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Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St001527
St001527: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> 1
[2]
=> 2
[1,1]
=> 1
[3]
=> 3
[2,1]
=> 1
[1,1,1]
=> 3
[4]
=> 4
[3,1]
=> 1
[2,2]
=> 4
[2,1,1]
=> 1
[1,1,1,1]
=> 2
[5]
=> 5
[4,1]
=> 1
[3,2]
=> 5
[3,1,1]
=> 5
[2,2,1]
=> 5
[2,1,1,1]
=> 1
[1,1,1,1,1]
=> 5
[6]
=> 6
[5,1]
=> 1
[4,2]
=> 6
[4,1,1]
=> 3
[3,3]
=> 3
[3,2,1]
=> 2
[3,1,1,1]
=> 3
[2,2,2]
=> 6
[2,2,1,1]
=> 3
[2,1,1,1,1]
=> 2
[1,1,1,1,1,1]
=> 3
[7]
=> 7
[6,1]
=> 1
[5,2]
=> 7
[5,1,1]
=> 7
[4,3]
=> 7
[4,2,1]
=> 7
[4,1,1,1]
=> 1
[3,3,1]
=> 7
[3,2,2]
=> 7
[3,2,1,1]
=> 7
[3,1,1,1,1]
=> 7
[2,2,2,1]
=> 7
[2,2,1,1,1]
=> 7
[2,1,1,1,1,1]
=> 1
[1,1,1,1,1,1,1]
=> 7
[8]
=> 8
[7,1]
=> 1
[6,2]
=> 8
[6,1,1]
=> 1
[5,3]
=> 1
[5,2,1]
=> 8
Description
The cyclic permutation representation number of an integer partition.
This is the size of the largest cyclic group $C$ such that the fake degree is the character of a permutation representation of $C$.
Matching statistic: St001614
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001614: Skew partitions ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 44%
St001614: Skew partitions ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 44%
Values
[1]
=> [[1],[]]
=> 1
[2]
=> [[2],[]]
=> 2
[1,1]
=> [[1,1],[]]
=> 1
[3]
=> [[3],[]]
=> 3
[2,1]
=> [[2,1],[]]
=> 1
[1,1,1]
=> [[1,1,1],[]]
=> 3
[4]
=> [[4],[]]
=> 4
[3,1]
=> [[3,1],[]]
=> 1
[2,2]
=> [[2,2],[]]
=> 4
[2,1,1]
=> [[2,1,1],[]]
=> 1
[1,1,1,1]
=> [[1,1,1,1],[]]
=> 2
[5]
=> [[5],[]]
=> 5
[4,1]
=> [[4,1],[]]
=> 1
[3,2]
=> [[3,2],[]]
=> 5
[3,1,1]
=> [[3,1,1],[]]
=> 5
[2,2,1]
=> [[2,2,1],[]]
=> 5
[2,1,1,1]
=> [[2,1,1,1],[]]
=> 1
[1,1,1,1,1]
=> [[1,1,1,1,1],[]]
=> 5
[6]
=> [[6],[]]
=> 6
[5,1]
=> [[5,1],[]]
=> 1
[4,2]
=> [[4,2],[]]
=> 6
[4,1,1]
=> [[4,1,1],[]]
=> 3
[3,3]
=> [[3,3],[]]
=> 3
[3,2,1]
=> [[3,2,1],[]]
=> 2
[3,1,1,1]
=> [[3,1,1,1],[]]
=> 3
[2,2,2]
=> [[2,2,2],[]]
=> 6
[2,2,1,1]
=> [[2,2,1,1],[]]
=> 3
[2,1,1,1,1]
=> [[2,1,1,1,1],[]]
=> 2
[1,1,1,1,1,1]
=> [[1,1,1,1,1,1],[]]
=> 3
[7]
=> [[7],[]]
=> 7
[6,1]
=> [[6,1],[]]
=> 1
[5,2]
=> [[5,2],[]]
=> 7
[5,1,1]
=> [[5,1,1],[]]
=> 7
[4,3]
=> [[4,3],[]]
=> 7
[4,2,1]
=> [[4,2,1],[]]
=> 7
[4,1,1,1]
=> [[4,1,1,1],[]]
=> 1
[3,3,1]
=> [[3,3,1],[]]
=> 7
[3,2,2]
=> [[3,2,2],[]]
=> 7
[3,2,1,1]
=> [[3,2,1,1],[]]
=> 7
[3,1,1,1,1]
=> [[3,1,1,1,1],[]]
=> 7
[2,2,2,1]
=> [[2,2,2,1],[]]
=> 7
[2,2,1,1,1]
=> [[2,2,1,1,1],[]]
=> 7
[2,1,1,1,1,1]
=> [[2,1,1,1,1,1],[]]
=> 1
[1,1,1,1,1,1,1]
=> [[1,1,1,1,1,1,1],[]]
=> 7
[8]
=> [[8],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[7,1]
=> [[7,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[6,2]
=> [[6,2],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[6,1,1]
=> [[6,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[5,3]
=> [[5,3],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[5,2,1]
=> [[5,2,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[5,1,1,1]
=> [[5,1,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[4,4]
=> [[4,4],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[4,3,1]
=> [[4,3,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[4,2,2]
=> [[4,2,2],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[4,2,1,1]
=> [[4,2,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[4,1,1,1,1]
=> [[4,1,1,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[3,3,2]
=> [[3,3,2],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[3,3,1,1]
=> [[3,3,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[3,2,2,1]
=> [[3,2,2,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[3,2,1,1,1]
=> [[3,2,1,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[3,1,1,1,1,1]
=> [[3,1,1,1,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[2,2,2,2]
=> [[2,2,2,2],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[2,2,2,1,1]
=> [[2,2,2,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[2,2,1,1,1,1]
=> [[2,2,1,1,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[2,1,1,1,1,1,1]
=> [[2,1,1,1,1,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[1,1,1,1,1,1,1,1]
=> [[1,1,1,1,1,1,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,2,4,8,8,8,8,8,8,8,8,8}
[9]
=> [[9],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[8,1]
=> [[8,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[7,2]
=> [[7,2],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[7,1,1]
=> [[7,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[6,3]
=> [[6,3],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[6,2,1]
=> [[6,2,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[6,1,1,1]
=> [[6,1,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[5,4]
=> [[5,4],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[5,3,1]
=> [[5,3,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[5,2,2]
=> [[5,2,2],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[5,2,1,1]
=> [[5,2,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[5,1,1,1,1]
=> [[5,1,1,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[4,4,1]
=> [[4,4,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[4,3,2]
=> [[4,3,2],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[4,3,1,1]
=> [[4,3,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[4,2,2,1]
=> [[4,2,2,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[4,2,1,1,1]
=> [[4,2,1,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[4,1,1,1,1,1]
=> [[4,1,1,1,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[3,3,3]
=> [[3,3,3],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[3,3,2,1]
=> [[3,3,2,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[3,3,1,1,1]
=> [[3,3,1,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[3,2,2,2]
=> [[3,2,2,2],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[3,2,2,1,1]
=> [[3,2,2,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[3,2,1,1,1,1]
=> [[3,2,1,1,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[3,1,1,1,1,1,1]
=> [[3,1,1,1,1,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[2,2,2,2,1]
=> [[2,2,2,2,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[2,2,2,1,1,1]
=> [[2,2,2,1,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
[2,2,1,1,1,1,1]
=> [[2,2,1,1,1,1,1],[]]
=> ? ∊ {1,1,1,1,1,1,1,1,1,3,3,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9}
Description
The cyclic permutation representation number of a skew partition.
This is the size of the largest cyclic group $C$ such that the fake degree is the character of a permutation representation of $C$.
See [[St001527]] for the restriction of this statistic to integer partitions.
Matching statistic: St001232
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 38%
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 38%
Values
[1]
=> [1,0,1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> 1
[2]
=> [1,1,0,0,1,0]
=> [1,1,0,1,0,0]
=> [1,1,0,1,0,0]
=> 2
[1,1]
=> [1,0,1,1,0,0]
=> [1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 1
[3]
=> [1,1,1,0,0,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3
[2,1]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ? = 3
[1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> [1,1,1,0,0,0,1,0]
=> 1
[4]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 4
[3,1]
=> [1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0]
=> ? ∊ {1,4}
[2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> ? ∊ {1,4}
[1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1
[5]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 5
[4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {1,5,5,5,5}
[3,2]
=> [1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> ? ∊ {1,5,5,5,5}
[3,1,1]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? ∊ {1,5,5,5,5}
[2,2,1]
=> [1,0,1,0,1,1,0,0]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> ? ∊ {1,5,5,5,5}
[2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> ? ∊ {1,5,5,5,5}
[1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> 1
[6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [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]
=> 6
[5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? ∊ {2,3,3,3,3,6,6}
[4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> ? ∊ {2,3,3,3,3,6,6}
[4,1,1]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> ? ∊ {2,3,3,3,3,6,6}
[3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3
[3,2,1]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {2,3,3,3,3,6,6}
[3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> ? ∊ {2,3,3,3,3,6,6}
[2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 2
[2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> ? ∊ {2,3,3,3,3,6,6}
[2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> ? ∊ {2,3,3,3,3,6,6}
[1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> 1
[7]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,7,7,7,7,7,7,7,7,7,7,7,7}
[6,1]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> [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]
=> ? ∊ {1,1,1,7,7,7,7,7,7,7,7,7,7,7,7}
[5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? ∊ {1,1,1,7,7,7,7,7,7,7,7,7,7,7,7}
[5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? ∊ {1,1,1,7,7,7,7,7,7,7,7,7,7,7,7}
[4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> ? ∊ {1,1,1,7,7,7,7,7,7,7,7,7,7,7,7}
[4,2,1]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> ? ∊ {1,1,1,7,7,7,7,7,7,7,7,7,7,7,7}
[4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ? ∊ {1,1,1,7,7,7,7,7,7,7,7,7,7,7,7}
[3,3,1]
=> [1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> ? ∊ {1,1,1,7,7,7,7,7,7,7,7,7,7,7,7}
[3,2,2]
=> [1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> ? ∊ {1,1,1,7,7,7,7,7,7,7,7,7,7,7,7}
[3,2,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {1,1,1,7,7,7,7,7,7,7,7,7,7,7,7}
[3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,0,0,1,0,1,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0]
=> ? ∊ {1,1,1,7,7,7,7,7,7,7,7,7,7,7,7}
[2,2,2,1]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ? ∊ {1,1,1,7,7,7,7,7,7,7,7,7,7,7,7}
[2,2,1,1,1]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> ? ∊ {1,1,1,7,7,7,7,7,7,7,7,7,7,7,7}
[2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {1,1,1,7,7,7,7,7,7,7,7,7,7,7,7}
[1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
=> ? ∊ {1,1,1,7,7,7,7,7,7,7,7,7,7,7,7}
[8]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[7,1]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[6,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
=> [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]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[6,1,1]
=> [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
=> [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]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[5,3]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[5,2,1]
=> [1,1,1,0,1,0,1,0,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[5,1,1,1]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[4,4]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 4
[4,3,1]
=> [1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[4,2,2]
=> [1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[4,2,1,1]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[4,1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,0,1,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[3,3,2]
=> [1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[3,3,1,1]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[3,2,2,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[3,2,1,1,1]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[3,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,0,1,1,0,0,0,1,0,1,0,1,0]
=> [1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[2,2,2,2]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 2
[2,2,2,1,1]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[2,2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[2,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[1,1,1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
=> ? ∊ {1,1,1,1,1,1,1,1,1,1,2,8,8,8,8,8,8,8,8,8}
[3,3,3]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 3
[5,5]
=> [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
=> 5
[2,2,2,2,2]
=> [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=> 2
[4,4,4]
=> [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=> 4
[3,3,3,3]
=> [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> 3
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
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