- FindStat

Identifier

Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 2466 entries. <<<

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).

Map

Robinson-Schensted insertion tableau

Description

Sends a permutation to its Robinson-Schensted insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.

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.