- FindStat

Identifier

Mp00161: Signed permutations —reverse⟶ Signed permutations
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 4359 entries. <<<

Map

reverse

Description

The reversal of a signed permutation.

Map

permutation

Description

The permutation obtained by forgetting the colours.

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.