- FindStat

Identifier

Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000275: Integer partitions ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

Number of permutations whose sorted list of non zero multiplicities of the Lehmer code is the given partition.

Map

first row removal

Description

Removes the first entry of an integer partition

Map

Robinson-Schensted tableau shape

Description

Sends a permutation to its Robinson-Schensted tableau shape.
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 the shape of its corresponding insertion and recording tableau.