- FindStat

Identifier

Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
St001908: Integer partitions ⟶ ℤ

Values

[1] => [1] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,2,5,4,3] => [3,1,1] => 6

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

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

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

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

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

[1,3,5,4,2] => [3,1,1] => 6

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

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

[1,4,3,2,5] => [3,1,1] => 6

[1,4,3,5,2] => [3,1,1] => 6

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

[1,4,5,3,2] => [3,1,1] => 6

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

[1,5,2,4,3] => [3,1,1] => 6

[1,5,3,2,4] => [3,1,1] => 6

[1,5,3,4,2] => [3,1,1] => 6

[1,5,4,2,3] => [3,1,1] => 6

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

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

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

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

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

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

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

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

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

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

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

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

[2,3,5,4,1] => [3,1,1] => 6

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

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

[2,4,3,1,5] => [3,1,1] => 6

[2,4,3,5,1] => [3,1,1] => 6

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

[2,4,5,3,1] => [3,1,1] => 6

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

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

[2,5,3,1,4] => [3,1,1] => 6

[2,5,3,4,1] => [3,1,1] => 6

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

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

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

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

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

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

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

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

[3,2,1,4,5] => [3,1,1] => 6

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

[3,2,4,1,5] => [3,1,1] => 6

[3,2,4,5,1] => [3,1,1] => 6

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

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

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

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

[3,4,2,1,5] => [3,1,1] => 6

[3,4,2,5,1] => [3,1,1] => 6

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

[3,4,5,2,1] => [3,1,1] => 6

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

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

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Description

The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition.
For example, there are eight tableaux of shape $[3,2,1]$ with maximal entry $3$, but two of them have the same weight.

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.