- FindStat

Identifier

Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
St000110: 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] => 3

[[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] => 3

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

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

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

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

[[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] => 4

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

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

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

[[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] => 3

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

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

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

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

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

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

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

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

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

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

[[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] => 4

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

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

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

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

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

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

[[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] => 4

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

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

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

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

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

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

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Description

The number of permutations less than or equal to a permutation in left weak order.
This is the same as the number of permutations less than or equal to the given permutation in right weak 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).