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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001232
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
=> [1] => [1]
=> [1,0,1,0]
=> 1
[[1,0],[0,1]]
=> [1,2] => [2]
=> [1,1,0,0,1,0]
=> 1
[[0,1],[1,0]]
=> [2,1] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[[1,0,0],[0,1,0],[0,0,1]]
=> [1,2,3] => [3]
=> [1,1,1,0,0,0,1,0]
=> 1
[[0,0,1],[0,1,0],[1,0,0]]
=> [3,2,1] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 3
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [1,2,3,4] => [4]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
=> [2,1,4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
=> [2,1,4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]]
=> [2,1,4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
=> [2,1,4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
=> [2,4,1,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[[0,0,1,0],[0,1,-1,1],[1,0,0,0],[0,0,1,0]]
=> [2,4,1,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
=> [3,1,4,2] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[[0,0,1,0],[0,1,0,0],[1,-1,0,1],[0,1,0,0]]
=> [3,1,4,2] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]
=> [3,4,1,2] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]
=> [4,3,2,1] => [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> 4
[[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,2,3,4,5] => [5]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> 1
[[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [3,2,1,4,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [4,2,1,3,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,4,3,2,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,4,3,2,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,4,3,2,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [4,1,3,2,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,4,3,2,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,4,3,2,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [4,1,3,2,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [4,3,1,2,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [3,2,4,1,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [2,4,3,1,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [2,4,3,1,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [4,2,3,1,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [3,4,2,1,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
=> [5,2,1,3,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,5,3,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,1,0,0,0],[1,-1,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,5,3,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,1,0,0],[1,0,-1,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,5,3,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,1,0],[1,0,0,-1,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,5,3,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [5,1,3,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,1,0,0,0],[0,0,0,0,1],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,5,3,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,1,0,0],[0,1,-1,0,1],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,5,3,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,1,0],[0,1,0,-1,1],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,5,3,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,0,1],[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [5,1,3,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [5,3,1,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0]]
=> [2,5,3,1,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0]]
=> [2,5,3,1,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0]]
=> [2,5,3,1,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0]]
=> [5,2,3,1,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [1,2,5,4,3] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [1,2,5,4,3] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [1,2,5,4,3] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001000
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001000: Dyck paths ⟶ ℤResult quality: 50% ●values known / values provided: 94%●distinct values known / distinct values provided: 50%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001000: Dyck paths ⟶ ℤResult quality: 50% ●values known / values provided: 94%●distinct values known / distinct values provided: 50%
Values
[[1]]
=> [1] => [1]
=> [1,0,1,0]
=> 1
[[1,0],[0,1]]
=> [1,2] => [2]
=> [1,1,0,0,1,0]
=> 1
[[0,1],[1,0]]
=> [2,1] => [1,1]
=> [1,0,1,1,0,0]
=> 2
[[1,0,0],[0,1,0],[0,0,1]]
=> [1,2,3] => [3]
=> [1,1,1,0,0,0,1,0]
=> 1
[[0,0,1],[0,1,0],[1,0,0]]
=> [3,2,1] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 3
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
=> [1,2,3,4] => [4]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
=> [2,1,4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
=> [2,1,4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]]
=> [2,1,4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
=> [2,1,4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
=> [2,4,1,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[[0,0,1,0],[0,1,-1,1],[1,0,0,0],[0,0,1,0]]
=> [2,4,1,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
=> [3,1,4,2] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[[0,0,1,0],[0,1,0,0],[1,-1,0,1],[0,1,0,0]]
=> [3,1,4,2] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]
=> [3,4,1,2] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> 2
[[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]
=> [4,3,2,1] => [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> 4
[[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [1,2,3,4,5] => [5]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> ? = 1
[[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
=> [3,2,1,4,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
=> [4,2,1,3,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,4,3,2,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,4,3,2,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,4,3,2,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [4,1,3,2,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,1,0,0,0],[0,0,0,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,4,3,2,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [1,4,3,2,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,1,0],[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [4,1,3,2,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1]]
=> [4,3,1,2,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [3,2,4,1,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [2,4,3,1,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [2,4,3,1,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [4,2,3,1,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]]
=> [3,4,2,1,5] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
=> [5,2,1,3,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,5,3,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,1,0,0,0],[1,-1,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,5,3,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,1,0,0],[1,0,-1,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,5,3,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,1,0],[1,0,0,-1,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,5,3,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [5,1,3,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,1,0,0,0],[0,0,0,0,1],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,5,3,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,1,0,0],[0,1,-1,0,1],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,5,3,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,1,0],[0,1,0,-1,1],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [1,5,3,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,0,1],[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [5,1,3,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0]]
=> [5,3,1,2,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0]]
=> [2,5,3,1,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,1,0,0],[0,1,-1,0,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0]]
=> [2,5,3,1,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,1,0],[0,1,0,-1,1],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0]]
=> [2,5,3,1,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0]]
=> [5,2,3,1,4] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [1,2,5,4,3] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [1,2,5,4,3] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [1,2,5,4,3] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[1,0,0,0,0],[0,0,0,1,0],[0,1,0,-1,1],[0,0,0,1,0],[0,0,1,0,0]]
=> [1,2,5,4,3] => [3,1,1]
=> [1,0,1,1,0,0,1,0]
=> 3
[[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]]
=> [5,4,3,2,1] => [1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> ? = 5
[[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]]
=> [1,2,3,4,5,6] => [6]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> ? = 1
[[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0]]
=> [6,5,4,3,2,1] => [1,1,1,1,1,1]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 6
[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]
=> [1,2,3,4,7,6,5] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]
=> [1,2,3,6,5,4,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
=> [1,2,5,4,3,6,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]
=> [1,2,7,6,5,4,3] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
=> [1,4,3,2,5,6,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1]]
=> [1,6,5,4,3,2,7] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 7
[[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
=> [3,2,1,4,5,6,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
=> [5,4,3,2,1,6,7] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]
=> [1,2,3,4,7,6,5] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]
=> [1,2,3,4,7,6,5] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]
=> [1,2,3,4,7,6,5] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]
=> [1,2,3,6,5,4,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]
=> [1,2,3,4,7,6,5] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]
=> [1,2,3,6,5,4,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]
=> [1,2,3,4,7,6,5] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]
=> [1,2,3,4,7,6,5] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]
=> [1,2,3,6,5,4,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]
=> [1,2,3,4,7,6,5] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
=> [1,2,5,4,3,6,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]
=> [1,2,3,6,5,4,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]
=> [1,2,3,4,7,6,5] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,0,1,0,0,0,0],[0,1,-1,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]
=> [1,2,7,6,5,4,3] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
=> [1,2,5,4,3,6,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]
=> [1,2,3,6,5,4,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]
=> [1,2,3,4,7,6,5] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,0,0,1,0,0,0],[0,0,1,-1,0,0,1],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]
=> [1,2,7,6,5,4,3] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]
=> [1,2,7,6,5,4,3] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 7
[[1,0,0,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0]]
=> [1,2,7,6,5,4,3] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 7
[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,1,0,0],[0,0,0,1,-1,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0]]
=> [1,2,3,4,7,6,5] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]
=> [1,2,3,6,5,4,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,1,0,0,0],[0,0,1,-1,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]
=> [1,2,3,4,7,6,5] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
=> [1,2,5,4,3,6,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]
=> [1,2,3,6,5,4,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,1,0,0],[0,0,0,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]
=> [1,2,3,4,7,6,5] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[0,1,0,0,0,0,0],[1,-1,1,0,0,0,0],[0,1,-1,0,0,0,1],[0,0,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]
=> [1,2,7,6,5,4,3] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 7
[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
=> [1,4,3,2,5,6,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
=> [1,2,5,4,3,6,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]
=> [1,2,3,6,5,4,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,-1,1],[0,0,0,1,-1,1,0],[0,0,0,0,1,0,0]]
=> [1,2,3,4,7,6,5] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[0,1,0,0,0,0,0],[1,-1,0,1,0,0,0],[0,0,1,-1,0,0,1],[0,1,-1,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]
=> [1,2,7,6,5,4,3] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 7
[[0,1,0,0,0,0,0],[1,-1,0,0,1,0,0],[0,0,0,1,-1,0,1],[0,0,1,-1,0,1,0],[0,1,-1,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0]]
=> [1,2,7,6,5,4,3] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 7
[[0,1,0,0,0,0,0],[1,-1,0,0,0,1,0],[0,0,0,0,1,0,0],[0,0,0,1,0,0,0],[0,0,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,0,0,1]]
=> [1,6,5,4,3,2,7] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 7
[[0,1,0,0,0,0,0],[1,-1,0,0,0,1,0],[0,0,0,0,1,-1,1],[0,0,0,1,-1,1,0],[0,0,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0]]
=> [1,2,7,6,5,4,3] => [3,1,1,1,1]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? = 7
[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,0,0,0,0],[0,1,0,0,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
=> [1,4,3,2,5,6,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,0,0,0],[0,0,1,0,0,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]]
=> [1,2,5,4,3,6,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
[[0,0,1,0,0,0,0],[0,1,-1,1,0,0,0],[1,-1,1,-1,1,0,0],[0,1,-1,1,-1,1,0],[0,0,1,-1,1,0,0],[0,0,0,1,0,0,0],[0,0,0,0,0,0,1]]
=> [1,2,3,6,5,4,7] => [5,1,1]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? = 7
Description
Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path.
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