- FindStat

Identifier

Mp00161: Signed permutations —reverse⟶ Signed permutations
Mp00267: Signed permutations —signs⟶ Binary words

Images

[1] => [1] => 0

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

[1,2] => [2,1] => 00

[1,-2] => [-2,1] => 10

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

[-1,-2] => [-2,-1] => 11

[2,1] => [1,2] => 00

[2,-1] => [-1,2] => 10

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

[-2,-1] => [-1,-2] => 11

[1,2,3] => [3,2,1] => 000

[1,2,-3] => [-3,2,1] => 100

[1,-2,3] => [3,-2,1] => 010

[1,-2,-3] => [-3,-2,1] => 110

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

[-1,2,-3] => [-3,2,-1] => 101

[-1,-2,3] => [3,-2,-1] => 011

[-1,-2,-3] => [-3,-2,-1] => 111

[1,3,2] => [2,3,1] => 000

[1,3,-2] => [-2,3,1] => 100

[1,-3,2] => [2,-3,1] => 010

[1,-3,-2] => [-2,-3,1] => 110

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

[-1,3,-2] => [-2,3,-1] => 101

[-1,-3,2] => [2,-3,-1] => 011

[-1,-3,-2] => [-2,-3,-1] => 111

[2,1,3] => [3,1,2] => 000

[2,1,-3] => [-3,1,2] => 100

[2,-1,3] => [3,-1,2] => 010

[2,-1,-3] => [-3,-1,2] => 110

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

[-2,1,-3] => [-3,1,-2] => 101

[-2,-1,3] => [3,-1,-2] => 011

[-2,-1,-3] => [-3,-1,-2] => 111

[2,3,1] => [1,3,2] => 000

[2,3,-1] => [-1,3,2] => 100

[2,-3,1] => [1,-3,2] => 010

[2,-3,-1] => [-1,-3,2] => 110

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

[-2,3,-1] => [-1,3,-2] => 101

[-2,-3,1] => [1,-3,-2] => 011

[-2,-3,-1] => [-1,-3,-2] => 111

[3,1,2] => [2,1,3] => 000

[3,1,-2] => [-2,1,3] => 100

[3,-1,2] => [2,-1,3] => 010

[3,-1,-2] => [-2,-1,3] => 110

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

[-3,1,-2] => [-2,1,-3] => 101

[-3,-1,2] => [2,-1,-3] => 011

[-3,-1,-2] => [-2,-1,-3] => 111

[3,2,1] => [1,2,3] => 000

[3,2,-1] => [-1,2,3] => 100

[3,-2,1] => [1,-2,3] => 010

[3,-2,-1] => [-1,-2,3] => 110

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

[-3,2,-1] => [-1,2,-3] => 101

[-3,-2,1] => [1,-2,-3] => 011

[-3,-2,-1] => [-1,-2,-3] => 111

[1,2,3,4] => [4,3,2,1] => 0000

[1,2,3,-4] => [-4,3,2,1] => 1000

[1,2,-3,4] => [4,-3,2,1] => 0100

[1,2,-3,-4] => [-4,-3,2,1] => 1100

[1,-2,3,4] => [4,3,-2,1] => 0010

[1,-2,3,-4] => [-4,3,-2,1] => 1010

[1,-2,-3,4] => [4,-3,-2,1] => 0110

[1,-2,-3,-4] => [-4,-3,-2,1] => 1110

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

[-1,2,3,-4] => [-4,3,2,-1] => 1001

[-1,2,-3,4] => [4,-3,2,-1] => 0101

[-1,2,-3,-4] => [-4,-3,2,-1] => 1101

[-1,-2,3,4] => [4,3,-2,-1] => 0011

[-1,-2,3,-4] => [-4,3,-2,-1] => 1011

[-1,-2,-3,4] => [4,-3,-2,-1] => 0111

[-1,-2,-3,-4] => [-4,-3,-2,-1] => 1111

[1,2,4,3] => [3,4,2,1] => 0000

[1,2,4,-3] => [-3,4,2,1] => 1000

[1,2,-4,3] => [3,-4,2,1] => 0100

[1,2,-4,-3] => [-3,-4,2,1] => 1100

[1,-2,4,3] => [3,4,-2,1] => 0010

[1,-2,4,-3] => [-3,4,-2,1] => 1010

[1,-2,-4,3] => [3,-4,-2,1] => 0110

[1,-2,-4,-3] => [-3,-4,-2,1] => 1110

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

[-1,2,4,-3] => [-3,4,2,-1] => 1001

[-1,2,-4,3] => [3,-4,2,-1] => 0101

[-1,2,-4,-3] => [-3,-4,2,-1] => 1101

[-1,-2,4,3] => [3,4,-2,-1] => 0011

[-1,-2,4,-3] => [-3,4,-2,-1] => 1011

[-1,-2,-4,3] => [3,-4,-2,-1] => 0111

[-1,-2,-4,-3] => [-3,-4,-2,-1] => 1111

[1,3,2,4] => [4,2,3,1] => 0000

[1,3,2,-4] => [-4,2,3,1] => 1000

[1,3,-2,4] => [4,-2,3,1] => 0100

[1,3,-2,-4] => [-4,-2,3,1] => 1100

[1,-3,2,4] => [4,2,-3,1] => 0010

[1,-3,2,-4] => [-4,2,-3,1] => 1010

[1,-3,-2,4] => [4,-2,-3,1] => 0110

[1,-3,-2,-4] => [-4,-2,-3,1] => 1110

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

[-1,3,2,-4] => [-4,2,3,-1] => 1001

[-1,3,-2,4] => [4,-2,3,-1] => 0101

>>> Load all 4452 entries. <<<

Map

reverse

Description

The reversal of a signed permutation.

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 $\pi(i) > 0$.