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Your data matches 339 different statistics following compositions of up to 3 maps.
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(click to perform a complete search on your data)
Matching statistic: St001199
(load all 21 compositions to match this statistic)
(load all 21 compositions to match this statistic)
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
Mp00123: Dyck paths —Barnabei-Castronuovo involution⟶ Dyck paths
St001199: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00030: Dyck paths —zeta map⟶ Dyck paths
Mp00123: Dyck paths —Barnabei-Castronuovo involution⟶ Dyck paths
St001199: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> 2
[1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> 2
[1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> 2
[1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> 2
[1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> 2
[1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> 2
[1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> 2
[1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> 2
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> 2
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> 2
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> 2
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> 2
[1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> 2
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,0,0,1,1,0,0]
=> 2
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0]
=> 2
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> 2
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> 2
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> 2
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> 2
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> 2
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> 2
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,0,0,1,1,0,0]
=> 2
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0]
=> 2
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> 2
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> 2
[1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,0,0,1,1,0,0]
=> 2
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0]
=> 2
[1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> 2
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> 3
[1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 2
[1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 2
[1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 2
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,0,0,1,1,0,1,1,0,0,0]
=> 2
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> 2
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 2
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 2
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 2
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> 1
Description
The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Matching statistic: St001195
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001195: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 48%●distinct values known / distinct values provided: 33%
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001195: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 48%●distinct values known / distinct values provided: 33%
Values
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> 1 = 2 - 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> 1 = 2 - 1
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> 1 = 2 - 1
[1,1,1,0,1,1,0,0,0,0]
=> [2,3,1,4,5] => [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> 1 = 2 - 1
[1,1,1,1,0,0,0,0,1,0]
=> [5,1,2,3,4] => [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> 1 = 2 - 1
[1,1,1,1,0,0,0,1,0,0]
=> [4,1,2,3,5] => [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> 1 = 2 - 1
[1,1,1,1,0,0,1,0,0,0]
=> [3,1,2,4,5] => [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> 1 = 2 - 1
[1,1,1,1,0,1,0,0,0,0]
=> [2,1,3,4,5] => [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> 1 = 2 - 1
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => [1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 2 - 1
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [3,4,5,6,2,1] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [3,4,5,2,6,1] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [3,4,2,5,6,1] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [6,2,3,4,5,1] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [5,2,3,4,6,1] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,0,1,1,1,1,0,0,1,0,0,0]
=> [4,2,3,5,6,1] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [3,2,4,5,6,1] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,6,1] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 2 - 1
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [3,4,5,6,1,2] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 2 - 1
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [3,4,5,2,1,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [3,4,2,5,1,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [6,2,3,4,1,5] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [5,2,3,4,1,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [4,2,3,5,1,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [3,2,4,5,1,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,1,6] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 2 - 1
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [3,4,5,1,2,6] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 2 - 1
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [3,4,2,1,5,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,1,0,1,1,0,0,0,0,1,0]
=> [6,2,3,1,4,5] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [5,2,3,1,4,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [4,2,3,1,5,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [3,2,4,1,5,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [2,3,4,1,5,6] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 2 - 1
[1,1,1,1,0,0,0,0,1,0,1,0]
=> [6,5,1,2,3,4] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [5,6,1,2,3,4] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 2 - 1
[1,1,1,1,0,0,0,1,0,0,1,0]
=> [6,4,1,2,3,5] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [5,4,1,2,3,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [4,5,1,2,3,6] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 2 - 1
[1,1,1,1,0,0,1,0,0,0,1,0]
=> [6,3,1,2,4,5] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,1,1,0,0,1,0,0,1,0,0]
=> [5,3,1,2,4,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [4,3,1,2,5,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [3,4,1,2,5,6] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 3 - 1
[1,1,1,1,0,1,0,0,0,0,1,0]
=> [6,2,1,3,4,5] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,1,1,0,1,0,0,0,1,0,0]
=> [5,2,1,3,4,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,1,1,0,1,0,0,1,0,0,0]
=> [4,2,1,3,5,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [3,2,1,4,5,6] => [3,1,1,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 1 = 2 - 1
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [2,3,1,4,5,6] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 2 - 1
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [6,1,2,3,4,5] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 2 - 1
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [5,1,2,3,4,6] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 2 - 1
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [4,1,2,3,5,6] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 2 - 1
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [3,1,2,4,5,6] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1 - 1
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [2,1,3,4,5,6] => [2,1,1,1,1]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? = 1 - 1
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,2,3,4,5,6] => [1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,3,2,1] => [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,7,2,1] => [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,7,2,1] => [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> [7,3,4,5,6,2,1] => [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> [6,3,4,5,7,2,1] => [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,7,2,1] => [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [4,3,5,6,7,2,1] => [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,2,1] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,2,3,1] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,2,7,1] => [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,2,7,1] => [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
=> [7,3,4,5,2,6,1] => [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
=> [6,3,4,5,2,7,1] => [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,2,7,1] => [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
=> [4,3,5,6,2,7,1] => [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,2,7,1] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [4,5,6,2,3,7,1] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [4,5,3,2,6,7,1] => [4,1,1,1]
=> [1,0,1,1,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> [3,4,5,2,6,7,1] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> [6,7,2,3,4,5,1] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=> [5,6,2,3,4,7,1] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [4,5,2,3,6,7,1] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [3,4,2,5,6,7,1] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> [7,2,3,4,5,6,1] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [6,2,3,4,5,7,1] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [5,2,3,4,6,7,1] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [4,2,3,5,6,7,1] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 3 - 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [3,2,4,5,6,7,1] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 3 - 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,3,1,2] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [4,5,6,3,7,1,2] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [4,5,3,6,7,1,2] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> [7,3,4,5,6,1,2] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
=> [6,3,4,5,7,1,2] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=> [5,3,4,6,7,1,2] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=> [4,3,5,6,7,1,2] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,1,2] => [2,1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 2 - 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,2,1,3] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,2,1,7] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [4,5,6,2,3,1,7] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [3,4,5,2,6,1,7] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
=> [6,7,2,3,4,1,5] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [5,6,2,3,4,1,7] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [4,5,2,3,6,1,7] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 1 - 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [3,4,2,5,6,1,7] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
=> [7,2,3,4,5,1,6] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
=> [6,2,3,4,5,1,7] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=> [5,2,3,4,6,1,7] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 2 - 1
Description
The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$.
Matching statistic: St000264
(load all 16 compositions to match this statistic)
(load all 16 compositions to match this statistic)
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 43%●distinct values known / distinct values provided: 33%
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 33% ●values known / values provided: 43%●distinct values known / distinct values provided: 33%
Values
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,2,3,4] => ([],4)
=> ? = 2 + 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 2 + 2
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 2
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [3,1,2,4,5] => ([(2,4),(3,4)],5)
=> ? = 2 + 2
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
=> ? = 2 + 2
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,2,5,3,4] => ([(2,4),(3,4)],5)
=> ? = 2 + 2
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,2,3,5,4] => ([(3,4)],5)
=> ? = 2 + 2
[1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,4,5] => ([(3,4)],5)
=> ? = 2 + 2
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => ([],5)
=> ? = 2 + 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [5,1,6,2,3,4] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [5,1,2,6,3,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [5,1,2,3,6,4] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 2 + 2
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 2 + 2
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,5,2,3,4,6] => ([(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [4,1,6,2,3,5] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [4,1,2,6,3,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ? = 2 + 2
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [4,1,2,3,6,5] => ([(0,1),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [2,5,1,3,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 2 + 2
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,4,2,3,5,6] => ([(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [3,1,6,2,4,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ? = 2 + 2
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [3,1,2,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6)
=> ? = 2 + 2
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> [3,1,2,4,6,5] => ([(1,2),(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6)
=> ? = 2 + 2
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,2,5,3,4,6] => ([(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,2,3,5,4,6] => ([(4,5)],6)
=> ? = 2 + 2
[1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,5,2,3,6,4] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 2 + 2
[1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,2,5,3,6,4] => ([(2,5),(3,4),(4,5)],6)
=> ? = 2 + 2
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,2,3,5,6,4] => ([(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,3,2,4,5,6] => ([(4,5)],6)
=> ? = 3 + 2
[1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [2,1,6,3,4,5] => ([(0,1),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [2,1,3,6,4,5] => ([(1,2),(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [2,1,3,4,6,5] => ([(2,5),(3,4)],6)
=> ? = 2 + 2
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,3,1,4,5,6] => ([(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [3,1,2,4,5,6] => ([(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,6,2,3,4,5] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,2,6,3,4,5] => ([(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,2,3,6,4,5] => ([(3,5),(4,5)],6)
=> ? = 2 + 2
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,2,3,4,6,5] => ([(4,5)],6)
=> ? = 1 + 2
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,1,3,4,5,6] => ([(4,5)],6)
=> ? = 1 + 2
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,2,3,4,5,6] => ([],6)
=> ? = 1 + 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=> [5,6,7,1,2,3,4] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 2 + 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=> [4,6,7,1,2,3,5] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [3,6,7,1,2,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,1,0,1,0,0,1,0,0,0]
=> [5,6,1,7,2,3,4] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
=> [5,6,1,2,7,3,4] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
=> [5,6,1,2,3,7,4] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> [2,6,7,1,3,4,5] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,1,0,1,0,0,0,0]
=> [1,5,7,2,3,4,6] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [4,5,7,1,2,3,6] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> 4 = 2 + 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=> [3,5,7,1,2,4,6] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 4 = 2 + 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,1,0,1,0,0,1,0,0,0]
=> [4,6,1,7,2,3,5] => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 2 + 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=> [4,6,1,2,7,3,5] => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
=> 4 = 2 + 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0,1,0]
=> [4,6,1,2,3,7,5] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)
=> 4 = 2 + 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> [2,5,7,1,3,4,6] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> [5,7,1,2,3,4,6] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,1,1,0,1,0,0,0,0]
=> [1,4,7,2,3,5,6] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,0,1,0,0,0,0]
=> [3,4,7,1,2,5,6] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=> [3,6,1,7,2,4,5] => ([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,1,0,0]
=> [3,6,1,2,7,4,5] => ([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0,1,0]
=> [3,6,1,2,4,7,5] => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
=> [2,4,7,1,3,5,6] => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,1,0,1,0,0,0,0,0]
=> [4,7,1,2,3,5,6] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,1,0,1,0,0,1,0,1,0,0,0]
=> [5,1,6,7,2,3,4] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,0,1,1,0,0,0]
=> [5,1,2,6,3,4,7] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,1,1,1,0,1,0,0,1,0,0,1,0,0]
=> [5,1,6,2,7,3,4] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
=> [5,1,2,6,7,3,4] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,1,0,0]
=> [5,1,2,3,6,4,7] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> ? = 2 + 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0,1,0]
=> [5,1,6,2,3,7,4] => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
=> [5,1,2,6,3,7,4] => ([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
=> [5,1,2,3,6,7,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ? = 2 + 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=> [1,3,7,2,4,5,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> ? = 1 + 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=> [2,6,1,7,3,4,5] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,1,0,0]
=> [2,6,1,3,7,4,5] => ([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0,1,0]
=> [2,6,1,3,4,7,5] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ? = 2 + 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,3,7,1,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> ? = 2 + 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> [3,7,1,2,4,5,6] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,1,0,0,0,0]
=> [6,1,7,2,3,4,5] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,1,1,1,0,1,0,0,0,1,0,0,0]
=> [6,1,2,7,3,4,5] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,1,0,0]
=> [6,1,2,3,7,4,5] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> [6,1,2,3,4,7,5] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> ? = 3 + 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [2,7,1,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> ? = 2 + 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> [7,1,2,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 3 + 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,1,0,0,0,0]
=> [5,1,6,2,3,4,7] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [4,1,6,2,3,5,7] => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [3,1,6,2,4,5,7] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ? = 2 + 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,0,1,1,0,0,1,0,0,0]
=> [1,5,2,7,3,4,6] => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,1,0,0]
=> [1,5,2,3,7,4,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ? = 2 + 2
Description
The girth of a graph, which is not a tree.
This is the length of the shortest cycle in the graph.
Matching statistic: St001200
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001200: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 41%●distinct values known / distinct values provided: 33%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001200: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 41%●distinct values known / distinct values provided: 33%
Values
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [4]
=> [1,0,1,0,1,0,1,0]
=> 3 = 2 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,4,5] => [4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> 3 = 2 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [3,1,2,4,5] => [4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> 3 = 2 + 1
[1,1,1,0,1,1,0,0,0,0]
=> [4,1,2,3,5] => [4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> 3 = 2 + 1
[1,1,1,1,0,0,0,0,1,0]
=> [1,2,3,5,4] => [4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> 3 = 2 + 1
[1,1,1,1,0,0,0,1,0,0]
=> [1,2,5,3,4] => [4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> 3 = 2 + 1
[1,1,1,1,0,0,1,0,0,0]
=> [1,5,2,3,4] => [4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> 3 = 2 + 1
[1,1,1,1,0,1,0,0,0,0]
=> [5,1,2,3,4] => [4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> 3 = 2 + 1
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => [5]
=> [1,0,1,0,1,0,1,0,1,0]
=> 3 = 2 + 1
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,3,1,4,5,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 + 1
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [2,4,1,3,5,6] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [2,5,1,3,4,6] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [2,1,3,4,6,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [2,1,3,6,4,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,1,1,0,0,1,0,0,0]
=> [2,1,6,3,4,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,6,1,3,4,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,1,3,4,5,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 + 1
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,3,2,4,5,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 + 1
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [3,4,1,2,5,6] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [3,5,1,2,4,6] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [3,1,2,4,6,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [3,1,2,6,4,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [3,1,6,2,4,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [3,6,1,2,4,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [3,1,2,4,5,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 + 1
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,4,2,3,5,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 + 1
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [4,5,1,2,3,6] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,1,0,1,1,0,0,0,0,1,0]
=> [4,1,2,3,6,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [4,1,2,6,3,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [4,1,6,2,3,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [4,6,1,2,3,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [4,1,2,3,5,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 + 1
[1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,2,3,5,6,4] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 + 1
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,2,3,5,4,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 + 1
[1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,2,5,3,6,4] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,2,5,6,3,4] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,2,5,3,4,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 + 1
[1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,5,2,3,6,4] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,5,2,6,3,4] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,5,6,2,3,4] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,5,2,3,4,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 3 + 1
[1,1,1,1,0,1,0,0,0,0,1,0]
=> [5,1,2,3,6,4] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,1,1,0,1,0,0,0,1,0,0]
=> [5,1,2,6,3,4] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,1,1,0,1,0,0,1,0,0,0]
=> [5,1,6,2,3,4] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [5,6,1,2,3,4] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [5,1,2,3,4,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 + 1
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,2,3,4,6,5] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 + 1
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,2,3,6,4,5] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 + 1
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,2,6,3,4,5] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 + 1
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,6,2,3,4,5] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1 + 1
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [6,1,2,3,4,5] => [5,1]
=> [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]
=> [1,2,3,4,5,6] => [6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 + 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,1,5,6,7] => [6,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 + 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [2,3,5,1,4,6,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [2,3,6,1,4,5,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> [2,3,1,4,5,7,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> [2,3,1,4,7,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=> [2,3,1,7,4,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,3,7,1,4,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,3,1,4,5,6,7] => [6,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 + 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [2,1,4,3,5,6,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [2,4,5,1,3,6,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [2,4,6,1,3,5,7] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
=> [2,4,1,3,5,7,6] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
=> [2,4,1,3,7,5,6] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
=> [2,4,1,7,3,5,6] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
=> [2,4,7,1,3,5,6] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,4,1,3,5,6,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [2,1,5,3,4,6,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [2,5,6,1,3,4,7] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
=> [2,5,1,3,4,7,6] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> [2,5,1,3,7,4,6] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
=> [2,5,1,7,3,4,6] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> [2,5,7,1,3,4,6] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> [2,5,1,3,4,6,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
=> [2,1,3,4,6,7,5] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> [2,1,3,4,6,5,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
=> [2,1,3,6,4,7,5] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [2,1,3,6,7,4,5] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=> [2,1,3,6,4,5,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
=> [2,1,6,3,4,7,5] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=> [2,1,6,3,7,4,5] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
=> [2,1,6,7,3,4,5] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 3 = 2 + 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [2,1,6,3,4,5,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 1 + 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [2,6,1,3,4,5,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> [2,1,3,4,5,7,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [2,1,3,4,7,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [2,1,3,7,4,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [2,1,7,3,4,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 3 + 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [2,7,1,3,4,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,1,3,4,5,6,7] => [6,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 3 + 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [1,3,4,2,5,6,7] => [6,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 + 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [1,3,5,2,4,6,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,3,6,2,4,5,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> [1,3,2,4,5,7,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
=> [1,3,2,4,7,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=> [1,3,2,7,4,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=> [1,3,7,2,4,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [1,3,2,4,5,6,7] => [6,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 + 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [3,1,4,2,5,6,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 + 1
Description
The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Matching statistic: St000510
(load all 28 compositions to match this statistic)
(load all 28 compositions to match this statistic)
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000510: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 41%●distinct values known / distinct values provided: 33%
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000510: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 41%●distinct values known / distinct values provided: 33%
Values
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> 0 = 2 - 2
[1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> 0 = 2 - 2
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [3,3,2,1]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [4,3,2]
=> 0 = 2 - 2
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,0,1,0]
=> [5,3,2]
=> 0 = 2 - 2
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [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]
=> ? = 2 - 2
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,1,0,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,0,0,1,0,1,0]
=> [5,4,2]
=> 0 = 2 - 2
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,0,1,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [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]
=> ? = 2 - 2
[1,1,1,1,0,0,0,1,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2,1]
=> ? = 2 - 2
[1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> [3,3,2,1,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [3,3,3,2,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,1]
=> ? = 3 - 2
[1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0]
=> [4,3,2,2]
=> 0 = 2 - 2
[1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,0,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2]
=> 0 = 2 - 2
[1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2]
=> ? = 2 - 2
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> [5,4,3]
=> 0 = 2 - 2
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [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]
=> ? = 2 - 2
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [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]
=> ? = 2 - 2
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2,1]
=> ? = 1 - 2
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2]
=> ? = 1 - 2
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [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 - 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=> [3,2,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,1,0,0,0]
=> [4,3,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [3,2,2,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,1,1,0,0,0,0]
=> [3,3,2,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,1,0,1,0,0,0]
=> [4,3,2]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [4,3,2,1]
=> 0 = 2 - 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,1,0,0]
=> [5,3,2,1,1,1]
=> ? = 2 - 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [5,4,2,1,1,1]
=> ? = 2 - 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0,1,0]
=> [6,3,2,2,1]
=> ? = 2 - 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0,1,0]
=> [6,3,3,2,1]
=> ? = 2 - 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,1,0,0]
=> [5,4,3,1,1,1]
=> ? = 1 - 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,1,0,0,0]
=> [4,4,3,2]
=> ? = 2 - 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [5,4,3,1]
=> ? = 2 - 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [4,3,3,2,1]
=> ? = 2 - 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [4,4,3,2,1]
=> ? = 3 - 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=> [5,4,3,2]
=> ? = 2 - 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [5,4,3,2,1]
=> ? = 3 - 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0,1,0]
=> [6,3,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0,1,0]
=> [6,4,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0,1,0]
=> [6,4,3,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,0,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,1,0,0]
=> [5,3,2,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,1,0,0]
=> [5,3,3,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,2]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,1,1]
=> ? = 2 - 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0,1,0]
=> [6,3,2,1,1,1]
=> ? = 2 - 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,0,1,1,0,0]
=> [5,5,2,1]
=> ? = 2 - 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0,1,0]
=> [6,4,2,1,1,1]
=> ? = 2 - 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0,1,1,0,0]
=> [5,5,3,1]
=> ? = 2 - 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
=> [6,4,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,0,1,1,0,0,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0,1,0]
=> [6,4,2,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=> [4,4,2,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0,1,1,1,0,0,0]
=> [4,4,4,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,0,1,0]
=> [6,4,3,1,1,1]
=> ? = 1 - 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,1,0,0]
=> [5,3,3,2]
=> ? = 2 - 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2]
=> ? = 2 - 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0,1,0]
=> [6,4,3]
=> ? = 2 - 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0,1,0]
=> [6,4,3,1]
=> ? = 2 - 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,1,1,0,1,1,0,0,0,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [5,3,2,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [5,3,3,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,1]
=> ? = 3 - 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2]
=> ? = 2 - 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,1]
=> ? = 3 - 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,2,1]
=> ? = 2 - 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0,1,0]
=> [6,5,2,1,1]
=> ? = 2 - 2
Description
The number of invariant oriented cycles when acting with a permutation of given cycle type.
Matching statistic: St000713
(load all 35 compositions to match this statistic)
(load all 35 compositions to match this statistic)
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000713: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 41%●distinct values known / distinct values provided: 33%
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000713: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 41%●distinct values known / distinct values provided: 33%
Values
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> 0 = 2 - 2
[1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> 0 = 2 - 2
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [3,3,2,1]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [4,3,2]
=> 0 = 2 - 2
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,0,1,0]
=> [5,3,2]
=> 0 = 2 - 2
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [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]
=> ? = 2 - 2
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,1,0,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,0,0,1,0,1,0]
=> [5,4,2]
=> 0 = 2 - 2
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,0,1,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [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]
=> ? = 2 - 2
[1,1,1,1,0,0,0,1,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2,1]
=> ? = 2 - 2
[1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> [3,3,2,1,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [3,3,3,2,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,1]
=> ? = 3 - 2
[1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0]
=> [4,3,2,2]
=> 0 = 2 - 2
[1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,0,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2]
=> 0 = 2 - 2
[1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2]
=> ? = 2 - 2
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> [5,4,3]
=> 0 = 2 - 2
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [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]
=> ? = 2 - 2
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [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]
=> ? = 2 - 2
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2,1]
=> ? = 1 - 2
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2]
=> ? = 1 - 2
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [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 - 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=> [3,2,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,1,0,0,0]
=> [4,3,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [3,2,2,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,1,1,0,0,0,0]
=> [3,3,2,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,1,0,1,0,0,0]
=> [4,3,2]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [4,3,2,1]
=> 0 = 2 - 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,1,0,0]
=> [5,3,2,1,1,1]
=> ? = 2 - 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [5,4,2,1,1,1]
=> ? = 2 - 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0,1,0]
=> [6,3,2,2,1]
=> ? = 2 - 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0,1,0]
=> [6,3,3,2,1]
=> ? = 2 - 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,1,0,0]
=> [5,4,3,1,1,1]
=> ? = 1 - 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,1,0,0,0]
=> [4,4,3,2]
=> ? = 2 - 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [5,4,3,1]
=> ? = 2 - 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [4,3,3,2,1]
=> ? = 2 - 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [4,4,3,2,1]
=> ? = 3 - 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=> [5,4,3,2]
=> ? = 2 - 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [5,4,3,2,1]
=> ? = 3 - 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0,1,0]
=> [6,3,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0,1,0]
=> [6,4,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0,1,0]
=> [6,4,3,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,0,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,1,0,0]
=> [5,3,2,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,1,0,0]
=> [5,3,3,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,2]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,1,1]
=> ? = 2 - 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0,1,0]
=> [6,3,2,1,1,1]
=> ? = 2 - 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,0,1,1,0,0]
=> [5,5,2,1]
=> ? = 2 - 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0,1,0]
=> [6,4,2,1,1,1]
=> ? = 2 - 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0,1,1,0,0]
=> [5,5,3,1]
=> ? = 2 - 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
=> [6,4,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,0,1,1,0,0,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0,1,0]
=> [6,4,2,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=> [4,4,2,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0,1,1,1,0,0,0]
=> [4,4,4,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,0,1,0]
=> [6,4,3,1,1,1]
=> ? = 1 - 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,1,0,0]
=> [5,3,3,2]
=> ? = 2 - 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2]
=> ? = 2 - 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0,1,0]
=> [6,4,3]
=> ? = 2 - 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0,1,0]
=> [6,4,3,1]
=> ? = 2 - 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,1,1,0,1,1,0,0,0,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [5,3,2,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [5,3,3,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,1]
=> ? = 3 - 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2]
=> ? = 2 - 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,1]
=> ? = 3 - 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,2,1]
=> ? = 2 - 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0,1,0]
=> [6,5,2,1,1]
=> ? = 2 - 2
Description
The dimension of the irreducible representation of Sp(4) labelled by an integer partition.
Consider the symplectic group $Sp(2n)$. Then the integer partition $(\mu_1,\dots,\mu_k)$ of length at most $n$ corresponds to the weight vector $(\mu_1-\mu_2,\dots,\mu_{k-2}-\mu_{k-1},\mu_n,0,\dots,0)$.
For example, the integer partition $(2)$ labels the symmetric square of the vector representation, whereas the integer partition $(1,1)$ labels the second fundamental representation.
Matching statistic: St000714
(load all 35 compositions to match this statistic)
(load all 35 compositions to match this statistic)
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000714: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 41%●distinct values known / distinct values provided: 33%
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000714: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 41%●distinct values known / distinct values provided: 33%
Values
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> 0 = 2 - 2
[1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> 0 = 2 - 2
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [3,3,2,1]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [4,3,2]
=> 0 = 2 - 2
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,0,1,0]
=> [5,3,2]
=> 0 = 2 - 2
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [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]
=> ? = 2 - 2
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,1,0,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,0,0,1,0,1,0]
=> [5,4,2]
=> 0 = 2 - 2
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,0,1,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [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]
=> ? = 2 - 2
[1,1,1,1,0,0,0,1,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2,1]
=> ? = 2 - 2
[1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> [3,3,2,1,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [3,3,3,2,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,1]
=> ? = 3 - 2
[1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0]
=> [4,3,2,2]
=> 0 = 2 - 2
[1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,0,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2]
=> 0 = 2 - 2
[1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2]
=> ? = 2 - 2
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> [5,4,3]
=> 0 = 2 - 2
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [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]
=> ? = 2 - 2
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [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]
=> ? = 2 - 2
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2,1]
=> ? = 1 - 2
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2]
=> ? = 1 - 2
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [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 - 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=> [3,2,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,1,0,0,0]
=> [4,3,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [3,2,2,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,1,1,0,0,0,0]
=> [3,3,2,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,1,0,1,0,0,0]
=> [4,3,2]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [4,3,2,1]
=> 0 = 2 - 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,1,0,0]
=> [5,3,2,1,1,1]
=> ? = 2 - 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [5,4,2,1,1,1]
=> ? = 2 - 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0,1,0]
=> [6,3,2,2,1]
=> ? = 2 - 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0,1,0]
=> [6,3,3,2,1]
=> ? = 2 - 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,1,0,0]
=> [5,4,3,1,1,1]
=> ? = 1 - 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,1,0,0,0]
=> [4,4,3,2]
=> ? = 2 - 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [5,4,3,1]
=> ? = 2 - 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [4,3,3,2,1]
=> ? = 2 - 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [4,4,3,2,1]
=> ? = 3 - 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=> [5,4,3,2]
=> ? = 2 - 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [5,4,3,2,1]
=> ? = 3 - 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0,1,0]
=> [6,3,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0,1,0]
=> [6,4,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0,1,0]
=> [6,4,3,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,0,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,1,0,0]
=> [5,3,2,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,1,0,0]
=> [5,3,3,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,2]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,1,1]
=> ? = 2 - 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0,1,0]
=> [6,3,2,1,1,1]
=> ? = 2 - 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,0,1,1,0,0]
=> [5,5,2,1]
=> ? = 2 - 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0,1,0]
=> [6,4,2,1,1,1]
=> ? = 2 - 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0,1,1,0,0]
=> [5,5,3,1]
=> ? = 2 - 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
=> [6,4,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,0,1,1,0,0,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0,1,0]
=> [6,4,2,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=> [4,4,2,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0,1,1,1,0,0,0]
=> [4,4,4,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,0,1,0]
=> [6,4,3,1,1,1]
=> ? = 1 - 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,1,0,0]
=> [5,3,3,2]
=> ? = 2 - 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2]
=> ? = 2 - 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0,1,0]
=> [6,4,3]
=> ? = 2 - 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0,1,0]
=> [6,4,3,1]
=> ? = 2 - 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,1,1,0,1,1,0,0,0,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [5,3,2,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [5,3,3,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,1]
=> ? = 3 - 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2]
=> ? = 2 - 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,1]
=> ? = 3 - 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,2,1]
=> ? = 2 - 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0,1,0]
=> [6,5,2,1,1]
=> ? = 2 - 2
Description
The number of semistandard Young tableau of given shape, with entries at most 2.
This is also the dimension of the corresponding irreducible representation of $GL_2$.
Matching statistic: St000929
(load all 35 compositions to match this statistic)
(load all 35 compositions to match this statistic)
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000929: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 41%●distinct values known / distinct values provided: 33%
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000929: Integer partitions ⟶ ℤResult quality: 33% ●values known / values provided: 41%●distinct values known / distinct values provided: 33%
Values
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> 0 = 2 - 2
[1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> 0 = 2 - 2
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [3,3,2,1]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [4,3,2]
=> 0 = 2 - 2
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,0,1,0]
=> [5,3,2]
=> 0 = 2 - 2
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [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]
=> ? = 2 - 2
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,1,0,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,0,0,1,0,1,0]
=> [5,4,2]
=> 0 = 2 - 2
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,0,1,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [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]
=> ? = 2 - 2
[1,1,1,1,0,0,0,1,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2,1]
=> ? = 2 - 2
[1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> [3,3,2,1,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [3,3,3,2,1]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,1]
=> ? = 3 - 2
[1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0]
=> [4,3,2,2]
=> 0 = 2 - 2
[1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,0,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2]
=> 0 = 2 - 2
[1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2]
=> ? = 2 - 2
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> [5,4,3]
=> 0 = 2 - 2
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [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]
=> ? = 2 - 2
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [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]
=> 0 = 2 - 2
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [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]
=> ? = 2 - 2
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2,1]
=> ? = 1 - 2
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2]
=> ? = 1 - 2
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [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 - 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=> [3,2,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,1,0,0,0]
=> [4,3,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> [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]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [3,2,2,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,1,1,0,0,0,0]
=> [3,3,2,1]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,1,0,1,0,0,0]
=> [4,3,2]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [4,3,2,1]
=> 0 = 2 - 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,1,0,0]
=> [5,3,2,1,1,1]
=> ? = 2 - 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [5,4,2,1,1,1]
=> ? = 2 - 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0,1,0]
=> [6,3,2,2,1]
=> ? = 2 - 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0,1,0]
=> [6,3,3,2,1]
=> ? = 2 - 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,1,0,0]
=> [5,4,3,1,1,1]
=> ? = 1 - 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,1,0,0,0]
=> [4,4,3,2]
=> ? = 2 - 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=> [5,4,3,1]
=> ? = 2 - 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [4,3,3,2,1]
=> ? = 2 - 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [4,4,3,2,1]
=> ? = 3 - 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=> [5,4,3,2]
=> ? = 2 - 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [5,4,3,2,1]
=> ? = 3 - 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0,1,0]
=> [6,3,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0,1,0]
=> [6,4,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0,1,0]
=> [6,4,3,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,0,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,1,0,0]
=> [5,3,2,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,1,0,0]
=> [5,3,3,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,1,1]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,2]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,1,1]
=> ? = 2 - 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0,1,0]
=> [6,3,2,1,1,1]
=> ? = 2 - 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,0,1,1,0,0]
=> [5,5,2,1]
=> ? = 2 - 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0,1,0]
=> [6,4,2,1,1,1]
=> ? = 2 - 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0,1,1,0,0]
=> [5,5,3,1]
=> ? = 2 - 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
=> [6,4,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,0,1,1,0,0,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0,1,0]
=> [6,4,2,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,1,0,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=> [4,4,2,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0,1,1,1,0,0,0]
=> [4,4,4,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,0,1,0]
=> [6,4,3,1,1,1]
=> ? = 1 - 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,1,0,0]
=> [5,3,3,2]
=> ? = 2 - 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2]
=> ? = 2 - 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0,1,0]
=> [6,4,3]
=> ? = 2 - 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0,1,0]
=> [6,4,3,1]
=> ? = 2 - 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,1,1,0,1,1,0,0,0,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [5,3,2,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [5,3,3,2,1]
=> ? = 2 - 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,1]
=> ? = 3 - 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2]
=> ? = 2 - 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,1]
=> ? = 3 - 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,2,1]
=> ? = 2 - 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0,1,0]
=> [6,5,2,1,1]
=> ? = 2 - 2
Description
The constant term of the character polynomial of an integer partition.
The definition of the character polynomial can be found in [1]. Indeed, this constant term is $0$ for partitions $\lambda \neq 1^n$ and $1$ for $\lambda = 1^n$.
Matching statistic: St001001
(load all 7 compositions to match this statistic)
(load all 7 compositions to match this statistic)
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001001: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 41%●distinct values known / distinct values provided: 33%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001001: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 41%●distinct values known / distinct values provided: 33%
Values
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [4]
=> [1,0,1,0,1,0,1,0]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,4,5] => [4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,0,0]
=> [3,1,2,4,5] => [4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,0,0]
=> [4,1,2,3,5] => [4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,0,1,0]
=> [1,2,3,5,4] => [4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,1,0,0]
=> [1,2,5,3,4] => [4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,0,0,0]
=> [1,5,2,3,4] => [4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> 0 = 2 - 2
[1,1,1,1,0,1,0,0,0,0]
=> [5,1,2,3,4] => [4,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> 0 = 2 - 2
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => [5]
=> [1,0,1,0,1,0,1,0,1,0]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,3,1,4,5,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 - 2
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [2,4,1,3,5,6] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [2,5,1,3,4,6] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [2,1,3,4,6,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [2,1,3,6,4,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,1,0,0,0]
=> [2,1,6,3,4,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,6,1,3,4,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,1,3,4,5,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,3,2,4,5,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 - 2
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [3,4,1,2,5,6] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [3,5,1,2,4,6] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [3,1,2,4,6,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [3,1,2,6,4,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [3,1,6,2,4,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [3,6,1,2,4,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [3,1,2,4,5,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 - 2
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,4,2,3,5,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 - 2
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [4,5,1,2,3,6] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,0,0,1,0]
=> [4,1,2,3,6,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [4,1,2,6,3,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [4,1,6,2,3,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [4,6,1,2,3,5] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [4,1,2,3,5,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 - 2
[1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,2,3,5,6,4] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 - 2
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,2,3,5,4,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 - 2
[1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,2,5,3,6,4] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,2,5,6,3,4] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,2,5,3,4,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 - 2
[1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,5,2,3,6,4] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,5,2,6,3,4] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,5,6,2,3,4] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,5,2,3,4,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 3 - 2
[1,1,1,1,0,1,0,0,0,0,1,0]
=> [5,1,2,3,6,4] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,1,1,0,1,0,0,0,1,0,0]
=> [5,1,2,6,3,4] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,1,1,0,1,0,0,1,0,0,0]
=> [5,1,6,2,3,4] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [5,6,1,2,3,4] => [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> 0 = 2 - 2
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [5,1,2,3,4,6] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 - 2
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,2,3,4,6,5] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 - 2
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,2,3,6,4,5] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 - 2
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,2,6,3,4,5] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 - 2
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,6,2,3,4,5] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1 - 2
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [6,1,2,3,4,5] => [5,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 1 - 2
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,2,3,4,5,6] => [6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? = 1 - 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,1,5,6,7] => [6,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 - 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [2,3,5,1,4,6,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [2,3,6,1,4,5,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> [2,3,1,4,5,7,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> [2,3,1,4,7,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=> [2,3,1,7,4,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,3,7,1,4,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,3,1,4,5,6,7] => [6,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 - 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [2,1,4,3,5,6,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [2,4,5,1,3,6,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [2,4,6,1,3,5,7] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
=> [2,4,1,3,5,7,6] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
=> [2,4,1,3,7,5,6] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
=> [2,4,1,7,3,5,6] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
=> [2,4,7,1,3,5,6] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,4,1,3,5,6,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [2,1,5,3,4,6,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [2,5,6,1,3,4,7] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
=> [2,5,1,3,4,7,6] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> [2,5,1,3,7,4,6] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
=> [2,5,1,7,3,4,6] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> [2,5,7,1,3,4,6] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> [2,5,1,3,4,6,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
=> [2,1,3,4,6,7,5] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> [2,1,3,4,6,5,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
=> [2,1,3,6,4,7,5] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [2,1,3,6,7,4,5] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=> [2,1,3,6,4,5,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
=> [2,1,6,3,4,7,5] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=> [2,1,6,3,7,4,5] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
=> [2,1,6,7,3,4,5] => [4,3]
=> [1,0,1,1,1,0,1,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [2,1,6,3,4,5,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 1 - 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [2,6,1,3,4,5,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> [2,1,3,4,5,7,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [2,1,3,4,7,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [2,1,3,7,4,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [2,1,7,3,4,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 3 - 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [2,7,1,3,4,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,1,3,4,5,6,7] => [6,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 3 - 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [1,3,4,2,5,6,7] => [6,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 - 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [1,3,5,2,4,6,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,3,6,2,4,5,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> [1,3,2,4,5,7,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
=> [1,3,2,4,7,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=> [1,3,2,7,4,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=> [1,3,7,2,4,5,6] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [1,3,2,4,5,6,7] => [6,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> ? = 2 - 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [3,1,4,2,5,6,7] => [5,2]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? = 2 - 2
Description
The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path.
Matching statistic: St001000
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001000: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 40%●distinct values known / distinct values provided: 33%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001000: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 40%●distinct values known / distinct values provided: 33%
Values
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [4]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,4,5] => [4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,1,0,1,1,1,0,0,0,0]
=> [3,1,2,4,5] => [4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,0,1,1,0,0,0,0]
=> [4,1,2,3,5] => [4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,1,0,0,0,0,1,0]
=> [1,2,3,5,4] => [4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,1,0,0,0,1,0,0]
=> [1,2,5,3,4] => [4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,1,0,0,1,0,0,0]
=> [1,5,2,3,4] => [4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,1,0,1,0,0,0,0]
=> [5,1,2,3,4] => [4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => [5]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,3,1,4,5,6] => [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [2,4,1,3,5,6] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [2,5,1,3,4,6] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [2,1,3,4,6,5] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [2,1,3,6,4,5] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,1,0,0,1,0,0,0]
=> [2,1,6,3,4,5] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,6,1,3,4,5] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,1,3,4,5,6] => [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> ? = 2 - 1
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,3,2,4,5,6] => [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> ? = 2 - 1
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [3,4,1,2,5,6] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [3,5,1,2,4,6] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [3,1,2,4,6,5] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [3,1,2,6,4,5] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [3,1,6,2,4,5] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [3,6,1,2,4,5] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [3,1,2,4,5,6] => [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> ? = 2 - 1
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,4,2,3,5,6] => [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> ? = 2 - 1
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [4,5,1,2,3,6] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,0,1,1,0,0,0,0,1,0]
=> [4,1,2,3,6,5] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [4,1,2,6,3,5] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [4,1,6,2,3,5] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [4,6,1,2,3,5] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [4,1,2,3,5,6] => [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> ? = 2 - 1
[1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,2,3,5,6,4] => [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> ? = 2 - 1
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,2,3,5,4,6] => [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> ? = 2 - 1
[1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,2,5,3,6,4] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,2,5,6,3,4] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,2,5,3,4,6] => [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> ? = 2 - 1
[1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,5,2,3,6,4] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,5,2,6,3,4] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,5,6,2,3,4] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,5,2,3,4,6] => [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> ? = 3 - 1
[1,1,1,1,0,1,0,0,0,0,1,0]
=> [5,1,2,3,6,4] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,1,0,1,0,0,0,1,0,0]
=> [5,1,2,6,3,4] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,1,0,1,0,0,1,0,0,0]
=> [5,1,6,2,3,4] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [5,6,1,2,3,4] => [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1 = 2 - 1
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [5,1,2,3,4,6] => [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> ? = 2 - 1
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,2,3,4,6,5] => [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> ? = 2 - 1
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,2,3,6,4,5] => [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> ? = 2 - 1
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,2,6,3,4,5] => [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> ? = 2 - 1
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,6,2,3,4,5] => [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> ? = 1 - 1
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [6,1,2,3,4,5] => [5,1]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> ? = 1 - 1
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,2,3,4,5,6] => [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1 - 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,1,5,6,7] => [6,1]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [2,3,5,1,4,6,7] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [2,3,6,1,4,5,7] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> [2,3,1,4,5,7,6] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=> [2,3,1,4,7,5,6] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=> [2,3,1,7,4,5,6] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,3,7,1,4,5,6] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,3,1,4,5,6,7] => [6,1]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [2,1,4,3,5,6,7] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [2,4,5,1,3,6,7] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [2,4,6,1,3,5,7] => [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
=> [2,4,1,3,5,7,6] => [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
=> [2,4,1,3,7,5,6] => [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
=> [2,4,1,7,3,5,6] => [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
=> [2,4,7,1,3,5,6] => [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,4,1,3,5,6,7] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [2,1,5,3,4,6,7] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [2,5,6,1,3,4,7] => [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
=> [2,5,1,3,4,7,6] => [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> [2,5,1,3,7,4,6] => [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
=> [2,5,1,7,3,4,6] => [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> [2,5,7,1,3,4,6] => [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> [2,5,1,3,4,6,7] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
=> [2,1,3,4,6,7,5] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> [2,1,3,4,6,5,7] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
=> [2,1,3,6,4,7,5] => [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [2,1,3,6,7,4,5] => [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=> [2,1,3,6,4,5,7] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
=> [2,1,6,3,4,7,5] => [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=> [2,1,6,3,7,4,5] => [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
=> [2,1,6,7,3,4,5] => [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [2,1,6,3,4,5,7] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 1 - 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
=> [2,6,1,3,4,7,5] => [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1 = 2 - 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [2,6,1,3,4,5,7] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> [2,1,3,4,5,7,6] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [2,1,3,4,7,5,6] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [2,1,3,7,4,5,6] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [2,1,7,3,4,5,6] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 3 - 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [2,7,1,3,4,5,6] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,1,3,4,5,6,7] => [6,1]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> ? = 3 - 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [1,3,4,2,5,6,7] => [6,1]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> ? = 2 - 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [1,3,5,2,4,6,7] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,3,6,2,4,5,7] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=> [1,3,2,4,5,7,6] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
=> [1,3,2,4,7,5,6] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=> [1,3,2,7,4,5,6] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=> [1,3,7,2,4,5,6] => [5,2]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> ? = 2 - 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [1,3,2,4,5,6,7] => [6,1]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> ? = 2 - 1
Description
Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path.
The following 329 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St000993The multiplicity of the largest part of an integer partition. St000479The Ramsey number of a graph. St000306The bounce count of a Dyck path. St000655The length of the minimal rise of a Dyck path. St001371The length of the longest Yamanouchi prefix of a binary word. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001139The number of occurrences of hills of size 2 in a Dyck path. St001141The number of occurrences of hills of size 3 in a Dyck path. St000477The weight of a partition according to Alladi. St000478Another weight of a partition according to Alladi. St000715The number of semistandard Young tableaux of given shape and entries at most 3. St000124The cardinality of the preimage of the Simion-Schmidt map. St000716The dimension of the irreducible representation of Sp(6) labelled by an integer partition. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001256Number of simple reflexive modules that are 2-stable reflexive. St001481The minimal height of a peak of a Dyck path. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St000667The greatest common divisor of the parts of the partition. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St000712The number of semistandard Young tableau of given shape, with entries at most 4. St001122The multiplicity of the sign representation in the Kronecker square corresponding to a partition. St001498The normalised height of a Nakayama algebra with magnitude 1. St000007The number of saliances of the permutation. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St000237The number of small exceedances. St000404The number of occurrences of the pattern 3241 or of the pattern 4231 in a permutation. St000408The number of occurrences of the pattern 4231 in a permutation. St000731The number of double exceedences of a permutation. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St000882The number of connected components of short braid edges in the graph of braid moves of a permutation. St000879The number of long braid edges in the graph of braid moves of a permutation. St001501The dominant dimension of magnitude 1 Nakayama algebras. St001571The Cartan determinant of the integer partition. St000687The dimension of $Hom(I,P)$ for the LNakayama algebra of a Dyck path. St000636The hull number of a graph. St001029The size of the core of a graph. St001109The number of proper colourings of a graph with as few colours as possible. St001111The weak 2-dynamic chromatic number of a graph. St001316The domatic number of a graph. St001654The monophonic hull number of a graph. St001716The 1-improper chromatic number of a graph. St000266The number of spanning subgraphs of a graph with the same connected components. St000267The number of maximal spanning forests contained in a graph. St000671The maximin edge-connectivity for choosing a subgraph. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St000775The multiplicity of the largest eigenvalue in a graph. St000785The number of distinct colouring schemes of a graph. St001116The game chromatic number of a graph. St001272The number of graphs with the same degree sequence. St001353The number of prime nodes in the modular decomposition of a graph. St001395The number of strictly unfriendly partitions of a graph. St001475The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,0). St001476The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,-1). St001496The number of graphs with the same Laplacian spectrum as the given graph. St001546The number of monomials in the Tutte polynomial of a graph. St001743The discrepancy of a graph. St001826The maximal number of leaves on a vertex of a graph. St000268The number of strongly connected orientations of a graph. St000283The size of the preimage of the map 'to graph' from Binary trees to Graphs. St000323The minimal crossing number of a graph. St000344The number of strongly connected outdegree sequences of a graph. St000351The determinant of the adjacency matrix of a graph. St000368The Altshuler-Steinberg determinant of a graph. St000370The genus of a graph. St000379The number of Hamiltonian cycles in a graph. St000403The Szeged index minus the Wiener index of a graph. St000637The length of the longest cycle in a graph. St000699The toughness times the least common multiple of 1,. St000948The chromatic discriminant of a graph. St001069The coefficient of the monomial xy of the Tutte polynomial of the graph. St001070The absolute value of the derivative of the chromatic polynomial of the graph at 1. St001071The beta invariant of the graph. St001073The number of nowhere zero 3-flows of a graph. St001119The length of a shortest maximal path in a graph. St001271The competition number of a graph. St001281The normalized isoperimetric number of a graph. St001305The number of induced cycles on four vertices in a graph. St001307The number of induced stars on four vertices in a graph. St001309The number of four-cliques in a graph. St001310The number of induced diamond graphs in a graph. St001311The cyclomatic number of a graph. St001317The minimal number of occurrences of the forest-pattern in a linear ordering of the vertices of the graph. St001320The minimal number of occurrences of the path-pattern in a linear ordering of the vertices of the graph. St001323The independence gap of a graph. St001324The minimal number of occurrences of the chordal-pattern in a linear ordering of the vertices of the graph. St001325The minimal number of occurrences of the comparability-pattern in a linear ordering of the vertices of the graph. St001326The minimal number of occurrences of the interval-pattern in a linear ordering of the vertices of the graph. St001327The minimal number of occurrences of the split-pattern in a linear ordering of the vertices of the graph. St001328The minimal number of occurrences of the bipartite-pattern in a linear ordering of the vertices of the graph. St001329The minimal number of occurrences of the outerplanar pattern in a linear ordering of the vertices of the graph. St001331The size of the minimal feedback vertex set. St001334The minimal number of occurrences of the 3-colorable pattern in a linear ordering of the vertices of the graph. St001335The cardinality of a minimal cycle-isolating set of a graph. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001354The number of series nodes in the modular decomposition of a graph. St001357The maximal degree of a regular spanning subgraph of a graph. St001367The smallest number which does not occur as degree of a vertex in a graph. St001477The number of nowhere zero 5-flows of a graph. St001478The number of nowhere zero 4-flows of a graph. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. St001638The book thickness of a graph. St001689The number of celebrities in a graph. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001736The total number of cycles in a graph. St001793The difference between the clique number and the chromatic number of a graph. St001794Half the number of sets of vertices in a graph which are dominating and non-blocking. St001795The binary logarithm of the evaluation of the Tutte polynomial of the graph at (x,y) equal to (-1,-1). St001796The absolute value of the quotient of the Tutte polynomial of the graph at (1,1) and (-1,-1). St001797The number of overfull subgraphs of a graph. St000685The dominant dimension of the LNakayama algebra associated to a Dyck path. St000805The number of peaks of the associated bargraph. St000657The smallest part of an integer composition. St000900The minimal number of repetitions of a part in an integer composition. St001322The size of a minimal independent dominating set in a graph. St001333The cardinality of a minimal edge-isolating set of a graph. St001339The irredundance number of a graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001363The Euler characteristic of a graph according to Knill. St001306The number of induced paths on four vertices in a graph. St001356The number of vertices in prime modules of a graph. St000842The breadth of a permutation. St000889The number of alternating sign matrices with the same antidiagonal sums. St001568The smallest positive integer that does not appear twice in the partition. St000405The number of occurrences of the pattern 1324 in a permutation. St001613The binary logarithm of the size of the center of a lattice. St001681The number of inclusion-wise minimal subsets of a lattice, whose meet is the bottom element. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001881The number of factors of a lattice as a Cartesian product of lattices. St001677The number of non-degenerate subsets of a lattice whose meet is the bottom element. St001845The number of join irreducibles minus the rank of a lattice. St000908The length of the shortest maximal antichain in a poset. St000914The sum of the values of the Möbius function of a poset. St001301The first Betti number of the order complex associated with the poset. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St001198The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St000455The second largest eigenvalue of a graph if it is integral. St000322The skewness of a graph. St000119The number of occurrences of the pattern 321 in a permutation. St000123The difference in Coxeter length of a permutation and its image under the Simion-Schmidt map. St000223The number of nestings in the permutation. St001283The number of finite solvable groups that are realised by the given partition over the complex numbers. St001284The number of finite groups that are realised by the given partition over the complex numbers. St001043The depth of the leaf closest to the root in the binary unordered tree associated with the perfect matching. St001133The smallest label in the subtree rooted at the sister of 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001134The largest label in the subtree rooted at the sister of 1 in the leaf labelled binary unordered tree associated with the perfect matching. St000788The number of nesting-similar perfect matchings of a perfect matching. St001132The number of leaves in the subtree whose sister has label 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St000787The number of flips required to make a perfect matching noncrossing. St000862The number of parts of the shifted shape of a permutation. St001330The hat guessing number of a graph. St000640The rank of the largest boolean interval in a poset. St000996The number of exclusive left-to-right maxima of a permutation. St001942The number of loops of the quiver corresponding to the reduced incidence algebra of a poset. St001085The number of occurrences of the vincular pattern |21-3 in a permutation. St001398Number of subsets of size 3 of elements in a poset that form a "v". St001741The largest integer such that all patterns of this size are contained in the permutation. St001928The number of non-overlapping descents in a permutation. St000470The number of runs in a permutation. St000487The length of the shortest cycle of a permutation. St000501The size of the first part in the decomposition of a permutation. St000542The number of left-to-right-minima of a permutation. St000619The number of cyclic descents of a permutation. St000781The number of proper colouring schemes of a Ferrers diagram. St000990The first ascent of a permutation. St001162The minimum jump of a permutation. St001344The neighbouring number of a permutation. St001385The number of conjugacy classes of subgroups with connected subgroups of sizes prescribed by an integer partition. St001468The smallest fixpoint of a permutation. St000210Minimum over maximum difference of elements in cycles. St000256The number of parts from which one can substract 2 and still get an integer partition. St000358The number of occurrences of the pattern 31-2. St000360The number of occurrences of the pattern 32-1. St000367The number of simsun double descents of a permutation. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$. St000406The number of occurrences of the pattern 3241 in a permutation. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000622The number of occurrences of the patterns 2143 or 4231 in a permutation. St000623The number of occurrences of the pattern 52341 in a permutation. St000732The number of double deficiencies of a permutation. St000750The number of occurrences of the pattern 4213 in a permutation. St000799The number of occurrences of the vincular pattern |213 in a permutation. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000801The number of occurrences of the vincular pattern |312 in a permutation. St000802The number of occurrences of the vincular pattern |321 in a permutation. St000864The number of circled entries of the shifted recording tableau of a permutation. St000962The 3-shifted major index of a permutation. St001381The fertility of a permutation. St001466The number of transpositions swapping cyclically adjacent numbers in a permutation. St001513The number of nested exceedences of a permutation. St001550The number of inversions between exceedances where the greater exceedance is linked. St001551The number of restricted non-inversions between exceedances where the rightmost exceedance is linked. St001552The number of inversions between excedances and fixed points of a permutation. St001559The number of transpositions that are smaller or equal to a permutation in Bruhat order while not being inversions. St001715The number of non-records in a permutation. St001728The number of invisible descents of a permutation. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001847The number of occurrences of the pattern 1432 in a permutation. St001906Half of the difference between the total displacement and the number of inversions and the reflection length of a permutation. St001735The number of permutations with the same set of runs. St000354The number of recoils of a permutation. St000454The largest eigenvalue of a graph if it is integral. St000829The Ulam distance of a permutation to the identity permutation. St001359The number of permutations in the equivalence class of a permutation obtained by taking inverses of cycles. St001489The maximum of the number of descents and the number of inverse descents. St000486The number of cycles of length at least 3 of a permutation. St000666The number of right tethers of a permutation. St000824The sum of the number of descents and the number of recoils of a permutation. St001549The number of restricted non-inversions between exceedances. St001850The number of Hecke atoms of a permutation. St001645The pebbling number of a connected graph. St000098The chromatic number of a graph. St001597The Frobenius rank of a skew partition. St001434The number of negative sum pairs of a signed permutation. St001060The distinguishing index of a graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St000298The order dimension or Dushnik-Miller dimension of a poset. St000451The length of the longest pattern of the form k 1 2. St000485The length of the longest cycle of a permutation. St000374The number of exclusive right-to-left minima of a permutation. St000741The Colin de Verdière graph invariant. St000883The number of longest increasing subsequences of a permutation. St000886The number of permutations with the same antidiagonal sums. St001532The leading coefficient of the Poincare polynomial of the poset cone. St001737The number of descents of type 2 in a permutation. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St000407The number of occurrences of the pattern 2143 in a permutation. St000432The number of occurrences of the pattern 231 or of the pattern 312 in a permutation. St000436The number of occurrences of the pattern 231 or of the pattern 321 in a permutation. St000440The number of occurrences of the pattern 4132 or of the pattern 4231 in a permutation. St000516The number of stretching pairs of a permutation. St000710The number of big deficiencies of a permutation. St000779The tier of a permutation. St000872The number of very big descents of a permutation. St000963The 2-shifted major index of a permutation. St000989The number of final rises of a permutation. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St001130The number of two successive successions in a permutation. St001396Number of triples of incomparable elements in a finite poset. St001411The number of patterns 321 or 3412 in a permutation. St001537The number of cyclic crossings of a permutation. St000717The number of ordinal summands of a poset. St000281The size of the preimage of the map 'to poset' from Binary trees to Posets. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St001260The permanent of an alternating sign matrix. St000297The number of leading ones in a binary word. St001725The harmonious chromatic number of a graph. St001545The second Elser number of a connected graph. St001616The number of neutral elements in a lattice. St001720The minimal length of a chain of small intervals in a lattice. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St000648The number of 2-excedences of a permutation. St001394The genus of a permutation. St001846The number of elements which do not have a complement in the lattice. St000288The number of ones in a binary word. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001729The number of visible descents of a permutation. St000054The first entry of the permutation. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001663The number of occurrences of the Hertzsprung pattern 132 in a permutation. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001877Number of indecomposable injective modules with projective dimension 2. St001947The number of ties in a parking function. St000141The maximum drop size of a permutation. St000662The staircase size of the code of a permutation. St000906The length of the shortest maximal chain in a poset. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St001873For a Nakayama algebra corresponding to a Dyck path, we define the matrix C with entries the Hom-spaces between $e_i J$ and $e_j J$ (the radical of the indecomposable projective modules). St000031The number of cycles in the cycle decomposition of a permutation. St000036The evaluation at 1 of the Kazhdan-Lusztig polynomial with parameters given by the identity and the permutation. St000352The Elizalde-Pak rank of a permutation. St000627The exponent of a binary word. St000891The number of distinct diagonal sums of a permutation matrix. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension with the regular module. St001533The largest coefficient of the Poincare polynomial of the poset cone. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St000022The number of fixed points of a permutation. St000153The number of adjacent cycles of a permutation. St000159The number of distinct parts of the integer partition. St000214The number of adjacencies of a permutation. St000215The number of adjacencies of a permutation, zero appended. St000366The number of double descents of a permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000546The number of global descents of a permutation. St000629The defect of a binary word. St000649The number of 3-excedences of a permutation. St001095The number of non-isomorphic posets with precisely one further covering relation. St001217The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. St001432The order dimension of the partition. St001695The natural comajor index of a standard Young tableau. St001698The comajor index of a standard tableau minus the weighted size of its shape. St001699The major index of a standard tableau minus the weighted size of its shape. St001712The number of natural descents of a standard Young tableau. St001621The number of atoms of a lattice. St001624The breadth of a lattice. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001625The Möbius invariant of a lattice. St000326The position of the first one in a binary word after appending a 1 at the end. St001665The number of pure excedances of a permutation. St000296The length of the symmetric border of a binary word. St000402Half the size of the symmetry class of a permutation. St000878The number of ones minus the number of zeros of a binary word. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001964The interval resolution global dimension of a poset. St000093The cardinality of a maximal independent set of vertices of a graph. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St001393The induced matching number of a graph. St000258The burning number of a graph. St000362The size of a minimal vertex cover of a graph. St000387The matching number of a graph. St000461The rix statistic of a permutation. St001090The number of pop-stack-sorts needed to sort a permutation. St001261The Castelnuovo-Mumford regularity of a graph. St001829The common independence number of a graph. St000312The number of leaves in a graph. St000313The number of degree 2 vertices of a graph. St000647The number of big descents of a permutation. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph.
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