- FindStat

Identifier

Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
St000109: Permutations ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,1],[2,2]] => [3,4,1,2] => 14

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,1],[2,3]] => [3,4,1,2] => 14

[[1,1],[3,3]] => [3,4,1,2] => 14

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

[[1,2],[3,3]] => [3,4,1,2] => 14

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Description

The number of elements less than or equal to the given element in Bruhat order.

Map

reading word permutation

Description

Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottommost row (in English notation).