- FindStat

Identifier

Mp00223: Permutations —runsort⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 12305 entries. <<<

Map

runsort

Description

The permutation obtained by sorting the increasing runs lexicographically.

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.

Map

horizontal strip sizes

Description

The composition of horizontal strip sizes.
We associate to a standard Young tableau

$T$ the composition

$(c_1,\dots,c_k)$ , such that

$k$ is minimal and the numbers

$c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in

$T$ for all

$i$ .