Identifier
-
Mp00080:
Set partitions
—to permutation⟶
Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00063: Permutations —to alternating sign matrix⟶ Alternating sign matrices
St000894: Alternating sign matrices ⟶ ℤ
Values
{{1,2}} => [2,1] => [1,2] => [[1,0],[0,1]] => 2
{{1},{2}} => [1,2] => [2,1] => [[0,1],[1,0]] => 0
{{1,2,3}} => [2,3,1] => [1,2,3] => [[1,0,0],[0,1,0],[0,0,1]] => 3
{{1,2},{3}} => [2,1,3] => [1,3,2] => [[1,0,0],[0,0,1],[0,1,0]] => 1
{{1,3},{2}} => [3,2,1] => [2,1,3] => [[0,1,0],[1,0,0],[0,0,1]] => 1
{{1},{2,3}} => [1,3,2] => [3,2,1] => [[0,0,1],[0,1,0],[1,0,0]] => 1
{{1},{2},{3}} => [1,2,3] => [2,3,1] => [[0,0,1],[1,0,0],[0,1,0]] => 0
{{1,2,3,4}} => [2,3,4,1] => [1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]] => 4
{{1,2,3},{4}} => [2,3,1,4] => [1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]] => 2
{{1,2,4},{3}} => [2,4,3,1] => [1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]] => 2
{{1,2},{3,4}} => [2,1,4,3] => [1,4,3,2] => [[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]] => 2
{{1,2},{3},{4}} => [2,1,3,4] => [1,3,4,2] => [[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]] => 1
{{1,3,4},{2}} => [3,2,4,1] => [2,1,3,4] => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]] => 2
{{1,3},{2,4}} => [3,4,1,2] => [4,1,2,3] => [[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]] => 0
{{1,3},{2},{4}} => [3,2,1,4] => [2,1,4,3] => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]] => 0
{{1,4},{2,3}} => [4,3,2,1] => [3,2,1,4] => [[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]] => 2
{{1},{2,3,4}} => [1,3,4,2] => [4,2,3,1] => [[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]] => 2
{{1},{2,3},{4}} => [1,3,2,4] => [3,2,4,1] => [[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]] => 1
{{1,4},{2},{3}} => [4,2,3,1] => [2,3,1,4] => [[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]] => 1
{{1},{2,4},{3}} => [1,4,3,2] => [4,3,2,1] => [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]] => 0
{{1},{2},{3,4}} => [1,2,4,3] => [2,4,3,1] => [[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]] => 1
{{1},{2},{3},{4}} => [1,2,3,4] => [2,3,4,1] => [[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]] => 0
{{1,2,3,4,5}} => [2,3,4,5,1] => [1,2,3,4,5] => [[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]] => 5
{{1,2,3,4},{5}} => [2,3,4,1,5] => [1,2,3,5,4] => [[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]] => 3
{{1,2,3,5},{4}} => [2,3,5,4,1] => [1,2,4,3,5] => [[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]] => 3
{{1,2,3},{4,5}} => [2,3,1,5,4] => [1,2,5,4,3] => [[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]] => 3
{{1,2,3},{4},{5}} => [2,3,1,4,5] => [1,2,4,5,3] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]] => 2
{{1,2,4,5},{3}} => [2,4,3,5,1] => [1,3,2,4,5] => [[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]] => 3
{{1,2,4},{3,5}} => [2,4,5,1,3] => [1,5,2,3,4] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0]] => 1
{{1,2,4},{3},{5}} => [2,4,3,1,5] => [1,3,2,5,4] => [[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
{{1,2,5},{3,4}} => [2,5,4,3,1] => [1,4,3,2,5] => [[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]] => 3
{{1,2},{3,4,5}} => [2,1,4,5,3] => [1,5,3,4,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0]] => 3
{{1,2},{3,4},{5}} => [2,1,4,3,5] => [1,4,3,5,2] => [[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]] => 2
{{1,2,5},{3},{4}} => [2,5,3,4,1] => [1,3,4,2,5] => [[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]] => 2
{{1,2},{3,5},{4}} => [2,1,5,4,3] => [1,5,4,3,2] => [[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
{{1,2},{3},{4,5}} => [2,1,3,5,4] => [1,3,5,4,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]] => 2
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => [1,3,4,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => 1
{{1,3,4,5},{2}} => [3,2,4,5,1] => [2,1,3,4,5] => [[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]] => 3
{{1,3,4},{2,5}} => [3,5,4,1,2] => [5,1,3,2,4] => [[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0]] => 1
{{1,3,4},{2},{5}} => [3,2,4,1,5] => [2,1,3,5,4] => [[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]] => 1
{{1,3,5},{2,4}} => [3,4,5,2,1] => [4,1,2,3,5] => [[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1]] => 1
{{1,3},{2,4,5}} => [3,4,1,5,2] => [5,1,2,4,3] => [[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0],[1,0,0,0,0]] => 1
{{1,3},{2,4},{5}} => [3,4,1,2,5] => [4,1,2,5,3] => [[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0]] => 0
{{1,3,5},{2},{4}} => [3,2,5,4,1] => [2,1,4,3,5] => [[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]] => 1
{{1,3},{2,5},{4}} => [3,5,1,4,2] => [5,1,4,2,3] => [[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[1,0,0,0,0]] => 0
{{1,3},{2},{4,5}} => [3,2,1,5,4] => [2,1,5,4,3] => [[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]] => 1
{{1,3},{2},{4},{5}} => [3,2,1,4,5] => [2,1,4,5,3] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]] => 0
{{1,4,5},{2,3}} => [4,3,2,5,1] => [3,2,1,4,5] => [[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
{{1,4},{2,3,5}} => [4,3,5,1,2] => [5,2,1,3,4] => [[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,0,0,0]] => 1
{{1,4},{2,3},{5}} => [4,3,2,1,5] => [3,2,1,5,4] => [[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]] => 1
{{1,5},{2,3,4}} => [5,3,4,2,1] => [4,2,3,1,5] => [[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]] => 3
{{1},{2,3,4,5}} => [1,3,4,5,2] => [5,2,3,4,1] => [[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0]] => 3
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [4,2,3,5,1] => [[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]] => 2
{{1,5},{2,3},{4}} => [5,3,2,4,1] => [3,2,4,1,5] => [[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]] => 2
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [5,2,4,3,1] => [[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[1,0,0,0,0]] => 1
{{1},{2,3},{4,5}} => [1,3,2,5,4] => [3,2,5,4,1] => [[0,0,0,0,1],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0]] => 2
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [3,2,4,5,1] => [[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]] => 1
{{1,4,5},{2},{3}} => [4,2,3,5,1] => [2,3,1,4,5] => [[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]] => 2
{{1,4},{2,5},{3}} => [4,5,3,1,2] => [5,3,1,2,4] => [[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[1,0,0,0,0]] => 0
{{1,4},{2},{3,5}} => [4,2,5,1,3] => [2,5,1,3,4] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0]] => 0
{{1,4},{2},{3},{5}} => [4,2,3,1,5] => [2,3,1,5,4] => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]] => 0
{{1,5},{2,4},{3}} => [5,4,3,2,1] => [4,3,2,1,5] => [[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]] => 1
{{1},{2,4,5},{3}} => [1,4,3,5,2] => [5,3,2,4,1] => [[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[1,0,0,0,0]] => 1
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [4,5,2,3,1] => [[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0]] => 0
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [4,3,2,5,1] => [[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0]] => 0
{{1,5},{2},{3,4}} => [5,2,4,3,1] => [2,4,3,1,5] => [[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]] => 2
{{1},{2,5},{3,4}} => [1,5,4,3,2] => [5,4,3,2,1] => [[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]] => 1
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [2,5,3,4,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0]] => 2
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [2,4,3,5,1] => [[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]] => 1
{{1,5},{2},{3},{4}} => [5,2,3,4,1] => [2,3,4,1,5] => [[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]] => 1
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [5,3,4,2,1] => [[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0]] => 0
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [2,5,4,3,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]] => 0
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [2,3,5,4,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]] => 1
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [2,3,4,5,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]] => 0
{{1,2,3,4,5,6}} => [2,3,4,5,6,1] => [1,2,3,4,5,6] => [[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]] => 6
{{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => [1,2,3,4,6,5] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 4
{{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => [1,2,3,5,4,6] => [[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]] => 4
{{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => [1,2,4,3,5,6] => [[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]] => 4
{{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => [1,2,4,3,6,5] => [[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]] => 2
{{1,2,3,6},{4,5}} => [2,3,6,5,4,1] => [1,2,5,4,3,6] => [[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]] => 4
{{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => [1,2,4,5,3,6] => [[1,0,0,0,0,0],[0,1,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 3
{{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => [1,3,2,4,5,6] => [[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]] => 4
{{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => [1,3,2,4,6,5] => [[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]] => 2
{{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => [1,5,2,3,4,6] => [[1,0,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => 2
{{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => [1,3,2,5,4,6] => [[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]] => 2
{{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => [1,4,3,2,5,6] => [[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]] => 4
{{1,2,5},{3,4},{6}} => [2,5,4,3,1,6] => [1,4,3,2,6,5] => [[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]] => 2
{{1,2,6},{3,4,5}} => [2,6,4,5,3,1] => [1,5,3,4,2,6] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,0,0,0,1]] => 4
{{1,2,6},{3,4},{5}} => [2,6,4,3,5,1] => [1,4,3,5,2,6] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,1,0,0,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 3
{{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => [1,3,4,2,5,6] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 3
{{1,2,5},{3},{4},{6}} => [2,5,3,4,1,6] => [1,3,4,2,6,5] => [[1,0,0,0,0,0],[0,0,0,1,0,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 1
{{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => [1,5,4,3,2,6] => [[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]] => 2
{{1,2,6},{3},{4,5}} => [2,6,3,5,4,1] => [1,3,5,4,2,6] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,0,1]] => 3
{{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => [1,3,4,5,2,6] => [[1,0,0,0,0,0],[0,0,0,0,1,0],[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[0,0,0,0,0,1]] => 2
{{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => [2,1,3,4,5,6] => [[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]] => 4
{{1,3,4,5},{2},{6}} => [3,2,4,5,1,6] => [2,1,3,4,6,5] => [[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},{2,5}} => [3,5,4,6,2,1] => [5,1,3,2,4,6] => [[0,1,0,0,0,0],[0,0,0,1,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 2
{{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => [2,1,3,5,4,6] => [[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
{{1,3,5,6},{2,4}} => [3,4,5,2,6,1] => [4,1,2,3,5,6] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1]] => 2
{{1,3,5},{2,4},{6}} => [3,4,5,2,1,6] => [4,1,2,3,6,5] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1],[0,0,0,0,1,0]] => 0
{{1,3,6},{2,4,5}} => [3,4,6,5,2,1] => [5,1,2,4,3,6] => [[0,1,0,0,0,0],[0,0,1,0,0,0],[0,0,0,0,1,0],[0,0,0,1,0,0],[1,0,0,0,0,0],[0,0,0,0,0,1]] => 2
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Description
The trace of an alternating sign matrix.
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 alternating sign matrix
Description
Maps a permutation to its permutation matrix as an alternating sign matrix.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
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