
=> ? = 1 + 2
[1,0,1,0]
=> [2,1] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,1,0,0]
=> [1,2] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,0,1,0]
=> [3,2,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,1,0,0]
=> [2,3,1] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,2,2} + 2
[1,1,0,0,1,0]
=> [3,1,2] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,2,2} + 2
[1,1,0,1,0,0]
=> [2,1,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ? ∊ {1,2,2} + 2
[1,1,1,0,0,0]
=> [1,2,3] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} + 2
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} + 2
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} + 2
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} + 2
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} + 2
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} + 2
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} + 2
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} + 2
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} + 2
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} + 2
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,5,5,5,7,7} + 2
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(2,8),(3,8),(3,10),(4,9),(4,10),(6,5),(7,5),(8,6),(9,7),(10,6),(10,7)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,11),(3,10),(4,9),(4,12),(5,10),(5,12),(7,6),(8,6),(9,7),(10,8),(11,9),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(1,9),(2,7),(3,7),(4,6),(5,6),(6,9),(7,8),(8,10),(9,10)],11)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(7,9),(8,10),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,7),(6,9),(7,8),(8,9)],10)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
=> ([],1)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,1,0,0,1,1,0,0,0]
=> [3,4,1,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,1,0,1,0,0,0,1,0]
=> [5,2,1,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,1,0,1,0,1,0,0,0]
=> [3,2,1,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,1,0,1,1,0,0,0,0]
=> [2,3,1,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,1,1,0,0,0,0,1,0]
=> [5,1,2,3,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,11),(2,10),(3,6),(4,10),(4,12),(5,11),(5,12),(7,9),(8,9),(9,6),(10,7),(11,8),(12,7),(12,8)],13)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,1,1,0,0,0,1,0,0]
=> [4,1,2,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,1,1,0,0,1,0,0,0]
=> [3,1,2,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
=> ([(0,1)],2)
=> ? ∊ {1,1,2,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} + 2
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,5,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(2,17),(3,13),(4,12),(5,12),(5,15),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,14),(16,9),(16,14),(17,15),(17,16)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [6,4,3,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [6,3,4,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,5,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,13),(5,14),(6,14),(8,7),(9,7),(10,8),(11,9),(12,8),(12,9),(13,10),(13,12),(14,11),(14,12)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [6,3,4,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [6,5,2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [6,4,2,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [6,3,2,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [6,2,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,12),(5,12),(5,15),(6,13),(6,15),(8,14),(9,14),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,9)],16)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 3 = 1 + 2
Description
The number of simple modules with projective dimension at most 1.
Matching statistic: St001568
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001568: Integer partitions ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 12%
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001568: Integer partitions ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 12%
Values
[1,0]
=> [[1],[]]
=> []
=> ?
=> ? = 1
[1,0,1,0]
=> [[1,1],[]]
=> []
=> ?
=> ? ∊ {1,1}
[1,1,0,0]
=> [[2],[]]
=> []
=> ?
=> ? ∊ {1,1}
[1,0,1,0,1,0]
=> [[1,1,1],[]]
=> []
=> ?
=> ? ∊ {1,1,1,2,2}
[1,0,1,1,0,0]
=> [[2,1],[]]
=> []
=> ?
=> ? ∊ {1,1,1,2,2}
[1,1,0,0,1,0]
=> [[2,2],[1]]
=> [1]
=> []
=> ? ∊ {1,1,1,2,2}
[1,1,0,1,0,0]
=> [[3],[]]
=> []
=> ?
=> ? ∊ {1,1,1,2,2}
[1,1,1,0,0,0]
=> [[2,2],[]]
=> []
=> ?
=> ? ∊ {1,1,1,2,2}
[1,0,1,0,1,0,1,0]
=> [[1,1,1,1],[]]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,2,2,2,2,5,5,5,7,7}
[1,0,1,0,1,1,0,0]
=> [[2,1,1],[]]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,2,2,2,2,5,5,5,7,7}
[1,0,1,1,0,0,1,0]
=> [[2,2,1],[1]]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,2,2,2,2,5,5,5,7,7}
[1,0,1,1,0,1,0,0]
=> [[3,1],[]]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,2,2,2,2,5,5,5,7,7}
[1,0,1,1,1,0,0,0]
=> [[2,2,1],[]]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,2,2,2,2,5,5,5,7,7}
[1,1,0,0,1,0,1,0]
=> [[2,2,2],[1,1]]
=> [1,1]
=> [1]
=> ? ∊ {1,1,1,1,1,2,2,2,2,5,5,5,7,7}
[1,1,0,0,1,1,0,0]
=> [[3,2],[1]]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,2,2,2,2,5,5,5,7,7}
[1,1,0,1,0,0,1,0]
=> [[3,3],[2]]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,2,2,2,2,5,5,5,7,7}
[1,1,0,1,0,1,0,0]
=> [[4],[]]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,2,2,2,2,5,5,5,7,7}
[1,1,0,1,1,0,0,0]
=> [[3,3],[1]]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,2,2,2,2,5,5,5,7,7}
[1,1,1,0,0,0,1,0]
=> [[2,2,2],[1]]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,2,2,2,2,5,5,5,7,7}
[1,1,1,0,0,1,0,0]
=> [[3,2],[]]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,2,2,2,2,5,5,5,7,7}
[1,1,1,0,1,0,0,0]
=> [[2,2,2],[]]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,2,2,2,2,5,5,5,7,7}
[1,1,1,1,0,0,0,0]
=> [[3,3],[]]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,2,2,2,2,5,5,5,7,7}
[1,0,1,0,1,0,1,0,1,0]
=> [[1,1,1,1,1],[]]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,0,1,0,1,1,0,0]
=> [[2,1,1,1],[]]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,0,1,1,0,0,1,0]
=> [[2,2,1,1],[1]]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,0,1,1,0,1,0,0]
=> [[3,1,1],[]]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,0,1,1,1,0,0,0]
=> [[2,2,1,1],[]]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,0,0,1,0,1,0]
=> [[2,2,2,1],[1,1]]
=> [1,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1],[1]]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,0,1,0,0,1,0]
=> [[3,3,1],[2]]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,0,1,0,1,0,0]
=> [[4,1],[]]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,0,1,1,0,0,0]
=> [[3,3,1],[1]]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,1,0,0,0,1,0]
=> [[2,2,2,1],[1]]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,1,0,0,1,0,0]
=> [[3,2,1],[]]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,1,0,1,0,0,0]
=> [[2,2,2,1],[]]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,1,1,0,0,0,0]
=> [[3,3,1],[]]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2],[1,1,1]]
=> [1,1,1]
=> [1,1]
=> 2
[1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2],[1,1]]
=> [1,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2],[2,1]]
=> [2,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,0,1,1,0,1,0,0]
=> [[4,2],[1]]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2],[1,1]]
=> [1,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3],[2,2]]
=> [2,2]
=> [2]
=> 1
[1,1,0,1,0,0,1,1,0,0]
=> [[4,3],[2]]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,0,1,0,0,1,0]
=> [[4,4],[3]]
=> [3]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,0,1,0,1,0,0]
=> [[5],[]]
=> []
=> ?
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,0,1,1,0,0,0]
=> [[4,4],[2]]
=> [2]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3],[2,1]]
=> [2,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,1,0,0,1,0,0]
=> [[4,3],[1]]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3],[1,1]]
=> [1,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,0,1,1,1,0,0,0,0]
=> [[4,4],[1]]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,0,0,1,0,1,0]
=> [[2,2,2,2],[1,1]]
=> [1,1]
=> [1]
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2],[1]]
=> [1]
=> []
=> ? ∊ {1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42}
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2,1],[1,1,1]]
=> [1,1,1]
=> [1,1]
=> 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3,1],[2,2]]
=> [2,2]
=> [2]
=> 1
[1,1,0,0,1,0,1,0,1,0,1,0]
=> [[2,2,2,2,2],[1,1,1,1]]
=> [1,1,1,1]
=> [1,1,1]
=> 2
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [[3,2,2,2],[1,1,1]]
=> [1,1,1]
=> [1,1]
=> 2
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [[3,3,2,2],[2,1,1]]
=> [2,1,1]
=> [1,1]
=> 2
[1,1,0,0,1,0,1,1,1,0,0,0]
=> [[3,3,2,2],[1,1,1]]
=> [1,1,1]
=> [1,1]
=> 2
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [[3,3,3,2],[2,2,1]]
=> [2,2,1]
=> [2,1]
=> 1
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [[3,3,3,2],[2,1,1]]
=> [2,1,1]
=> [1,1]
=> 2
[1,1,0,0,1,1,1,0,1,0,0,0]
=> [[3,3,3,2],[1,1,1]]
=> [1,1,1]
=> [1,1]
=> 2
[1,1,0,1,0,0,1,0,1,0,1,0]
=> [[3,3,3,3],[2,2,2]]
=> [2,2,2]
=> [2,2]
=> 1
[1,1,0,1,0,0,1,0,1,1,0,0]
=> [[4,3,3],[2,2]]
=> [2,2]
=> [2]
=> 1
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [[4,4,3],[3,2]]
=> [3,2]
=> [2]
=> 1
[1,1,0,1,0,0,1,1,1,0,0,0]
=> [[4,4,3],[2,2]]
=> [2,2]
=> [2]
=> 1
[1,1,0,1,0,1,0,0,1,0,1,0]
=> [[4,4,4],[3,3]]
=> [3,3]
=> [3]
=> 1
[1,1,0,1,0,1,1,0,0,0,1,0]
=> [[4,4,4],[3,2]]
=> [3,2]
=> [2]
=> 1
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [[4,4,4],[2,2]]
=> [2,2]
=> [2]
=> 1
[1,1,0,1,1,0,0,0,1,0,1,0]
=> [[3,3,3,3],[2,2,1]]
=> [2,2,1]
=> [2,1]
=> 1
[1,1,0,1,1,0,1,0,0,0,1,0]
=> [[3,3,3,3],[2,1,1]]
=> [2,1,1]
=> [1,1]
=> 2
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [[3,3,3,3],[1,1,1]]
=> [1,1,1]
=> [1,1]
=> 2
[1,1,1,0,0,0,1,0,1,0,1,0]
=> [[2,2,2,2,2],[1,1,1]]
=> [1,1,1]
=> [1,1]
=> 2
[1,1,1,0,0,1,0,0,1,0,1,0]
=> [[3,3,3,2],[2,2]]
=> [2,2]
=> [2]
=> 1
[1,1,1,1,0,0,0,0,1,0,1,0]
=> [[3,3,3,3],[2,2]]
=> [2,2]
=> [2]
=> 1
Description
The smallest positive integer that does not appear twice in the partition.
Matching statistic: St001964
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001964: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 12%
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001964: Posets ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 12%
Values
[1,0]
=> [1,1,0,0]
=> [2,1] => ([],2)
=> 0 = 1 - 1
[1,0,1,0]
=> [1,1,0,1,0,0]
=> [2,3,1] => ([(1,2)],3)
=> ? = 1 - 1
[1,1,0,0]
=> [1,1,1,0,0,0]
=> [3,2,1] => ([],3)
=> 0 = 1 - 1
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [2,3,4,1] => ([(1,2),(2,3)],4)
=> 0 = 1 - 1
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [2,4,3,1] => ([(1,2),(1,3)],4)
=> ? ∊ {2,2} - 1
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [3,2,4,1] => ([(1,3),(2,3)],4)
=> 0 = 1 - 1
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [4,2,3,1] => ([(2,3)],4)
=> ? ∊ {2,2} - 1
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [4,3,2,1] => ([],4)
=> 0 = 1 - 1
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
=> 0 = 1 - 1
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,4,1] => ([(1,4),(4,2),(4,3)],5)
=> ? ∊ {2,2,2,5,5,5,7,7} - 1
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [2,4,3,5,1] => ([(1,2),(1,3),(2,4),(3,4)],5)
=> ? ∊ {2,2,2,5,5,5,7,7} - 1
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [2,5,3,4,1] => ([(1,3),(1,4),(4,2)],5)
=> ? ∊ {2,2,2,5,5,5,7,7} - 1
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [2,5,4,3,1] => ([(1,2),(1,3),(1,4)],5)
=> ? ∊ {2,2,2,5,5,5,7,7} - 1
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
=> 1 = 2 - 1
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [3,2,5,4,1] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {2,2,2,5,5,5,7,7} - 1
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
=> 0 = 1 - 1
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [5,2,3,4,1] => ([(2,3),(3,4)],5)
=> 0 = 1 - 1
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [5,2,4,3,1] => ([(2,3),(2,4)],5)
=> ? ∊ {2,2,2,5,5,5,7,7} - 1
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
=> ? ∊ {2,2,2,5,5,5,7,7} - 1
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [5,3,2,4,1] => ([(2,4),(3,4)],5)
=> 0 = 1 - 1
[1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [5,3,4,2,1] => ([(3,4)],5)
=> ? ∊ {2,2,2,5,5,5,7,7} - 1
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [5,4,3,2,1] => ([],5)
=> 0 = 1 - 1
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
=> 0 = 1 - 1
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [2,3,4,6,5,1] => ([(1,4),(4,5),(5,2),(5,3)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [2,3,5,4,6,1] => ([(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [2,3,6,4,5,1] => ([(1,5),(4,3),(5,2),(5,4)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [2,3,6,5,4,1] => ([(1,5),(5,2),(5,3),(5,4)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [2,4,3,5,6,1] => ([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,4,3,6,5,1] => ([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [2,5,3,4,6,1] => ([(1,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [2,6,3,4,5,1] => ([(1,3),(1,5),(4,2),(5,4)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [2,6,3,5,4,1] => ([(1,4),(1,5),(5,2),(5,3)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [2,5,4,3,6,1] => ([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [2,6,4,3,5,1] => ([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [2,6,4,5,3,1] => ([(1,3),(1,4),(1,5),(5,2)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,6,5,4,3,1] => ([(1,2),(1,3),(1,4),(1,5)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6)
=> 1 = 2 - 1
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [3,2,4,6,5,1] => ([(1,5),(2,5),(5,3),(5,4)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [3,2,5,4,6,1] => ([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [3,2,6,4,5,1] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [3,2,6,5,4,1] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [4,2,3,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6)
=> 1 = 2 - 1
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [4,2,3,6,5,1] => ([(1,4),(1,5),(2,3),(3,4),(3,5)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6)
=> 0 = 1 - 1
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6)
=> 0 = 1 - 1
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [6,2,3,5,4,1] => ([(2,3),(3,4),(3,5)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [5,2,4,3,6,1] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [6,2,4,3,5,1] => ([(2,3),(2,4),(3,5),(4,5)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [6,2,4,5,3,1] => ([(2,3),(2,4),(4,5)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [6,2,5,4,3,1] => ([(2,3),(2,4),(2,5)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [4,3,2,5,6,1] => ([(1,5),(2,5),(3,5),(5,4)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [4,3,2,6,5,1] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [5,3,2,4,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6)
=> 1 = 2 - 1
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [6,3,2,4,5,1] => ([(2,5),(3,5),(5,4)],6)
=> 1 = 2 - 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [6,3,2,5,4,1] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [5,3,4,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> 1 = 2 - 1
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [6,3,4,2,5,1] => ([(2,5),(3,4),(4,5)],6)
=> 0 = 1 - 1
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [6,3,4,5,2,1] => ([(3,4),(4,5)],6)
=> 0 = 1 - 1
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [6,3,5,4,2,1] => ([(3,4),(3,5)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [5,4,3,2,6,1] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [6,4,3,2,5,1] => ([(2,5),(3,5),(4,5)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [6,4,3,5,2,1] => ([(3,5),(4,5)],6)
=> 0 = 1 - 1
[1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [6,5,3,4,2,1] => ([(4,5)],6)
=> ? ∊ {1,2,2,2,2,2,5,5,5,5,5,5,7,7,7,7,14,14,14,14,14,21,21,21,21,35,35,35,42,42} - 1
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [6,5,4,3,2,1] => ([],6)
=> 0 = 1 - 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,6,7,1] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429} - 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [2,3,4,5,7,6,1] => ([(1,5),(4,6),(5,4),(6,2),(6,3)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429} - 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [2,3,4,6,5,7,1] => ([(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429} - 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [2,3,4,7,5,6,1] => ([(1,5),(4,3),(5,6),(6,2),(6,4)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429} - 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [2,3,4,7,6,5,1] => ([(1,5),(5,6),(6,2),(6,3),(6,4)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429} - 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=> [2,3,5,4,6,7,1] => ([(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429} - 1
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=> [2,3,5,4,7,6,1] => ([(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429} - 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [2,3,6,4,5,7,1] => ([(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429} - 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> [2,3,7,4,5,6,1] => ([(1,6),(4,5),(5,3),(6,2),(6,4)],7)
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,14,14,14,14,14,14,14,14,14,14,21,21,21,21,21,21,21,21,35,35,35,35,35,35,42,42,42,42,42,42,42,42,42,42,42,42,65,65,65,65,65,65,65,65,68,68,119,119,119,119,119,119,147,147,147,147,219,219,219,219,219,282,282,282,282,387,387,387,429,429} - 1
Description
The interval resolution global dimension of a poset.
This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
The following 3 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
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