- FindStat

Identifier

Mp00170: Permutations —to signed permutation⟶ Signed permutations
Mp00167: Signed permutations —inverse Kreweras complement⟶ Signed permutations
Mp00267: Signed permutations —signs⟶ Binary words

Images

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

[1,2] => [1,2] => [2,-1] => 01

[2,1] => [2,1] => [1,-2] => 01

[1,2,3] => [1,2,3] => [2,3,-1] => 001

[1,3,2] => [1,3,2] => [3,2,-1] => 001

[2,1,3] => [2,1,3] => [1,3,-2] => 001

[2,3,1] => [2,3,1] => [1,2,-3] => 001

[3,1,2] => [3,1,2] => [3,1,-2] => 001

[3,2,1] => [3,2,1] => [2,1,-3] => 001

[1,2,3,4] => [1,2,3,4] => [2,3,4,-1] => 0001

[1,2,4,3] => [1,2,4,3] => [2,4,3,-1] => 0001

[1,3,2,4] => [1,3,2,4] => [3,2,4,-1] => 0001

[1,3,4,2] => [1,3,4,2] => [4,2,3,-1] => 0001

[1,4,2,3] => [1,4,2,3] => [3,4,2,-1] => 0001

[1,4,3,2] => [1,4,3,2] => [4,3,2,-1] => 0001

[2,1,3,4] => [2,1,3,4] => [1,3,4,-2] => 0001

[2,1,4,3] => [2,1,4,3] => [1,4,3,-2] => 0001

[2,3,1,4] => [2,3,1,4] => [1,2,4,-3] => 0001

[2,3,4,1] => [2,3,4,1] => [1,2,3,-4] => 0001

[2,4,1,3] => [2,4,1,3] => [1,4,2,-3] => 0001

[2,4,3,1] => [2,4,3,1] => [1,3,2,-4] => 0001

[3,1,2,4] => [3,1,2,4] => [3,1,4,-2] => 0001

[3,1,4,2] => [3,1,4,2] => [4,1,3,-2] => 0001

[3,2,1,4] => [3,2,1,4] => [2,1,4,-3] => 0001

[3,2,4,1] => [3,2,4,1] => [2,1,3,-4] => 0001

[3,4,1,2] => [3,4,1,2] => [4,1,2,-3] => 0001

[3,4,2,1] => [3,4,2,1] => [3,1,2,-4] => 0001

[4,1,2,3] => [4,1,2,3] => [3,4,1,-2] => 0001

[4,1,3,2] => [4,1,3,2] => [4,3,1,-2] => 0001

[4,2,1,3] => [4,2,1,3] => [2,4,1,-3] => 0001

[4,2,3,1] => [4,2,3,1] => [2,3,1,-4] => 0001

[4,3,1,2] => [4,3,1,2] => [4,2,1,-3] => 0001

[4,3,2,1] => [4,3,2,1] => [3,2,1,-4] => 0001

[1,2,3,4,5] => [1,2,3,4,5] => [2,3,4,5,-1] => 00001

[1,2,3,5,4] => [1,2,3,5,4] => [2,3,5,4,-1] => 00001

[1,2,4,3,5] => [1,2,4,3,5] => [2,4,3,5,-1] => 00001

[1,2,4,5,3] => [1,2,4,5,3] => [2,5,3,4,-1] => 00001

[1,2,5,3,4] => [1,2,5,3,4] => [2,4,5,3,-1] => 00001

[1,2,5,4,3] => [1,2,5,4,3] => [2,5,4,3,-1] => 00001

[1,3,2,4,5] => [1,3,2,4,5] => [3,2,4,5,-1] => 00001

[1,3,2,5,4] => [1,3,2,5,4] => [3,2,5,4,-1] => 00001

[1,3,4,2,5] => [1,3,4,2,5] => [4,2,3,5,-1] => 00001

[1,3,4,5,2] => [1,3,4,5,2] => [5,2,3,4,-1] => 00001

[1,3,5,2,4] => [1,3,5,2,4] => [4,2,5,3,-1] => 00001

[1,3,5,4,2] => [1,3,5,4,2] => [5,2,4,3,-1] => 00001

[1,4,2,3,5] => [1,4,2,3,5] => [3,4,2,5,-1] => 00001

[1,4,2,5,3] => [1,4,2,5,3] => [3,5,2,4,-1] => 00001

[1,4,3,2,5] => [1,4,3,2,5] => [4,3,2,5,-1] => 00001

[1,4,3,5,2] => [1,4,3,5,2] => [5,3,2,4,-1] => 00001

[1,4,5,2,3] => [1,4,5,2,3] => [4,5,2,3,-1] => 00001

[1,4,5,3,2] => [1,4,5,3,2] => [5,4,2,3,-1] => 00001

[1,5,2,3,4] => [1,5,2,3,4] => [3,4,5,2,-1] => 00001

[1,5,2,4,3] => [1,5,2,4,3] => [3,5,4,2,-1] => 00001

[1,5,3,2,4] => [1,5,3,2,4] => [4,3,5,2,-1] => 00001

[1,5,3,4,2] => [1,5,3,4,2] => [5,3,4,2,-1] => 00001

[1,5,4,2,3] => [1,5,4,2,3] => [4,5,3,2,-1] => 00001

[1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,2,-1] => 00001

[2,1,3,4,5] => [2,1,3,4,5] => [1,3,4,5,-2] => 00001

[2,1,3,5,4] => [2,1,3,5,4] => [1,3,5,4,-2] => 00001

[2,1,4,3,5] => [2,1,4,3,5] => [1,4,3,5,-2] => 00001

[2,1,4,5,3] => [2,1,4,5,3] => [1,5,3,4,-2] => 00001

[2,1,5,3,4] => [2,1,5,3,4] => [1,4,5,3,-2] => 00001

[2,1,5,4,3] => [2,1,5,4,3] => [1,5,4,3,-2] => 00001

[2,3,1,4,5] => [2,3,1,4,5] => [1,2,4,5,-3] => 00001

[2,3,1,5,4] => [2,3,1,5,4] => [1,2,5,4,-3] => 00001

[2,3,4,1,5] => [2,3,4,1,5] => [1,2,3,5,-4] => 00001

[2,3,4,5,1] => [2,3,4,5,1] => [1,2,3,4,-5] => 00001

[2,3,5,1,4] => [2,3,5,1,4] => [1,2,5,3,-4] => 00001

[2,3,5,4,1] => [2,3,5,4,1] => [1,2,4,3,-5] => 00001

[2,4,1,3,5] => [2,4,1,3,5] => [1,4,2,5,-3] => 00001

[2,4,1,5,3] => [2,4,1,5,3] => [1,5,2,4,-3] => 00001

[2,4,3,1,5] => [2,4,3,1,5] => [1,3,2,5,-4] => 00001

[2,4,3,5,1] => [2,4,3,5,1] => [1,3,2,4,-5] => 00001

[2,4,5,1,3] => [2,4,5,1,3] => [1,5,2,3,-4] => 00001

[2,4,5,3,1] => [2,4,5,3,1] => [1,4,2,3,-5] => 00001

[2,5,1,3,4] => [2,5,1,3,4] => [1,4,5,2,-3] => 00001

[2,5,1,4,3] => [2,5,1,4,3] => [1,5,4,2,-3] => 00001

[2,5,3,1,4] => [2,5,3,1,4] => [1,3,5,2,-4] => 00001

[2,5,3,4,1] => [2,5,3,4,1] => [1,3,4,2,-5] => 00001

[2,5,4,1,3] => [2,5,4,1,3] => [1,5,3,2,-4] => 00001

[2,5,4,3,1] => [2,5,4,3,1] => [1,4,3,2,-5] => 00001

[3,1,2,4,5] => [3,1,2,4,5] => [3,1,4,5,-2] => 00001

[3,1,2,5,4] => [3,1,2,5,4] => [3,1,5,4,-2] => 00001

[3,1,4,2,5] => [3,1,4,2,5] => [4,1,3,5,-2] => 00001

[3,1,4,5,2] => [3,1,4,5,2] => [5,1,3,4,-2] => 00001

[3,1,5,2,4] => [3,1,5,2,4] => [4,1,5,3,-2] => 00001

[3,1,5,4,2] => [3,1,5,4,2] => [5,1,4,3,-2] => 00001

[3,2,1,4,5] => [3,2,1,4,5] => [2,1,4,5,-3] => 00001

[3,2,1,5,4] => [3,2,1,5,4] => [2,1,5,4,-3] => 00001

[3,2,4,1,5] => [3,2,4,1,5] => [2,1,3,5,-4] => 00001

[3,2,4,5,1] => [3,2,4,5,1] => [2,1,3,4,-5] => 00001

[3,2,5,1,4] => [3,2,5,1,4] => [2,1,5,3,-4] => 00001

[3,2,5,4,1] => [3,2,5,4,1] => [2,1,4,3,-5] => 00001

[3,4,1,2,5] => [3,4,1,2,5] => [4,1,2,5,-3] => 00001

[3,4,1,5,2] => [3,4,1,5,2] => [5,1,2,4,-3] => 00001

[3,4,2,1,5] => [3,4,2,1,5] => [3,1,2,5,-4] => 00001

[3,4,2,5,1] => [3,4,2,5,1] => [3,1,2,4,-5] => 00001

[3,4,5,1,2] => [3,4,5,1,2] => [5,1,2,3,-4] => 00001

[3,4,5,2,1] => [3,4,5,2,1] => [4,1,2,3,-5] => 00001

[3,5,1,2,4] => [3,5,1,2,4] => [4,1,5,2,-3] => 00001

[3,5,1,4,2] => [3,5,1,4,2] => [5,1,4,2,-3] => 00001

>>> Load all 247 entries. <<<

Map

to signed permutation

Description

The signed permutation with all signs positive.

Map

inverse Kreweras complement

Description

The inverse Kreweras complement of a signed permutation.
This is the signed permutation

$c \pi^{-1}$ where

$c = (1,\ldots,n,-1,-2,\dots,-n)$ is the long cycle.
The order of the inverse Kreweras complement on signed permutations of

$\{\pm 1,\dots, \pm n\}$ is

$2n$ .

Map

signs

Description

The binary word recording the signs of a signed permutation.
This map sends a signed permutation

$\pi\in\mathfrak H_n$ to the binary word

$w$ of length

$n$ such that

$w_i = 0$ if

$\pi(i) > 0$ .