- FindStat

Identifier

Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Mp00084: Standard tableaux —conjugate⟶ Standard tableaux

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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

conjugate

Description

Sends a standard tableau to its conjugate tableau.