- FindStat

Identifier

Mp00223: Permutations —runsort⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000514: Integer partitions ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 9547 entries. <<<

search for individual values

searching the database for the individual values of this statistic

Description

The number of invariant simple graphs when acting with a permutation of given cycle type.

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.

Map

first row removal

Description

Removes the first entry of an integer partition

Map

runsort

Description

The permutation obtained by sorting the increasing runs lexicographically.