- FindStat

Identifier

Mp00137: Dyck paths —to symmetric ASM⟶ Alternating sign matrices
Mp00002: Alternating sign matrices —to left key permutation⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
St000235: Permutations ⟶ ℤ

Values

[1,0] => [[1]] => [1] => [1] => 0

[1,0,1,0] => [[1,0],[0,1]] => [1,2] => [2,1] => 0

[1,1,0,0] => [[0,1],[1,0]] => [2,1] => [1,2] => 2

[1,0,1,0,1,0] => [[1,0,0],[0,1,0],[0,0,1]] => [1,2,3] => [2,3,1] => 0

[1,0,1,1,0,0] => [[1,0,0],[0,0,1],[0,1,0]] => [1,3,2] => [3,2,1] => 2

[1,1,0,0,1,0] => [[0,1,0],[1,0,0],[0,0,1]] => [2,1,3] => [1,3,2] => 2

[1,1,0,1,0,0] => [[0,1,0],[1,-1,1],[0,1,0]] => [1,3,2] => [3,2,1] => 2

[1,1,1,0,0,0] => [[0,0,1],[0,1,0],[1,0,0]] => [3,2,1] => [2,1,3] => 2

[1,0,1,0,1,0,1,0] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]] => [1,2,3,4] => [2,3,4,1] => 0

[1,0,1,0,1,1,0,0] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]] => [1,2,4,3] => [2,4,3,1] => 2

[1,0,1,1,0,0,1,0] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]] => [1,3,2,4] => [3,2,4,1] => 2

[1,0,1,1,0,1,0,0] => [[1,0,0,0],[0,0,1,0],[0,1,-1,1],[0,0,1,0]] => [1,2,4,3] => [2,4,3,1] => 2

[1,0,1,1,1,0,0,0] => [[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]] => [1,4,3,2] => [4,3,2,1] => 2

[1,1,0,0,1,0,1,0] => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]] => [2,1,3,4] => [1,3,4,2] => 2

[1,1,0,0,1,1,0,0] => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]] => [2,1,4,3] => [1,4,3,2] => 4

[1,1,0,1,0,0,1,0] => [[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]] => [1,3,2,4] => [3,2,4,1] => 2

[1,1,0,1,0,1,0,0] => [[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]] => [1,2,4,3] => [2,4,3,1] => 2

[1,1,0,1,1,0,0,0] => [[0,1,0,0],[1,-1,0,1],[0,0,1,0],[0,1,0,0]] => [1,4,3,2] => [4,3,2,1] => 2

[1,1,1,0,0,0,1,0] => [[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]] => [3,2,1,4] => [2,1,4,3] => 2

[1,1,1,0,0,1,0,0] => [[0,0,1,0],[0,1,0,0],[1,0,-1,1],[0,0,1,0]] => [2,1,4,3] => [1,4,3,2] => 4

[1,1,1,0,1,0,0,0] => [[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]] => [1,4,3,2] => [4,3,2,1] => 2

[1,1,1,1,0,0,0,0] => [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]] => [4,3,2,1] => [3,2,1,4] => 4

[1,0,1,0,1,0,1,0,1,0] => [[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]] => [1,2,3,4,5] => [2,3,4,5,1] => 0

[1,0,1,0,1,0,1,1,0,0] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [1,2,3,5,4] => [2,3,5,4,1] => 2

[1,0,1,0,1,1,0,0,1,0] => [[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] => 2

[1,0,1,0,1,1,0,1,0,0] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]] => [1,2,3,5,4] => [2,3,5,4,1] => 2

[1,0,1,0,1,1,1,0,0,0] => [[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] => [2,5,4,3,1] => 2

[1,0,1,1,0,0,1,0,1,0] => [[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] => 2

[1,0,1,1,0,0,1,1,0,0] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [1,3,2,5,4] => [3,2,5,4,1] => 4

[1,0,1,1,0,1,0,0,1,0] => [[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] => 2

[1,0,1,1,0,1,0,1,0,0] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]] => [1,2,3,5,4] => [2,3,5,4,1] => 2

[1,0,1,1,0,1,1,0,0,0] => [[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] => [2,5,4,3,1] => 2

[1,0,1,1,1,0,0,0,1,0] => [[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] => [4,3,2,5,1] => 2

[1,0,1,1,1,0,0,1,0,0] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]] => [1,3,2,5,4] => [3,2,5,4,1] => 4

[1,0,1,1,1,0,1,0,0,0] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]] => [1,2,5,4,3] => [2,5,4,3,1] => 2

[1,0,1,1,1,1,0,0,0,0] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]] => [1,5,4,3,2] => [5,4,3,2,1] => 4

[1,1,0,0,1,0,1,0,1,0] => [[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] => 2

[1,1,0,0,1,0,1,1,0,0] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [2,1,3,5,4] => [1,3,5,4,2] => 4

[1,1,0,0,1,1,0,0,1,0] => [[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] => 4

[1,1,0,0,1,1,0,1,0,0] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,-1,1],[0,0,0,1,0]] => [2,1,3,5,4] => [1,3,5,4,2] => 4

[1,1,0,0,1,1,1,0,0,0] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]] => [2,1,5,4,3] => [1,5,4,3,2] => 4

[1,1,0,1,0,0,1,0,1,0] => [[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] => 2

[1,1,0,1,0,0,1,1,0,0] => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [1,3,2,5,4] => [3,2,5,4,1] => 4

[1,1,0,1,0,1,0,0,1,0] => [[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] => 2

[1,1,0,1,0,1,0,1,0,0] => [[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]] => [1,2,3,5,4] => [2,3,5,4,1] => 2

[1,1,0,1,0,1,1,0,0,0] => [[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] => [2,5,4,3,1] => 2

[1,1,0,1,1,0,0,0,1,0] => [[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] => [4,3,2,5,1] => 2

[1,1,0,1,1,0,0,1,0,0] => [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]] => [1,3,2,5,4] => [3,2,5,4,1] => 4

[1,1,0,1,1,0,1,0,0,0] => [[0,1,0,0,0],[1,-1,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]] => [1,2,5,4,3] => [2,5,4,3,1] => 2

[1,1,0,1,1,1,0,0,0,0] => [[0,1,0,0,0],[1,-1,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]] => [1,5,4,3,2] => [5,4,3,2,1] => 4

[1,1,1,0,0,0,1,0,1,0] => [[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] => 2

[1,1,1,0,0,0,1,1,0,0] => [[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]] => [3,2,1,5,4] => [2,1,5,4,3] => 4

[1,1,1,0,0,1,0,0,1,0] => [[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] => 4

[1,1,1,0,0,1,0,1,0,0] => [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]] => [2,1,3,5,4] => [1,3,5,4,2] => 4

[1,1,1,0,0,1,1,0,0,0] => [[0,0,1,0,0],[0,1,0,0,0],[1,0,-1,0,1],[0,0,0,1,0],[0,0,1,0,0]] => [2,1,5,4,3] => [1,5,4,3,2] => 4

[1,1,1,0,1,0,0,0,1,0] => [[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] => [4,3,2,5,1] => 2

[1,1,1,0,1,0,0,1,0,0] => [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,-1,1],[0,0,0,1,0]] => [1,3,2,5,4] => [3,2,5,4,1] => 4

[1,1,1,0,1,0,1,0,0,0] => [[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]] => [1,2,5,4,3] => [2,5,4,3,1] => 2

[1,1,1,0,1,1,0,0,0,0] => [[0,0,1,0,0],[0,1,-1,0,1],[1,-1,0,1,0],[0,0,1,0,0],[0,1,0,0,0]] => [1,5,4,3,2] => [5,4,3,2,1] => 4

[1,1,1,1,0,0,0,0,1,0] => [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1]] => [4,3,2,1,5] => [3,2,1,5,4] => 4

[1,1,1,1,0,0,0,1,0,0] => [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,-1,1],[0,0,0,1,0]] => [3,2,1,5,4] => [2,1,5,4,3] => 4

[1,1,1,1,0,0,1,0,0,0] => [[0,0,0,1,0],[0,0,1,0,0],[0,1,0,-1,1],[1,0,-1,1,0],[0,0,1,0,0]] => [2,1,5,4,3] => [1,5,4,3,2] => 4

[1,1,1,1,0,1,0,0,0,0] => [[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0]] => [1,5,4,3,2] => [5,4,3,2,1] => 4

[1,1,1,1,1,0,0,0,0,0] => [[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] => [4,3,2,1,5] => 4

[1,0,1,0,1,0,1,0,1,0,1,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [1,2,3,4,5,6] => [2,3,4,5,6,1] => 0

[1,0,1,0,1,0,1,0,1,1,0,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => 2

[1,0,1,0,1,0,1,1,0,0,1,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => 2

[1,0,1,0,1,0,1,1,0,1,0,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => 2

[1,0,1,0,1,0,1,1,1,0,0,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => 2

[1,0,1,0,1,1,0,0,1,0,1,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => 2

[1,0,1,0,1,1,0,0,1,1,0,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => 4

[1,0,1,0,1,1,0,1,0,0,1,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => 2

[1,0,1,0,1,1,0,1,0,1,0,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => 2

[1,0,1,0,1,1,0,1,1,0,0,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => 2

[1,0,1,0,1,1,1,0,0,0,1,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [1,2,5,4,3,6] => [2,5,4,3,6,1] => 2

[1,0,1,0,1,1,1,0,0,1,0,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => 4

[1,0,1,0,1,1,1,0,1,0,0,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => 2

[1,0,1,0,1,1,1,1,0,0,0,0] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [1,2,6,5,4,3] => [2,6,5,4,3,1] => 4

[1,0,1,1,0,0,1,0,1,0,1,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => 2

[1,0,1,1,0,0,1,0,1,1,0,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [1,3,2,4,6,5] => [3,2,4,6,5,1] => 4

[1,0,1,1,0,0,1,1,0,0,1,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [1,3,2,5,4,6] => [3,2,5,4,6,1] => 4

[1,0,1,1,0,0,1,1,0,1,0,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [1,3,2,4,6,5] => [3,2,4,6,5,1] => 4

[1,0,1,1,0,0,1,1,1,0,0,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [1,3,2,6,5,4] => [3,2,6,5,4,1] => 4

[1,0,1,1,0,1,0,0,1,0,1,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => 2

[1,0,1,1,0,1,0,0,1,1,0,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => 4

[1,0,1,1,0,1,0,1,0,0,1,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => 2

[1,0,1,1,0,1,0,1,0,1,0,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => 2

[1,0,1,1,0,1,0,1,1,0,0,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => 2

[1,0,1,1,0,1,1,0,0,0,1,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [1,2,5,4,3,6] => [2,5,4,3,6,1] => 2

[1,0,1,1,0,1,1,0,0,1,0,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => 4

[1,0,1,1,0,1,1,0,1,0,0,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => 2

[1,0,1,1,0,1,1,1,0,0,0,0] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,1,-1,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [1,2,6,5,4,3] => [2,6,5,4,3,1] => 4

[1,0,1,1,1,0,0,0,1,0,1,0] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [1,4,3,2,5,6] => [4,3,2,5,6,1] => 2

[1,0,1,1,1,0,0,0,1,1,0,0] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [1,4,3,2,6,5] => [4,3,2,6,5,1] => 4

[1,0,1,1,1,0,0,1,0,0,1,0] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [1,3,2,5,4,6] => [3,2,5,4,6,1] => 4

[1,0,1,1,1,0,0,1,0,1,0,0] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [1,3,2,4,6,5] => [3,2,4,6,5,1] => 4

[1,0,1,1,1,0,0,1,1,0,0,0] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [1,3,2,6,5,4] => [3,2,6,5,4,1] => 4

[1,0,1,1,1,0,1,0,0,0,1,0] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [1,2,5,4,3,6] => [2,5,4,3,6,1] => 2

[1,0,1,1,1,0,1,0,0,1,0,0] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => 4

[1,0,1,1,1,0,1,0,1,0,0,0] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => 2

[1,0,1,1,1,0,1,1,0,0,0,0] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [1,2,6,5,4,3] => [2,6,5,4,3,1] => 4

>>> Load all 196 entries. <<<

[1,0,1,1,1,1,0,0,0,0,1,0] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => [1,5,4,3,2,6] => [5,4,3,2,6,1] => 4

[1,0,1,1,1,1,0,0,0,1,0,0] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]] => [1,4,3,2,6,5] => [4,3,2,6,5,1] => 4

[1,0,1,1,1,1,0,0,1,0,0,0] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]] => [1,3,2,6,5,4] => [3,2,6,5,4,1] => 4

[1,0,1,1,1,1,0,1,0,0,0,0] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]] => [1,2,6,5,4,3] => [2,6,5,4,3,1] => 4

[1,0,1,1,1,1,1,0,0,0,0,0] => [[1,0,0,0,0,0],[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]] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => 4

[1,1,0,0,1,0,1,0,1,0,1,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => 2

[1,1,0,0,1,0,1,0,1,1,0,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [2,1,3,4,6,5] => [1,3,4,6,5,2] => 4

[1,1,0,0,1,0,1,1,0,0,1,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [2,1,3,5,4,6] => [1,3,5,4,6,2] => 4

[1,1,0,0,1,0,1,1,0,1,0,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [2,1,3,4,6,5] => [1,3,4,6,5,2] => 4

[1,1,0,0,1,0,1,1,1,0,0,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [2,1,3,6,5,4] => [1,3,6,5,4,2] => 4

[1,1,0,0,1,1,0,0,1,0,1,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [2,1,4,3,5,6] => [1,4,3,5,6,2] => 4

[1,1,0,0,1,1,0,0,1,1,0,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 6

[1,1,0,0,1,1,0,1,0,0,1,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [2,1,3,5,4,6] => [1,3,5,4,6,2] => 4

[1,1,0,0,1,1,0,1,0,1,0,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [2,1,3,4,6,5] => [1,3,4,6,5,2] => 4

[1,1,0,0,1,1,0,1,1,0,0,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [2,1,3,6,5,4] => [1,3,6,5,4,2] => 4

[1,1,0,0,1,1,1,0,0,0,1,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [2,1,5,4,3,6] => [1,5,4,3,6,2] => 4

[1,1,0,0,1,1,1,0,0,1,0,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 6

[1,1,0,0,1,1,1,0,1,0,0,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [2,1,3,6,5,4] => [1,3,6,5,4,2] => 4

[1,1,0,0,1,1,1,1,0,0,0,0] => [[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [2,1,6,5,4,3] => [1,6,5,4,3,2] => 6

[1,1,0,1,0,0,1,0,1,0,1,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [1,3,2,4,5,6] => [3,2,4,5,6,1] => 2

[1,1,0,1,0,0,1,0,1,1,0,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [1,3,2,4,6,5] => [3,2,4,6,5,1] => 4

[1,1,0,1,0,0,1,1,0,0,1,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [1,3,2,5,4,6] => [3,2,5,4,6,1] => 4

[1,1,0,1,0,0,1,1,0,1,0,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [1,3,2,4,6,5] => [3,2,4,6,5,1] => 4

[1,1,0,1,0,0,1,1,1,0,0,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [1,3,2,6,5,4] => [3,2,6,5,4,1] => 4

[1,1,0,1,0,1,0,0,1,0,1,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [1,2,4,3,5,6] => [2,4,3,5,6,1] => 2

[1,1,0,1,0,1,0,0,1,1,0,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => 4

[1,1,0,1,0,1,0,1,0,0,1,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [1,2,3,5,4,6] => [2,3,5,4,6,1] => 2

[1,1,0,1,0,1,0,1,0,1,0,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [1,2,3,4,6,5] => [2,3,4,6,5,1] => 2

[1,1,0,1,0,1,0,1,1,0,0,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => 2

[1,1,0,1,0,1,1,0,0,0,1,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [1,2,5,4,3,6] => [2,5,4,3,6,1] => 2

[1,1,0,1,0,1,1,0,0,1,0,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => 4

[1,1,0,1,0,1,1,0,1,0,0,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => 2

[1,1,0,1,0,1,1,1,0,0,0,0] => [[0,1,0,0,0,0],[1,-1,1,0,0,0],[0,1,-1,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [1,2,6,5,4,3] => [2,6,5,4,3,1] => 4

[1,1,0,1,1,0,0,0,1,0,1,0] => [[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [1,4,3,2,5,6] => [4,3,2,5,6,1] => 2

[1,1,0,1,1,0,0,0,1,1,0,0] => [[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [1,4,3,2,6,5] => [4,3,2,6,5,1] => 4

[1,1,0,1,1,0,0,1,0,0,1,0] => [[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [1,3,2,5,4,6] => [3,2,5,4,6,1] => 4

[1,1,0,1,1,0,0,1,0,1,0,0] => [[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [1,3,2,4,6,5] => [3,2,4,6,5,1] => 4

[1,1,0,1,1,0,0,1,1,0,0,0] => [[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [1,3,2,6,5,4] => [3,2,6,5,4,1] => 4

[1,1,0,1,1,0,1,0,0,0,1,0] => [[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [1,2,5,4,3,6] => [2,5,4,3,6,1] => 2

[1,1,0,1,1,0,1,0,0,1,0,0] => [[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => 4

[1,1,0,1,1,0,1,0,1,0,0,0] => [[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => 2

[1,1,0,1,1,0,1,1,0,0,0,0] => [[0,1,0,0,0,0],[1,-1,0,1,0,0],[0,0,1,-1,0,1],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [1,2,6,5,4,3] => [2,6,5,4,3,1] => 4

[1,1,0,1,1,1,0,0,0,0,1,0] => [[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => [1,5,4,3,2,6] => [5,4,3,2,6,1] => 4

[1,1,0,1,1,1,0,0,0,1,0,0] => [[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]] => [1,4,3,2,6,5] => [4,3,2,6,5,1] => 4

[1,1,0,1,1,1,0,0,1,0,0,0] => [[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]] => [1,3,2,6,5,4] => [3,2,6,5,4,1] => 4

[1,1,0,1,1,1,0,1,0,0,0,0] => [[0,1,0,0,0,0],[1,-1,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]] => [1,2,6,5,4,3] => [2,6,5,4,3,1] => 4

[1,1,0,1,1,1,1,0,0,0,0,0] => [[0,1,0,0,0,0],[1,-1,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => 4

[1,1,1,0,0,0,1,0,1,0,1,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [3,2,1,4,5,6] => [2,1,4,5,6,3] => 2

[1,1,1,0,0,0,1,0,1,1,0,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [3,2,1,4,6,5] => [2,1,4,6,5,3] => 4

[1,1,1,0,0,0,1,1,0,0,1,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [3,2,1,5,4,6] => [2,1,5,4,6,3] => 4

[1,1,1,0,0,0,1,1,0,1,0,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [3,2,1,4,6,5] => [2,1,4,6,5,3] => 4

[1,1,1,0,0,0,1,1,1,0,0,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [3,2,1,6,5,4] => [2,1,6,5,4,3] => 4

[1,1,1,0,0,1,0,0,1,0,1,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [2,1,4,3,5,6] => [1,4,3,5,6,2] => 4

[1,1,1,0,0,1,0,0,1,1,0,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 6

[1,1,1,0,0,1,0,1,0,0,1,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [2,1,3,5,4,6] => [1,3,5,4,6,2] => 4

[1,1,1,0,0,1,0,1,0,1,0,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [2,1,3,4,6,5] => [1,3,4,6,5,2] => 4

[1,1,1,0,0,1,0,1,1,0,0,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,1,0,0],[0,0,1,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [2,1,3,6,5,4] => [1,3,6,5,4,2] => 4

[1,1,1,0,0,1,1,0,0,0,1,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [2,1,5,4,3,6] => [1,5,4,3,6,2] => 4

[1,1,1,0,0,1,1,0,0,1,0,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 6

[1,1,1,0,0,1,1,0,1,0,0,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [2,1,3,6,5,4] => [1,3,6,5,4,2] => 4

[1,1,1,0,0,1,1,1,0,0,0,0] => [[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,-1,0,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [2,1,6,5,4,3] => [1,6,5,4,3,2] => 6

[1,1,1,0,1,0,0,0,1,0,1,0] => [[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [1,4,3,2,5,6] => [4,3,2,5,6,1] => 2

[1,1,1,0,1,0,0,0,1,1,0,0] => [[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [1,4,3,2,6,5] => [4,3,2,6,5,1] => 4

[1,1,1,0,1,0,0,1,0,0,1,0] => [[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [1,3,2,5,4,6] => [3,2,5,4,6,1] => 4

[1,1,1,0,1,0,0,1,0,1,0,0] => [[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [1,3,2,4,6,5] => [3,2,4,6,5,1] => 4

[1,1,1,0,1,0,0,1,1,0,0,0] => [[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [1,3,2,6,5,4] => [3,2,6,5,4,1] => 4

[1,1,1,0,1,0,1,0,0,0,1,0] => [[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [1,2,5,4,3,6] => [2,5,4,3,6,1] => 2

[1,1,1,0,1,0,1,0,0,1,0,0] => [[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [1,2,4,3,6,5] => [2,4,3,6,5,1] => 4

[1,1,1,0,1,0,1,0,1,0,0,0] => [[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,1,0],[0,1,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [1,2,3,6,5,4] => [2,3,6,5,4,1] => 2

[1,1,1,0,1,0,1,1,0,0,0,0] => [[0,0,1,0,0,0],[0,1,-1,1,0,0],[1,-1,1,-1,0,1],[0,1,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [1,2,6,5,4,3] => [2,6,5,4,3,1] => 4

[1,1,1,0,1,1,0,0,0,0,1,0] => [[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => [1,5,4,3,2,6] => [5,4,3,2,6,1] => 4

[1,1,1,0,1,1,0,0,0,1,0,0] => [[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]] => [1,4,3,2,6,5] => [4,3,2,6,5,1] => 4

[1,1,1,0,1,1,0,0,1,0,0,0] => [[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]] => [1,3,2,6,5,4] => [3,2,6,5,4,1] => 4

[1,1,1,0,1,1,0,1,0,0,0,0] => [[0,0,1,0,0,0],[0,1,-1,0,1,0],[1,-1,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]] => [1,2,6,5,4,3] => [2,6,5,4,3,1] => 4

[1,1,1,0,1,1,1,0,0,0,0,0] => [[0,0,1,0,0,0],[0,1,-1,0,0,1],[1,-1,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => 4

[1,1,1,1,0,0,0,0,1,0,1,0] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => [4,3,2,1,5,6] => [3,2,1,5,6,4] => 4

[1,1,1,1,0,0,0,0,1,1,0,0] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => [4,3,2,1,6,5] => [3,2,1,6,5,4] => 6

[1,1,1,1,0,0,0,1,0,0,1,0] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => [3,2,1,5,4,6] => [2,1,5,4,6,3] => 4

[1,1,1,1,0,0,0,1,0,1,0,0] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,-1,1,0],[0,0,0,1,-1,1],[0,0,0,0,1,0]] => [3,2,1,4,6,5] => [2,1,4,6,5,3] => 4

[1,1,1,1,0,0,0,1,1,0,0,0] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,-1,0,1],[0,0,0,0,1,0],[0,0,0,1,0,0]] => [3,2,1,6,5,4] => [2,1,6,5,4,3] => 4

[1,1,1,1,0,0,1,0,0,0,1,0] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => [2,1,5,4,3,6] => [1,5,4,3,6,2] => 4

[1,1,1,1,0,0,1,0,0,1,0,0] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,-1,1],[0,0,0,0,1,0]] => [2,1,4,3,6,5] => [1,4,3,6,5,2] => 6

[1,1,1,1,0,0,1,0,1,0,0,0] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,1,0],[1,0,-1,1,-1,1],[0,0,1,-1,1,0],[0,0,0,1,0,0]] => [2,1,3,6,5,4] => [1,3,6,5,4,2] => 4

[1,1,1,1,0,0,1,1,0,0,0,0] => [[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,-1,0,1],[1,0,-1,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0]] => [2,1,6,5,4,3] => [1,6,5,4,3,2] => 6

[1,1,1,1,0,1,0,0,0,0,1,0] => [[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => [1,5,4,3,2,6] => [5,4,3,2,6,1] => 4

[1,1,1,1,0,1,0,0,0,1,0,0] => [[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,-1,1],[0,0,0,0,1,0]] => [1,4,3,2,6,5] => [4,3,2,6,5,1] => 4

[1,1,1,1,0,1,0,0,1,0,0,0] => [[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,-1,1],[0,1,0,-1,1,0],[0,0,0,1,0,0]] => [1,3,2,6,5,4] => [3,2,6,5,4,1] => 4

[1,1,1,1,0,1,0,1,0,0,0,0] => [[0,0,0,1,0,0],[0,0,1,-1,1,0],[0,1,-1,1,-1,1],[1,-1,1,-1,1,0],[0,1,-1,1,0,0],[0,0,1,0,0,0]] => [1,2,6,5,4,3] => [2,6,5,4,3,1] => 4

[1,1,1,1,0,1,1,0,0,0,0,0] => [[0,0,0,1,0,0],[0,0,1,-1,0,1],[0,1,-1,0,1,0],[1,-1,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0]] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => 4

[1,1,1,1,1,0,0,0,0,0,1,0] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => [5,4,3,2,1,6] => [4,3,2,1,6,5] => 4

[1,1,1,1,1,0,0,0,0,1,0,0] => [[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,-1,1],[0,0,0,0,1,0]] => [4,3,2,1,6,5] => [3,2,1,6,5,4] => 6

[1,1,1,1,1,0,0,0,1,0,0,0] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,1,0,0,-1,1],[1,0,0,-1,1,0],[0,0,0,1,0,0]] => [3,2,1,6,5,4] => [2,1,6,5,4,3] => 4

[1,1,1,1,1,0,0,1,0,0,0,0] => [[0,0,0,0,1,0],[0,0,0,1,0,0],[0,0,1,0,-1,1],[0,1,0,-1,1,0],[1,0,-1,1,0,0],[0,0,1,0,0,0]] => [2,1,6,5,4,3] => [1,6,5,4,3,2] => 6

[1,1,1,1,1,0,1,0,0,0,0,0] => [[0,0,0,0,1,0],[0,0,0,1,-1,1],[0,0,1,-1,1,0],[0,1,-1,1,0,0],[1,-1,1,0,0,0],[0,1,0,0,0,0]] => [1,6,5,4,3,2] => [6,5,4,3,2,1] => 4

[1,1,1,1,1,1,0,0,0,0,0,0] => [[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] => [5,4,3,2,1,6] => 6

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$F_{1} = 1$

$F_{2} = 1 + q^{2}$

$F_{3} = 1 + 4\ q^{2}$

$F_{4} = 1 + 10\ q^{2} + 3\ q^{4}$

$F_{5} = 1 + 20\ q^{2} + 21\ q^{4}$

$F_{6} = 1 + 35\ q^{2} + 84\ q^{4} + 12\ q^{6}$

Description

The number of indices that are not cyclical small weak excedances.
A cyclical small weak excedance is an index

$i < n$ such that

$\pi_i = i+1$ , or the index

$i = n$ if

$\pi_n = 1$ .

Map

Inverse Kreweras complement

Description

Sends the permutation

$\pi \in \mathfrak{S}_n$ to the permutation

$c\pi^{-1}$ where

$c = (1,\ldots,n)$ is the long cycle.

Map

to left key permutation

Description

Return the permutation of the left key of an alternating sign matrix.
This was originally defined by Lascoux and then further studied by Aval [1].

Map

to symmetric ASM

Description

The diagonally symmetric alternating sign matrix corresponding to a Dyck path.