- FindStat

Identifier

Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St000078: Permutations ⟶ ℤ

Values

[[1]] => [1] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => 8

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

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

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

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

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

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

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

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

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

[[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 8

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => 10

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

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Description

The number of alternating sign matrices whose left key is the permutation.
The left key of an alternating sign matrix was defined by Lascoux
in [2] and is obtained by successively removing all the `-1`'s until what remains is a permutation matrix. This notion corresponds to the notion of left key for semistandard tableaux.

Map

reading word permutation

Description

Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.