- FindStat

Identifier

Mp00302: Parking functions —insertion tableau⟶ Semistandard tableaux
Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 5291 entries. <<<

Map

insertion tableau

Description

The insertion tableau obtained by applying RSK to the parking function regarded as a word.

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 recording tableau

Description

Sends a permutation to its Robinson-Schensted recording 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 recording tableau.