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Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001200
Mapping
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001200: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[0,1],[1,0]]
 => [2,1] => [1,2] => [1,0,1,0]
 => 2
[[1,0,0],[0,1,0],[0,0,1]]
 => [1,2,3] => [2,3,1] => [1,1,0,1,0,0]
 => 2
[[0,1,0],[1,0,0],[0,0,1]]
 => [2,1,3] => [1,3,2] => [1,0,1,1,0,0]
 => 2
[[0,1,0],[0,0,1],[1,0,0]]
 => [2,3,1] => [1,2,3] => [1,0,1,0,1,0]
 => 3
[[0,0,1],[0,1,0],[1,0,0]]
 => [3,2,1] => [2,1,3] => [1,1,0,0,1,0]
 => 2
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => [1,2,3,4] => [2,3,4,1] => [1,1,0,1,0,1,0,0]
 => 3
[[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => [2,1,3,4] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
 => 3
[[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,3,2,4] => [3,2,4,1] => [1,1,1,0,0,1,0,0]
 => 2
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]]
 => [1,3,2,4] => [3,2,4,1] => [1,1,1,0,0,1,0,0]
 => 2
[[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => [3,1,2,4] => [3,1,4,2] => [1,1,1,0,0,1,0,0]
 => 2
[[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]
 => [2,3,1,4] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 3
[[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
 => [3,2,1,4] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
 => 2
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => [1,2,4,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
 => 2
[[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => [2,1,4,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 2
[[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,2,4,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
 => 2
[[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]]
 => [1,2,4,3] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
 => 2
[[0,0,1,0],[1,0,0,0],[0,1,-1,1],[0,0,1,0]]
 => [2,1,4,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 2
[[0,1,0,0],[0,0,1,0],[1,0,-1,1],[0,0,1,0]]
 => [2,1,4,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 2
[[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]]
 => [2,1,4,3] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 2
[[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
 => 2
[[0,1,0,0],[1,-1,0,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
 => 2
[[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]]
 => [1,4,2,3] => [3,4,2,1] => [1,1,1,0,1,0,0,0]
 => 2
[[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
 => [4,1,2,3] => [3,4,1,2] => [1,1,1,0,1,0,0,0]
 => 2
[[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
 => [2,4,1,3] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
 => 2
[[0,0,1,0],[0,1,-1,1],[1,0,0,0],[0,0,1,0]]
 => [2,4,1,3] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
 => 2
[[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
 => [4,2,1,3] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
 => 2
[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]]
 => [2,3,4,1] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 3
[[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]]
 => [3,2,4,1] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
 => 3
[[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
 => [2,4,3,1] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 3
[[0,0,1,0],[0,1,-1,1],[0,0,1,0],[1,0,0,0]]
 => [2,4,3,1] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 3
[[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
 => [4,2,3,1] => [2,3,1,4] => [1,1,0,1,0,0,1,0]
 => 3
[[0,0,1,0],[0,0,0,1],[0,1,0,0],[1,0,0,0]]
 => [3,4,2,1] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
 => 2
[[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]
 => [4,3,2,1] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
 => 2
[[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] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0]
 => 4
[[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [2,1,3,4,5] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
 => 4
[[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,3,2,4,5] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0]
 => 3
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [1,3,2,4,5] => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0]
 => 3
[[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [3,1,2,4,5] => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0]
 => 3
[[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [2,3,1,4,5] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
 => 3
[[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] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0]
 => 3
[[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0]
 => 3
[[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
 => 3
[[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0]
 => 3
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,2,4,3,5] => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0]
 => 3
[[0,0,1,0,0],[1,0,0,0,0],[0,1,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
 => 3
[[0,1,0,0,0],[0,0,1,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
 => 3
[[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [2,1,4,3,5] => [1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
 => 3
[[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,4,2,3,5] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0]
 => 3
[[0,1,0,0,0],[1,-1,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,4,2,3,5] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0]
 => 3
[[0,0,1,0,0],[1,0,-1,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [1,4,2,3,5] => [3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0]
 => 3
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.