Identifier
Mp00170: Permutations —to signed permutation⟶ Signed permutations
Mp00267: Signed permutations —signs⟶ Binary words
Images
[1] => [1] => 0
[1,2] => [1,2] => 00
[2,1] => [2,1] => 00
[1,2,3] => [1,2,3] => 000
[1,3,2] => [1,3,2] => 000
[2,1,3] => [2,1,3] => 000
[2,3,1] => [2,3,1] => 000
[3,1,2] => [3,1,2] => 000
[3,2,1] => [3,2,1] => 000
[1,2,3,4] => [1,2,3,4] => 0000
[1,2,4,3] => [1,2,4,3] => 0000
[1,3,2,4] => [1,3,2,4] => 0000
[1,3,4,2] => [1,3,4,2] => 0000
[1,4,2,3] => [1,4,2,3] => 0000
[1,4,3,2] => [1,4,3,2] => 0000
[2,1,3,4] => [2,1,3,4] => 0000
[2,1,4,3] => [2,1,4,3] => 0000
[2,3,1,4] => [2,3,1,4] => 0000
[2,3,4,1] => [2,3,4,1] => 0000
[2,4,1,3] => [2,4,1,3] => 0000
[2,4,3,1] => [2,4,3,1] => 0000
[3,1,2,4] => [3,1,2,4] => 0000
[3,1,4,2] => [3,1,4,2] => 0000
[3,2,1,4] => [3,2,1,4] => 0000
[3,2,4,1] => [3,2,4,1] => 0000
[3,4,1,2] => [3,4,1,2] => 0000
[3,4,2,1] => [3,4,2,1] => 0000
[4,1,2,3] => [4,1,2,3] => 0000
[4,1,3,2] => [4,1,3,2] => 0000
[4,2,1,3] => [4,2,1,3] => 0000
[4,2,3,1] => [4,2,3,1] => 0000
[4,3,1,2] => [4,3,1,2] => 0000
[4,3,2,1] => [4,3,2,1] => 0000
[1,2,3,4,5] => [1,2,3,4,5] => 00000
[1,2,3,5,4] => [1,2,3,5,4] => 00000
[1,2,4,3,5] => [1,2,4,3,5] => 00000
[1,2,4,5,3] => [1,2,4,5,3] => 00000
[1,2,5,3,4] => [1,2,5,3,4] => 00000
[1,2,5,4,3] => [1,2,5,4,3] => 00000
[1,3,2,4,5] => [1,3,2,4,5] => 00000
[1,3,2,5,4] => [1,3,2,5,4] => 00000
[1,3,4,2,5] => [1,3,4,2,5] => 00000
[1,3,4,5,2] => [1,3,4,5,2] => 00000
[1,3,5,2,4] => [1,3,5,2,4] => 00000
[1,3,5,4,2] => [1,3,5,4,2] => 00000
[1,4,2,3,5] => [1,4,2,3,5] => 00000
[1,4,2,5,3] => [1,4,2,5,3] => 00000
[1,4,3,2,5] => [1,4,3,2,5] => 00000
[1,4,3,5,2] => [1,4,3,5,2] => 00000
[1,4,5,2,3] => [1,4,5,2,3] => 00000
[1,4,5,3,2] => [1,4,5,3,2] => 00000
[1,5,2,3,4] => [1,5,2,3,4] => 00000
[1,5,2,4,3] => [1,5,2,4,3] => 00000
[1,5,3,2,4] => [1,5,3,2,4] => 00000
[1,5,3,4,2] => [1,5,3,4,2] => 00000
[1,5,4,2,3] => [1,5,4,2,3] => 00000
[1,5,4,3,2] => [1,5,4,3,2] => 00000
[2,1,3,4,5] => [2,1,3,4,5] => 00000
[2,1,3,5,4] => [2,1,3,5,4] => 00000
[2,1,4,3,5] => [2,1,4,3,5] => 00000
[2,1,4,5,3] => [2,1,4,5,3] => 00000
[2,1,5,3,4] => [2,1,5,3,4] => 00000
[2,1,5,4,3] => [2,1,5,4,3] => 00000
[2,3,1,4,5] => [2,3,1,4,5] => 00000
[2,3,1,5,4] => [2,3,1,5,4] => 00000
[2,3,4,1,5] => [2,3,4,1,5] => 00000
[2,3,4,5,1] => [2,3,4,5,1] => 00000
[2,3,5,1,4] => [2,3,5,1,4] => 00000
[2,3,5,4,1] => [2,3,5,4,1] => 00000
[2,4,1,3,5] => [2,4,1,3,5] => 00000
[2,4,1,5,3] => [2,4,1,5,3] => 00000
[2,4,3,1,5] => [2,4,3,1,5] => 00000
[2,4,3,5,1] => [2,4,3,5,1] => 00000
[2,4,5,1,3] => [2,4,5,1,3] => 00000
[2,4,5,3,1] => [2,4,5,3,1] => 00000
[2,5,1,3,4] => [2,5,1,3,4] => 00000
[2,5,1,4,3] => [2,5,1,4,3] => 00000
[2,5,3,1,4] => [2,5,3,1,4] => 00000
[2,5,3,4,1] => [2,5,3,4,1] => 00000
[2,5,4,1,3] => [2,5,4,1,3] => 00000
[2,5,4,3,1] => [2,5,4,3,1] => 00000
[3,1,2,4,5] => [3,1,2,4,5] => 00000
[3,1,2,5,4] => [3,1,2,5,4] => 00000
[3,1,4,2,5] => [3,1,4,2,5] => 00000
[3,1,4,5,2] => [3,1,4,5,2] => 00000
[3,1,5,2,4] => [3,1,5,2,4] => 00000
[3,1,5,4,2] => [3,1,5,4,2] => 00000
[3,2,1,4,5] => [3,2,1,4,5] => 00000
[3,2,1,5,4] => [3,2,1,5,4] => 00000
[3,2,4,1,5] => [3,2,4,1,5] => 00000
[3,2,4,5,1] => [3,2,4,5,1] => 00000
[3,2,5,1,4] => [3,2,5,1,4] => 00000
[3,2,5,4,1] => [3,2,5,4,1] => 00000
[3,4,1,2,5] => [3,4,1,2,5] => 00000
[3,4,1,5,2] => [3,4,1,5,2] => 00000
[3,4,2,1,5] => [3,4,2,1,5] => 00000
[3,4,2,5,1] => [3,4,2,5,1] => 00000
[3,4,5,1,2] => [3,4,5,1,2] => 00000
[3,4,5,2,1] => [3,4,5,2,1] => 00000
[3,5,1,2,4] => [3,5,1,2,4] => 00000
[3,5,1,4,2] => [3,5,1,4,2] => 00000
>>> Load all 258 entries. <<<
[3,5,2,1,4] => [3,5,2,1,4] => 00000
[3,5,2,4,1] => [3,5,2,4,1] => 00000
[3,5,4,1,2] => [3,5,4,1,2] => 00000
[3,5,4,2,1] => [3,5,4,2,1] => 00000
[4,1,2,3,5] => [4,1,2,3,5] => 00000
[4,1,2,5,3] => [4,1,2,5,3] => 00000
[4,1,3,2,5] => [4,1,3,2,5] => 00000
[4,1,3,5,2] => [4,1,3,5,2] => 00000
[4,1,5,2,3] => [4,1,5,2,3] => 00000
[4,1,5,3,2] => [4,1,5,3,2] => 00000
[4,2,1,3,5] => [4,2,1,3,5] => 00000
[4,2,1,5,3] => [4,2,1,5,3] => 00000
[4,2,3,1,5] => [4,2,3,1,5] => 00000
[4,2,3,5,1] => [4,2,3,5,1] => 00000
[4,2,5,1,3] => [4,2,5,1,3] => 00000
[4,2,5,3,1] => [4,2,5,3,1] => 00000
[4,3,1,2,5] => [4,3,1,2,5] => 00000
[4,3,1,5,2] => [4,3,1,5,2] => 00000
[4,3,2,1,5] => [4,3,2,1,5] => 00000
[4,3,2,5,1] => [4,3,2,5,1] => 00000
[4,3,5,1,2] => [4,3,5,1,2] => 00000
[4,3,5,2,1] => [4,3,5,2,1] => 00000
[4,5,1,2,3] => [4,5,1,2,3] => 00000
[4,5,1,3,2] => [4,5,1,3,2] => 00000
[4,5,2,1,3] => [4,5,2,1,3] => 00000
[4,5,2,3,1] => [4,5,2,3,1] => 00000
[4,5,3,1,2] => [4,5,3,1,2] => 00000
[4,5,3,2,1] => [4,5,3,2,1] => 00000
[5,1,2,3,4] => [5,1,2,3,4] => 00000
[5,1,2,4,3] => [5,1,2,4,3] => 00000
[5,1,3,2,4] => [5,1,3,2,4] => 00000
[5,1,3,4,2] => [5,1,3,4,2] => 00000
[5,1,4,2,3] => [5,1,4,2,3] => 00000
[5,1,4,3,2] => [5,1,4,3,2] => 00000
[5,2,1,3,4] => [5,2,1,3,4] => 00000
[5,2,1,4,3] => [5,2,1,4,3] => 00000
[5,2,3,1,4] => [5,2,3,1,4] => 00000
[5,2,3,4,1] => [5,2,3,4,1] => 00000
[5,2,4,1,3] => [5,2,4,1,3] => 00000
[5,2,4,3,1] => [5,2,4,3,1] => 00000
[5,3,1,2,4] => [5,3,1,2,4] => 00000
[5,3,1,4,2] => [5,3,1,4,2] => 00000
[5,3,2,1,4] => [5,3,2,1,4] => 00000
[5,3,2,4,1] => [5,3,2,4,1] => 00000
[5,3,4,1,2] => [5,3,4,1,2] => 00000
[5,3,4,2,1] => [5,3,4,2,1] => 00000
[5,4,1,2,3] => [5,4,1,2,3] => 00000
[5,4,1,3,2] => [5,4,1,3,2] => 00000
[5,4,2,1,3] => [5,4,2,1,3] => 00000
[5,4,2,3,1] => [5,4,2,3,1] => 00000
[5,4,3,1,2] => [5,4,3,1,2] => 00000
[5,4,3,2,1] => [5,4,3,2,1] => 00000
[1,2,3,4,5,6] => [1,2,3,4,5,6] => 000000
[1,2,3,6,4,5] => [1,2,3,6,4,5] => 000000
[1,2,5,3,4,6] => [1,2,5,3,4,6] => 000000
[1,2,5,6,3,4] => [1,2,5,6,3,4] => 000000
[1,4,2,3,5,6] => [1,4,2,3,5,6] => 000000
[1,4,2,6,3,5] => [1,4,2,6,3,5] => 000000
[1,4,5,2,3,6] => [1,4,5,2,3,6] => 000000
[1,4,5,6,2,3] => [1,4,5,6,2,3] => 000000
[1,5,2,3,4,6] => [1,5,2,3,4,6] => 000000
[1,5,6,2,3,4] => [1,5,6,2,3,4] => 000000
[1,6,2,3,4,5] => [1,6,2,3,4,5] => 000000
[1,6,2,5,3,4] => [1,6,2,5,3,4] => 000000
[1,6,4,2,3,5] => [1,6,4,2,3,5] => 000000
[1,6,4,5,2,3] => [1,6,4,5,2,3] => 000000
[3,1,2,4,5,6] => [3,1,2,4,5,6] => 000000
[3,1,2,6,4,5] => [3,1,2,6,4,5] => 000000
[3,1,5,2,4,6] => [3,1,5,2,4,6] => 000000
[3,1,5,6,2,4] => [3,1,5,6,2,4] => 000000
[3,4,1,2,5,6] => [3,4,1,2,5,6] => 000000
[3,4,1,6,2,5] => [3,4,1,6,2,5] => 000000
[3,4,5,1,2,6] => [3,4,5,1,2,6] => 000000
[3,4,5,6,1,2] => [3,4,5,6,1,2] => 000000
[3,4,6,1,2,5] => [3,4,6,1,2,5] => 000000
[3,5,1,2,4,6] => [3,5,1,2,4,6] => 000000
[3,5,6,1,2,4] => [3,5,6,1,2,4] => 000000
[3,6,1,2,4,5] => [3,6,1,2,4,5] => 000000
[3,6,1,5,2,4] => [3,6,1,5,2,4] => 000000
[3,6,4,1,2,5] => [3,6,4,1,2,5] => 000000
[3,6,4,5,1,2] => [3,6,4,5,1,2] => 000000
[4,1,2,3,5,6] => [4,1,2,3,5,6] => 000000
[4,5,1,2,3,6] => [4,5,1,2,3,6] => 000000
[4,5,6,1,2,3] => [4,5,6,1,2,3] => 000000
[4,6,1,2,3,5] => [4,6,1,2,3,5] => 000000
[4,6,5,1,2,3] => [4,6,5,1,2,3] => 000000
[5,1,2,3,4,6] => [5,1,2,3,4,6] => 000000
[5,1,2,6,3,4] => [5,1,2,6,3,4] => 000000
[5,1,4,2,3,6] => [5,1,4,2,3,6] => 000000
[5,1,4,6,2,3] => [5,1,4,6,2,3] => 000000
[5,1,6,2,3,4] => [5,1,6,2,3,4] => 000000
[5,3,1,2,4,6] => [5,3,1,2,4,6] => 000000
[5,3,1,6,2,4] => [5,3,1,6,2,4] => 000000
[5,3,4,1,2,6] => [5,3,4,1,2,6] => 000000
[5,3,4,6,1,2] => [5,3,4,6,1,2] => 000000
[5,6,1,2,3,4] => [5,6,1,2,3,4] => 000000
[5,6,1,4,2,3] => [5,6,1,4,2,3] => 000000
[5,6,3,1,2,4] => [5,6,3,1,2,4] => 000000
[5,6,3,4,1,2] => [5,6,3,4,1,2] => 000000
[6,1,2,3,4,5] => [6,1,2,3,4,5] => 000000
[6,2,1,5,3,4] => [6,2,1,5,3,4] => 000000
[6,2,4,1,3,5] => [6,2,4,1,3,5] => 000000
[6,3,1,2,4,5] => [6,3,1,2,4,5] => 000000
[1,2,3,4,7,5,6] => [1,2,3,4,7,5,6] => 0000000
[1,2,5,3,7,4,6] => [1,2,5,3,7,4,6] => 0000000
[1,2,7,3,4,5,6] => [1,2,7,3,4,5,6] => 0000000
[1,2,7,3,6,4,5] => [1,2,7,3,6,4,5] => 0000000
[1,4,7,2,3,5,6] => [1,4,7,2,3,5,6] => 0000000
[1,5,7,2,3,4,6] => [1,5,7,2,3,4,6] => 0000000
[1,6,7,2,3,4,5] => [1,6,7,2,3,4,5] => 0000000
[1,6,7,2,5,3,4] => [1,6,7,2,5,3,4] => 0000000
[1,6,7,4,2,3,5] => [1,6,7,4,2,3,5] => 0000000
[3,1,7,2,4,5,6] => [3,1,7,2,4,5,6] => 0000000
[3,1,7,5,2,4,6] => [3,1,7,5,2,4,6] => 0000000
[3,4,7,1,2,5,6] => [3,4,7,1,2,5,6] => 0000000
[3,4,7,1,6,2,5] => [3,4,7,1,6,2,5] => 0000000
[3,4,7,5,1,2,6] => [3,4,7,5,1,2,6] => 0000000
[3,4,7,5,6,1,2] => [3,4,7,5,6,1,2] => 0000000
[3,5,7,1,2,4,6] => [3,5,7,1,2,4,6] => 0000000
[3,6,1,2,7,4,5] => [3,6,1,2,7,4,5] => 0000000
[3,7,4,1,2,5,6] => [3,7,4,1,2,5,6] => 0000000
[3,7,4,5,1,2,6] => [3,7,4,5,1,2,6] => 0000000
[3,7,4,5,6,1,2] => [3,7,4,5,6,1,2] => 0000000
[3,7,4,6,1,2,5] => [3,7,4,6,1,2,5] => 0000000
[3,7,5,1,2,4,6] => [3,7,5,1,2,4,6] => 0000000
[3,7,5,6,1,2,4] => [3,7,5,6,1,2,4] => 0000000
[3,7,6,1,2,4,5] => [3,7,6,1,2,4,5] => 0000000
[4,7,5,6,1,2,3] => [4,7,5,6,1,2,3] => 0000000
[5,3,4,7,1,2,6] => [5,3,4,7,1,2,6] => 0000000
[5,3,7,1,2,4,6] => [5,3,7,1,2,4,6] => 0000000
[5,4,7,1,2,3,6] => [5,4,7,1,2,3,6] => 0000000
[7,1,2,5,3,4,6] => [7,1,2,5,3,4,6] => 0000000
[7,1,3,2,4,5,6] => [7,1,3,2,4,5,6] => 0000000
[7,1,4,2,3,5,6] => [7,1,4,2,3,5,6] => 0000000
[7,1,4,2,6,3,5] => [7,1,4,2,6,3,5] => 0000000
[7,1,4,5,2,3,6] => [7,1,4,5,2,3,6] => 0000000
[7,1,4,6,2,3,5] => [7,1,4,6,2,3,5] => 0000000
[7,1,5,2,3,4,6] => [7,1,5,2,3,4,6] => 0000000
[7,1,5,6,2,3,4] => [7,1,5,6,2,3,4] => 0000000
[7,1,6,2,3,4,5] => [7,1,6,2,3,4,5] => 0000000
[7,1,6,4,5,2,3] => [7,1,6,4,5,2,3] => 0000000
[7,2,4,1,3,5,6] => [7,2,4,1,3,5,6] => 0000000
[7,2,5,1,3,4,6] => [7,2,5,1,3,4,6] => 0000000
[7,2,6,1,3,4,5] => [7,2,6,1,3,4,5] => 0000000
[7,3,1,2,4,5,6] => [7,3,1,2,4,5,6] => 0000000
[7,3,5,1,2,4,6] => [7,3,5,1,2,4,6] => 0000000
[7,3,5,6,1,2,4] => [7,3,5,6,1,2,4] => 0000000
[7,3,6,1,2,4,5] => [7,3,6,1,2,4,5] => 0000000
[7,5,1,4,2,3,6] => [7,5,1,4,2,3,6] => 0000000
[7,8,5,6,3,4,1,2] => [7,8,5,6,3,4,1,2] => 00000000
[5,6,7,8,3,4,1,2] => [5,6,7,8,3,4,1,2] => 00000000
[5,6,7,8,4,1,2,3] => [5,6,7,8,4,1,2,3] => 00000000
[5,6,7,8,3,1,2,4] => [5,6,7,8,3,1,2,4] => 00000000
[3,4,7,8,1,2,5,6] => [3,4,7,8,1,2,5,6] => 00000000
[5,6,7,1,8,2,3,4] => [5,6,7,1,8,2,3,4] => 00000000
[1,2,5,6,7,8,3,4] => [1,2,5,6,7,8,3,4] => 00000000
[5,6,7,8,1,4,2,3] => [5,6,7,8,1,4,2,3] => 00000000
Map
to signed permutation
Description
The signed permutation with all signs positive.
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 $\pi(i) > 0$.