Identifier
Mp00170: Permutations —to signed permutation⟶ Signed permutations
Mp00168: Signed permutations —Kreweras complement⟶ Signed permutations
Mp00162: Signed permutations —inverse⟶ Signed permutations
Mp00267: Signed permutations —signs⟶ Binary words
Images
[1] => [1] => [-1] => [-1] => 1
[1,2] => [1,2] => [2,-1] => [-2,1] => 10
[2,1] => [2,1] => [-1,2] => [-1,2] => 10
[1,2,3] => [1,2,3] => [2,3,-1] => [-3,1,2] => 100
[1,3,2] => [1,3,2] => [2,-1,3] => [-2,1,3] => 100
[2,1,3] => [2,1,3] => [3,2,-1] => [-3,2,1] => 100
[2,3,1] => [2,3,1] => [-1,2,3] => [-1,2,3] => 100
[3,1,2] => [3,1,2] => [3,-1,2] => [-2,3,1] => 100
[3,2,1] => [3,2,1] => [-1,3,2] => [-1,3,2] => 100
[1,2,3,4] => [1,2,3,4] => [2,3,4,-1] => [-4,1,2,3] => 1000
[1,2,4,3] => [1,2,4,3] => [2,3,-1,4] => [-3,1,2,4] => 1000
[1,3,2,4] => [1,3,2,4] => [2,4,3,-1] => [-4,1,3,2] => 1000
[1,3,4,2] => [1,3,4,2] => [2,-1,3,4] => [-2,1,3,4] => 1000
[1,4,2,3] => [1,4,2,3] => [2,4,-1,3] => [-3,1,4,2] => 1000
[1,4,3,2] => [1,4,3,2] => [2,-1,4,3] => [-2,1,4,3] => 1000
[2,1,3,4] => [2,1,3,4] => [3,2,4,-1] => [-4,2,1,3] => 1000
[2,1,4,3] => [2,1,4,3] => [3,2,-1,4] => [-3,2,1,4] => 1000
[2,3,1,4] => [2,3,1,4] => [4,2,3,-1] => [-4,2,3,1] => 1000
[2,3,4,1] => [2,3,4,1] => [-1,2,3,4] => [-1,2,3,4] => 1000
[2,4,1,3] => [2,4,1,3] => [4,2,-1,3] => [-3,2,4,1] => 1000
[2,4,3,1] => [2,4,3,1] => [-1,2,4,3] => [-1,2,4,3] => 1000
[3,1,2,4] => [3,1,2,4] => [3,4,2,-1] => [-4,3,1,2] => 1000
[3,1,4,2] => [3,1,4,2] => [3,-1,2,4] => [-2,3,1,4] => 1000
[3,2,1,4] => [3,2,1,4] => [4,3,2,-1] => [-4,3,2,1] => 1000
[3,2,4,1] => [3,2,4,1] => [-1,3,2,4] => [-1,3,2,4] => 1000
[3,4,1,2] => [3,4,1,2] => [4,-1,2,3] => [-2,3,4,1] => 1000
[3,4,2,1] => [3,4,2,1] => [-1,4,2,3] => [-1,3,4,2] => 1000
[4,1,2,3] => [4,1,2,3] => [3,4,-1,2] => [-3,4,1,2] => 1000
[4,1,3,2] => [4,1,3,2] => [3,-1,4,2] => [-2,4,1,3] => 1000
[4,2,1,3] => [4,2,1,3] => [4,3,-1,2] => [-3,4,2,1] => 1000
[4,2,3,1] => [4,2,3,1] => [-1,3,4,2] => [-1,4,2,3] => 1000
[4,3,1,2] => [4,3,1,2] => [4,-1,3,2] => [-2,4,3,1] => 1000
[4,3,2,1] => [4,3,2,1] => [-1,4,3,2] => [-1,4,3,2] => 1000
[1,2,3,4,5] => [1,2,3,4,5] => [2,3,4,5,-1] => [-5,1,2,3,4] => 10000
[1,2,3,5,4] => [1,2,3,5,4] => [2,3,4,-1,5] => [-4,1,2,3,5] => 10000
[1,2,4,3,5] => [1,2,4,3,5] => [2,3,5,4,-1] => [-5,1,2,4,3] => 10000
[1,2,4,5,3] => [1,2,4,5,3] => [2,3,-1,4,5] => [-3,1,2,4,5] => 10000
[1,2,5,3,4] => [1,2,5,3,4] => [2,3,5,-1,4] => [-4,1,2,5,3] => 10000
[1,2,5,4,3] => [1,2,5,4,3] => [2,3,-1,5,4] => [-3,1,2,5,4] => 10000
[1,3,2,4,5] => [1,3,2,4,5] => [2,4,3,5,-1] => [-5,1,3,2,4] => 10000
[1,3,2,5,4] => [1,3,2,5,4] => [2,4,3,-1,5] => [-4,1,3,2,5] => 10000
[1,3,4,2,5] => [1,3,4,2,5] => [2,5,3,4,-1] => [-5,1,3,4,2] => 10000
[1,3,4,5,2] => [1,3,4,5,2] => [2,-1,3,4,5] => [-2,1,3,4,5] => 10000
[1,3,5,2,4] => [1,3,5,2,4] => [2,5,3,-1,4] => [-4,1,3,5,2] => 10000
[1,3,5,4,2] => [1,3,5,4,2] => [2,-1,3,5,4] => [-2,1,3,5,4] => 10000
[1,4,2,3,5] => [1,4,2,3,5] => [2,4,5,3,-1] => [-5,1,4,2,3] => 10000
[1,4,2,5,3] => [1,4,2,5,3] => [2,4,-1,3,5] => [-3,1,4,2,5] => 10000
[1,4,3,2,5] => [1,4,3,2,5] => [2,5,4,3,-1] => [-5,1,4,3,2] => 10000
[1,4,3,5,2] => [1,4,3,5,2] => [2,-1,4,3,5] => [-2,1,4,3,5] => 10000
[1,4,5,2,3] => [1,4,5,2,3] => [2,5,-1,3,4] => [-3,1,4,5,2] => 10000
[1,4,5,3,2] => [1,4,5,3,2] => [2,-1,5,3,4] => [-2,1,4,5,3] => 10000
[1,5,2,3,4] => [1,5,2,3,4] => [2,4,5,-1,3] => [-4,1,5,2,3] => 10000
[1,5,2,4,3] => [1,5,2,4,3] => [2,4,-1,5,3] => [-3,1,5,2,4] => 10000
[1,5,3,2,4] => [1,5,3,2,4] => [2,5,4,-1,3] => [-4,1,5,3,2] => 10000
[1,5,3,4,2] => [1,5,3,4,2] => [2,-1,4,5,3] => [-2,1,5,3,4] => 10000
[1,5,4,2,3] => [1,5,4,2,3] => [2,5,-1,4,3] => [-3,1,5,4,2] => 10000
[1,5,4,3,2] => [1,5,4,3,2] => [2,-1,5,4,3] => [-2,1,5,4,3] => 10000
[2,1,3,4,5] => [2,1,3,4,5] => [3,2,4,5,-1] => [-5,2,1,3,4] => 10000
[2,1,3,5,4] => [2,1,3,5,4] => [3,2,4,-1,5] => [-4,2,1,3,5] => 10000
[2,1,4,3,5] => [2,1,4,3,5] => [3,2,5,4,-1] => [-5,2,1,4,3] => 10000
[2,1,4,5,3] => [2,1,4,5,3] => [3,2,-1,4,5] => [-3,2,1,4,5] => 10000
[2,1,5,3,4] => [2,1,5,3,4] => [3,2,5,-1,4] => [-4,2,1,5,3] => 10000
[2,1,5,4,3] => [2,1,5,4,3] => [3,2,-1,5,4] => [-3,2,1,5,4] => 10000
[2,3,1,4,5] => [2,3,1,4,5] => [4,2,3,5,-1] => [-5,2,3,1,4] => 10000
[2,3,1,5,4] => [2,3,1,5,4] => [4,2,3,-1,5] => [-4,2,3,1,5] => 10000
[2,3,4,1,5] => [2,3,4,1,5] => [5,2,3,4,-1] => [-5,2,3,4,1] => 10000
[2,3,4,5,1] => [2,3,4,5,1] => [-1,2,3,4,5] => [-1,2,3,4,5] => 10000
[2,3,5,1,4] => [2,3,5,1,4] => [5,2,3,-1,4] => [-4,2,3,5,1] => 10000
[2,3,5,4,1] => [2,3,5,4,1] => [-1,2,3,5,4] => [-1,2,3,5,4] => 10000
[2,4,1,3,5] => [2,4,1,3,5] => [4,2,5,3,-1] => [-5,2,4,1,3] => 10000
[2,4,1,5,3] => [2,4,1,5,3] => [4,2,-1,3,5] => [-3,2,4,1,5] => 10000
[2,4,3,1,5] => [2,4,3,1,5] => [5,2,4,3,-1] => [-5,2,4,3,1] => 10000
[2,4,3,5,1] => [2,4,3,5,1] => [-1,2,4,3,5] => [-1,2,4,3,5] => 10000
[2,4,5,1,3] => [2,4,5,1,3] => [5,2,-1,3,4] => [-3,2,4,5,1] => 10000
[2,4,5,3,1] => [2,4,5,3,1] => [-1,2,5,3,4] => [-1,2,4,5,3] => 10000
[2,5,1,3,4] => [2,5,1,3,4] => [4,2,5,-1,3] => [-4,2,5,1,3] => 10000
[2,5,1,4,3] => [2,5,1,4,3] => [4,2,-1,5,3] => [-3,2,5,1,4] => 10000
[2,5,3,1,4] => [2,5,3,1,4] => [5,2,4,-1,3] => [-4,2,5,3,1] => 10000
[2,5,3,4,1] => [2,5,3,4,1] => [-1,2,4,5,3] => [-1,2,5,3,4] => 10000
[2,5,4,1,3] => [2,5,4,1,3] => [5,2,-1,4,3] => [-3,2,5,4,1] => 10000
[2,5,4,3,1] => [2,5,4,3,1] => [-1,2,5,4,3] => [-1,2,5,4,3] => 10000
[3,1,2,4,5] => [3,1,2,4,5] => [3,4,2,5,-1] => [-5,3,1,2,4] => 10000
[3,1,2,5,4] => [3,1,2,5,4] => [3,4,2,-1,5] => [-4,3,1,2,5] => 10000
[3,1,4,2,5] => [3,1,4,2,5] => [3,5,2,4,-1] => [-5,3,1,4,2] => 10000
[3,1,4,5,2] => [3,1,4,5,2] => [3,-1,2,4,5] => [-2,3,1,4,5] => 10000
[3,1,5,2,4] => [3,1,5,2,4] => [3,5,2,-1,4] => [-4,3,1,5,2] => 10000
[3,1,5,4,2] => [3,1,5,4,2] => [3,-1,2,5,4] => [-2,3,1,5,4] => 10000
[3,2,1,4,5] => [3,2,1,4,5] => [4,3,2,5,-1] => [-5,3,2,1,4] => 10000
[3,2,1,5,4] => [3,2,1,5,4] => [4,3,2,-1,5] => [-4,3,2,1,5] => 10000
[3,2,4,1,5] => [3,2,4,1,5] => [5,3,2,4,-1] => [-5,3,2,4,1] => 10000
[3,2,4,5,1] => [3,2,4,5,1] => [-1,3,2,4,5] => [-1,3,2,4,5] => 10000
[3,2,5,1,4] => [3,2,5,1,4] => [5,3,2,-1,4] => [-4,3,2,5,1] => 10000
[3,2,5,4,1] => [3,2,5,4,1] => [-1,3,2,5,4] => [-1,3,2,5,4] => 10000
[3,4,1,2,5] => [3,4,1,2,5] => [4,5,2,3,-1] => [-5,3,4,1,2] => 10000
[3,4,1,5,2] => [3,4,1,5,2] => [4,-1,2,3,5] => [-2,3,4,1,5] => 10000
[3,4,2,1,5] => [3,4,2,1,5] => [5,4,2,3,-1] => [-5,3,4,2,1] => 10000
[3,4,2,5,1] => [3,4,2,5,1] => [-1,4,2,3,5] => [-1,3,4,2,5] => 10000
[3,4,5,1,2] => [3,4,5,1,2] => [5,-1,2,3,4] => [-2,3,4,5,1] => 10000
[3,4,5,2,1] => [3,4,5,2,1] => [-1,5,2,3,4] => [-1,3,4,5,2] => 10000
[3,5,1,2,4] => [3,5,1,2,4] => [4,5,2,-1,3] => [-4,3,5,1,2] => 10000
[3,5,1,4,2] => [3,5,1,4,2] => [4,-1,2,5,3] => [-2,3,5,1,4] => 10000
>>> Load all 279 entries. <<<
[3,5,2,1,4] => [3,5,2,1,4] => [5,4,2,-1,3] => [-4,3,5,2,1] => 10000
[3,5,2,4,1] => [3,5,2,4,1] => [-1,4,2,5,3] => [-1,3,5,2,4] => 10000
[3,5,4,1,2] => [3,5,4,1,2] => [5,-1,2,4,3] => [-2,3,5,4,1] => 10000
[3,5,4,2,1] => [3,5,4,2,1] => [-1,5,2,4,3] => [-1,3,5,4,2] => 10000
[4,1,2,3,5] => [4,1,2,3,5] => [3,4,5,2,-1] => [-5,4,1,2,3] => 10000
[4,1,2,5,3] => [4,1,2,5,3] => [3,4,-1,2,5] => [-3,4,1,2,5] => 10000
[4,1,3,2,5] => [4,1,3,2,5] => [3,5,4,2,-1] => [-5,4,1,3,2] => 10000
[4,1,3,5,2] => [4,1,3,5,2] => [3,-1,4,2,5] => [-2,4,1,3,5] => 10000
[4,1,5,2,3] => [4,1,5,2,3] => [3,5,-1,2,4] => [-3,4,1,5,2] => 10000
[4,1,5,3,2] => [4,1,5,3,2] => [3,-1,5,2,4] => [-2,4,1,5,3] => 10000
[4,2,1,3,5] => [4,2,1,3,5] => [4,3,5,2,-1] => [-5,4,2,1,3] => 10000
[4,2,1,5,3] => [4,2,1,5,3] => [4,3,-1,2,5] => [-3,4,2,1,5] => 10000
[4,2,3,1,5] => [4,2,3,1,5] => [5,3,4,2,-1] => [-5,4,2,3,1] => 10000
[4,2,3,5,1] => [4,2,3,5,1] => [-1,3,4,2,5] => [-1,4,2,3,5] => 10000
[4,2,5,1,3] => [4,2,5,1,3] => [5,3,-1,2,4] => [-3,4,2,5,1] => 10000
[4,2,5,3,1] => [4,2,5,3,1] => [-1,3,5,2,4] => [-1,4,2,5,3] => 10000
[4,3,1,2,5] => [4,3,1,2,5] => [4,5,3,2,-1] => [-5,4,3,1,2] => 10000
[4,3,1,5,2] => [4,3,1,5,2] => [4,-1,3,2,5] => [-2,4,3,1,5] => 10000
[4,3,2,1,5] => [4,3,2,1,5] => [5,4,3,2,-1] => [-5,4,3,2,1] => 10000
[4,3,2,5,1] => [4,3,2,5,1] => [-1,4,3,2,5] => [-1,4,3,2,5] => 10000
[4,3,5,1,2] => [4,3,5,1,2] => [5,-1,3,2,4] => [-2,4,3,5,1] => 10000
[4,3,5,2,1] => [4,3,5,2,1] => [-1,5,3,2,4] => [-1,4,3,5,2] => 10000
[4,5,1,2,3] => [4,5,1,2,3] => [4,5,-1,2,3] => [-3,4,5,1,2] => 10000
[4,5,1,3,2] => [4,5,1,3,2] => [4,-1,5,2,3] => [-2,4,5,1,3] => 10000
[4,5,2,1,3] => [4,5,2,1,3] => [5,4,-1,2,3] => [-3,4,5,2,1] => 10000
[4,5,2,3,1] => [4,5,2,3,1] => [-1,4,5,2,3] => [-1,4,5,2,3] => 10000
[4,5,3,1,2] => [4,5,3,1,2] => [5,-1,4,2,3] => [-2,4,5,3,1] => 10000
[4,5,3,2,1] => [4,5,3,2,1] => [-1,5,4,2,3] => [-1,4,5,3,2] => 10000
[5,1,2,3,4] => [5,1,2,3,4] => [3,4,5,-1,2] => [-4,5,1,2,3] => 10000
[5,1,2,4,3] => [5,1,2,4,3] => [3,4,-1,5,2] => [-3,5,1,2,4] => 10000
[5,1,3,2,4] => [5,1,3,2,4] => [3,5,4,-1,2] => [-4,5,1,3,2] => 10000
[5,1,3,4,2] => [5,1,3,4,2] => [3,-1,4,5,2] => [-2,5,1,3,4] => 10000
[5,1,4,2,3] => [5,1,4,2,3] => [3,5,-1,4,2] => [-3,5,1,4,2] => 10000
[5,1,4,3,2] => [5,1,4,3,2] => [3,-1,5,4,2] => [-2,5,1,4,3] => 10000
[5,2,1,3,4] => [5,2,1,3,4] => [4,3,5,-1,2] => [-4,5,2,1,3] => 10000
[5,2,1,4,3] => [5,2,1,4,3] => [4,3,-1,5,2] => [-3,5,2,1,4] => 10000
[5,2,3,1,4] => [5,2,3,1,4] => [5,3,4,-1,2] => [-4,5,2,3,1] => 10000
[5,2,3,4,1] => [5,2,3,4,1] => [-1,3,4,5,2] => [-1,5,2,3,4] => 10000
[5,2,4,1,3] => [5,2,4,1,3] => [5,3,-1,4,2] => [-3,5,2,4,1] => 10000
[5,2,4,3,1] => [5,2,4,3,1] => [-1,3,5,4,2] => [-1,5,2,4,3] => 10000
[5,3,1,2,4] => [5,3,1,2,4] => [4,5,3,-1,2] => [-4,5,3,1,2] => 10000
[5,3,1,4,2] => [5,3,1,4,2] => [4,-1,3,5,2] => [-2,5,3,1,4] => 10000
[5,3,2,1,4] => [5,3,2,1,4] => [5,4,3,-1,2] => [-4,5,3,2,1] => 10000
[5,3,2,4,1] => [5,3,2,4,1] => [-1,4,3,5,2] => [-1,5,3,2,4] => 10000
[5,3,4,1,2] => [5,3,4,1,2] => [5,-1,3,4,2] => [-2,5,3,4,1] => 10000
[5,3,4,2,1] => [5,3,4,2,1] => [-1,5,3,4,2] => [-1,5,3,4,2] => 10000
[5,4,1,2,3] => [5,4,1,2,3] => [4,5,-1,3,2] => [-3,5,4,1,2] => 10000
[5,4,1,3,2] => [5,4,1,3,2] => [4,-1,5,3,2] => [-2,5,4,1,3] => 10000
[5,4,2,1,3] => [5,4,2,1,3] => [5,4,-1,3,2] => [-3,5,4,2,1] => 10000
[5,4,2,3,1] => [5,4,2,3,1] => [-1,4,5,3,2] => [-1,5,4,2,3] => 10000
[5,4,3,1,2] => [5,4,3,1,2] => [5,-1,4,3,2] => [-2,5,4,3,1] => 10000
[5,4,3,2,1] => [5,4,3,2,1] => [-1,5,4,3,2] => [-1,5,4,3,2] => 10000
[1,2,3,4,5,6] => [1,2,3,4,5,6] => [2,3,4,5,6,-1] => [-6,1,2,3,4,5] => 100000
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [2,3,4,5,-1,6] => [-5,1,2,3,4,6] => 100000
[1,2,3,5,6,4] => [1,2,3,5,6,4] => [2,3,4,-1,5,6] => [-4,1,2,3,5,6] => 100000
[1,2,4,5,6,3] => [1,2,4,5,6,3] => [2,3,-1,4,5,6] => [-3,1,2,4,5,6] => 100000
[1,2,5,3,4,6] => [1,2,5,3,4,6] => [2,3,5,6,4,-1] => [-6,1,2,5,3,4] => 100000
[1,2,6,3,5,4] => [1,2,6,3,5,4] => [2,3,5,-1,6,4] => [-4,1,2,6,3,5] => 100000
[1,3,4,5,6,2] => [1,3,4,5,6,2] => [2,-1,3,4,5,6] => [-2,1,3,4,5,6] => 100000
[1,3,6,4,5,2] => [1,3,6,4,5,2] => [2,-1,3,5,6,4] => [-2,1,3,6,4,5] => 100000
[1,4,2,3,5,6] => [1,4,2,3,5,6] => [2,4,5,3,6,-1] => [-6,1,4,2,3,5] => 100000
[1,4,5,2,3,6] => [1,4,5,2,3,6] => [2,5,6,3,4,-1] => [-6,1,4,5,2,3] => 100000
[1,5,2,3,4,6] => [1,5,2,3,4,6] => [2,4,5,6,3,-1] => [-6,1,5,2,3,4] => 100000
[1,5,2,3,6,4] => [1,5,2,3,6,4] => [2,4,5,-1,3,6] => [-4,1,5,2,3,6] => 100000
[1,5,3,4,6,2] => [1,5,3,4,6,2] => [2,-1,4,5,3,6] => [-2,1,5,3,4,6] => 100000
[1,5,6,2,3,4] => [1,5,6,2,3,4] => [2,5,6,-1,3,4] => [-4,1,5,6,2,3] => 100000
[1,5,6,3,4,2] => [1,5,6,3,4,2] => [2,-1,5,6,3,4] => [-2,1,5,6,3,4] => 100000
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [3,2,4,5,6,-1] => [-6,2,1,3,4,5] => 100000
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [3,2,4,5,-1,6] => [-5,2,1,3,4,6] => 100000
[2,3,1,4,5,6] => [2,3,1,4,5,6] => [4,2,3,5,6,-1] => [-6,2,3,1,4,5] => 100000
[2,3,4,5,6,1] => [2,3,4,5,6,1] => [-1,2,3,4,5,6] => [-1,2,3,4,5,6] => 100000
[2,3,4,6,5,1] => [2,3,4,6,5,1] => [-1,2,3,4,6,5] => [-1,2,3,4,6,5] => 100000
[2,3,5,4,6,1] => [2,3,5,4,6,1] => [-1,2,3,5,4,6] => [-1,2,3,5,4,6] => 100000
[2,3,5,6,4,1] => [2,3,5,6,4,1] => [-1,2,3,6,4,5] => [-1,2,3,5,6,4] => 100000
[2,3,6,4,5,1] => [2,3,6,4,5,1] => [-1,2,3,5,6,4] => [-1,2,3,6,4,5] => 100000
[2,3,6,5,4,1] => [2,3,6,5,4,1] => [-1,2,3,6,5,4] => [-1,2,3,6,5,4] => 100000
[2,4,1,3,6,5] => [2,4,1,3,6,5] => [4,2,5,3,-1,6] => [-5,2,4,1,3,6] => 100000
[2,4,3,5,6,1] => [2,4,3,5,6,1] => [-1,2,4,3,5,6] => [-1,2,4,3,5,6] => 100000
[2,4,3,6,5,1] => [2,4,3,6,5,1] => [-1,2,4,3,6,5] => [-1,2,4,3,6,5] => 100000
[2,4,5,3,6,1] => [2,4,5,3,6,1] => [-1,2,5,3,4,6] => [-1,2,4,5,3,6] => 100000
[2,4,5,6,3,1] => [2,4,5,6,3,1] => [-1,2,6,3,4,5] => [-1,2,4,5,6,3] => 100000
[2,4,6,5,3,1] => [2,4,6,5,3,1] => [-1,2,6,3,5,4] => [-1,2,4,6,5,3] => 100000
[2,5,3,4,6,1] => [2,5,3,4,6,1] => [-1,2,4,5,3,6] => [-1,2,5,3,4,6] => 100000
[2,5,4,3,6,1] => [2,5,4,3,6,1] => [-1,2,5,4,3,6] => [-1,2,5,4,3,6] => 100000
[2,5,4,6,3,1] => [2,5,4,6,3,1] => [-1,2,6,4,3,5] => [-1,2,5,4,6,3] => 100000
[2,6,3,4,5,1] => [2,6,3,4,5,1] => [-1,2,4,5,6,3] => [-1,2,6,3,4,5] => 100000
[2,6,3,5,4,1] => [2,6,3,5,4,1] => [-1,2,4,6,5,3] => [-1,2,6,3,5,4] => 100000
[2,6,4,3,5,1] => [2,6,4,3,5,1] => [-1,2,5,4,6,3] => [-1,2,6,4,3,5] => 100000
[2,6,4,5,3,1] => [2,6,4,5,3,1] => [-1,2,6,4,5,3] => [-1,2,6,4,5,3] => 100000
[2,6,5,3,4,1] => [2,6,5,3,4,1] => [-1,2,5,6,4,3] => [-1,2,6,5,3,4] => 100000
[2,6,5,4,3,1] => [2,6,5,4,3,1] => [-1,2,6,5,4,3] => [-1,2,6,5,4,3] => 100000
[3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,4,2,5,6,-1] => [-6,3,1,2,4,5] => 100000
[3,1,2,4,6,5] => [3,1,2,4,6,5] => [3,4,2,5,-1,6] => [-5,3,1,2,4,6] => 100000
[3,1,2,5,6,4] => [3,1,2,5,6,4] => [3,4,2,-1,5,6] => [-4,3,1,2,5,6] => 100000
[3,2,4,5,6,1] => [3,2,4,5,6,1] => [-1,3,2,4,5,6] => [-1,3,2,4,5,6] => 100000
[3,2,4,6,5,1] => [3,2,4,6,5,1] => [-1,3,2,4,6,5] => [-1,3,2,4,6,5] => 100000
[3,2,5,4,6,1] => [3,2,5,4,6,1] => [-1,3,2,5,4,6] => [-1,3,2,5,4,6] => 100000
[3,2,5,6,4,1] => [3,2,5,6,4,1] => [-1,3,2,6,4,5] => [-1,3,2,5,6,4] => 100000
[3,2,6,4,5,1] => [3,2,6,4,5,1] => [-1,3,2,5,6,4] => [-1,3,2,6,4,5] => 100000
[3,2,6,5,4,1] => [3,2,6,5,4,1] => [-1,3,2,6,5,4] => [-1,3,2,6,5,4] => 100000
[3,4,1,2,5,6] => [3,4,1,2,5,6] => [4,5,2,3,6,-1] => [-6,3,4,1,2,5] => 100000
[3,4,2,5,6,1] => [3,4,2,5,6,1] => [-1,4,2,3,5,6] => [-1,3,4,2,5,6] => 100000
[3,4,2,6,5,1] => [3,4,2,6,5,1] => [-1,4,2,3,6,5] => [-1,3,4,2,6,5] => 100000
[3,4,5,2,6,1] => [3,4,5,2,6,1] => [-1,5,2,3,4,6] => [-1,3,4,5,2,6] => 100000
[3,4,5,6,2,1] => [3,4,5,6,2,1] => [-1,6,2,3,4,5] => [-1,3,4,5,6,2] => 100000
[3,4,6,5,2,1] => [3,4,6,5,2,1] => [-1,6,2,3,5,4] => [-1,3,4,6,5,2] => 100000
[3,5,1,2,4,6] => [3,5,1,2,4,6] => [4,5,2,6,3,-1] => [-6,3,5,1,2,4] => 100000
[3,5,1,2,6,4] => [3,5,1,2,6,4] => [4,5,2,-1,3,6] => [-4,3,5,1,2,6] => 100000
[3,5,4,2,6,1] => [3,5,4,2,6,1] => [-1,5,2,4,3,6] => [-1,3,5,4,2,6] => 100000
[3,5,4,6,2,1] => [3,5,4,6,2,1] => [-1,6,2,4,3,5] => [-1,3,5,4,6,2] => 100000
[3,5,6,1,2,4] => [3,5,6,1,2,4] => [5,6,2,-1,3,4] => [-4,3,5,6,1,2] => 100000
[3,6,1,2,4,5] => [3,6,1,2,4,5] => [4,5,2,6,-1,3] => [-5,3,6,1,2,4] => 100000
[3,6,4,5,2,1] => [3,6,4,5,2,1] => [-1,6,2,4,5,3] => [-1,3,6,4,5,2] => 100000
[3,6,5,4,2,1] => [3,6,5,4,2,1] => [-1,6,2,5,4,3] => [-1,3,6,5,4,2] => 100000
[4,1,2,3,5,6] => [4,1,2,3,5,6] => [3,4,5,2,6,-1] => [-6,4,1,2,3,5] => 100000
[4,2,3,5,6,1] => [4,2,3,5,6,1] => [-1,3,4,2,5,6] => [-1,4,2,3,5,6] => 100000
[4,2,3,6,5,1] => [4,2,3,6,5,1] => [-1,3,4,2,6,5] => [-1,4,2,3,6,5] => 100000
[4,3,2,5,6,1] => [4,3,2,5,6,1] => [-1,4,3,2,5,6] => [-1,4,3,2,5,6] => 100000
[4,3,2,6,5,1] => [4,3,2,6,5,1] => [-1,4,3,2,6,5] => [-1,4,3,2,6,5] => 100000
[4,3,5,2,6,1] => [4,3,5,2,6,1] => [-1,5,3,2,4,6] => [-1,4,3,5,2,6] => 100000
[4,3,5,6,2,1] => [4,3,5,6,2,1] => [-1,6,3,2,4,5] => [-1,4,3,5,6,2] => 100000
[4,3,6,5,2,1] => [4,3,6,5,2,1] => [-1,6,3,2,5,4] => [-1,4,3,6,5,2] => 100000
[4,5,2,3,6,1] => [4,5,2,3,6,1] => [-1,4,5,2,3,6] => [-1,4,5,2,3,6] => 100000
[4,5,3,2,6,1] => [4,5,3,2,6,1] => [-1,5,4,2,3,6] => [-1,4,5,3,2,6] => 100000
[4,5,3,6,2,1] => [4,5,3,6,2,1] => [-1,6,4,2,3,5] => [-1,4,5,3,6,2] => 100000
[4,5,6,1,3,2] => [4,5,6,1,3,2] => [5,-1,6,2,3,4] => [-2,4,5,6,1,3] => 100000
[4,5,6,2,3,1] => [4,5,6,2,3,1] => [-1,5,6,2,3,4] => [-1,4,5,6,2,3] => 100000
[4,5,6,3,2,1] => [4,5,6,3,2,1] => [-1,6,5,2,3,4] => [-1,4,5,6,3,2] => 100000
[5,1,2,3,6,4] => [5,1,2,3,6,4] => [3,4,5,-1,2,6] => [-4,5,1,2,3,6] => 100000
[5,1,4,2,3,6] => [5,1,4,2,3,6] => [3,5,6,4,2,-1] => [-6,5,1,4,2,3] => 100000
[5,2,3,4,6,1] => [5,2,3,4,6,1] => [-1,3,4,5,2,6] => [-1,5,2,3,4,6] => 100000
[5,2,4,3,6,1] => [5,2,4,3,6,1] => [-1,3,5,4,2,6] => [-1,5,2,4,3,6] => 100000
[5,3,1,2,4,6] => [5,3,1,2,4,6] => [4,5,3,6,2,-1] => [-6,5,3,1,2,4] => 100000
[5,3,2,4,6,1] => [5,3,2,4,6,1] => [-1,4,3,5,2,6] => [-1,5,3,2,4,6] => 100000
[5,3,4,1,2,6] => [5,3,4,1,2,6] => [5,6,3,4,2,-1] => [-6,5,3,4,1,2] => 100000
[5,3,4,2,6,1] => [5,3,4,2,6,1] => [-1,5,3,4,2,6] => [-1,5,3,4,2,6] => 100000
[5,3,4,6,2,1] => [5,3,4,6,2,1] => [-1,6,3,4,2,5] => [-1,5,3,4,6,2] => 100000
[5,4,2,3,6,1] => [5,4,2,3,6,1] => [-1,4,5,3,2,6] => [-1,5,4,2,3,6] => 100000
[5,4,3,2,6,1] => [5,4,3,2,6,1] => [-1,5,4,3,2,6] => [-1,5,4,3,2,6] => 100000
[5,4,3,6,2,1] => [5,4,3,6,2,1] => [-1,6,4,3,2,5] => [-1,5,4,3,6,2] => 100000
[5,4,6,2,3,1] => [5,4,6,2,3,1] => [-1,5,6,3,2,4] => [-1,5,4,6,2,3] => 100000
[5,4,6,3,2,1] => [5,4,6,3,2,1] => [-1,6,5,3,2,4] => [-1,5,4,6,3,2] => 100000
[5,6,1,2,3,4] => [5,6,1,2,3,4] => [4,5,6,-1,2,3] => [-4,5,6,1,2,3] => 100000
[5,6,2,3,4,1] => [5,6,2,3,4,1] => [-1,4,5,6,2,3] => [-1,5,6,2,3,4] => 100000
[5,6,3,2,4,1] => [5,6,3,2,4,1] => [-1,5,4,6,2,3] => [-1,5,6,3,2,4] => 100000
[5,6,3,4,2,1] => [5,6,3,4,2,1] => [-1,6,4,5,2,3] => [-1,5,6,3,4,2] => 100000
[5,6,4,2,3,1] => [5,6,4,2,3,1] => [-1,5,6,4,2,3] => [-1,5,6,4,2,3] => 100000
[5,6,4,3,2,1] => [5,6,4,3,2,1] => [-1,6,5,4,2,3] => [-1,5,6,4,3,2] => 100000
[6,1,2,3,4,5] => [6,1,2,3,4,5] => [3,4,5,6,-1,2] => [-5,6,1,2,3,4] => 100000
[6,1,2,3,5,4] => [6,1,2,3,5,4] => [3,4,5,-1,6,2] => [-4,6,1,2,3,5] => 100000
[6,1,3,4,5,2] => [6,1,3,4,5,2] => [3,-1,4,5,6,2] => [-2,6,1,3,4,5] => 100000
[6,2,1,3,4,5] => [6,2,1,3,4,5] => [4,3,5,6,-1,2] => [-5,6,2,1,3,4] => 100000
[6,2,3,4,5,1] => [6,2,3,4,5,1] => [-1,3,4,5,6,2] => [-1,6,2,3,4,5] => 100000
[6,2,3,5,4,1] => [6,2,3,5,4,1] => [-1,3,4,6,5,2] => [-1,6,2,3,5,4] => 100000
[6,2,4,3,5,1] => [6,2,4,3,5,1] => [-1,3,5,4,6,2] => [-1,6,2,4,3,5] => 100000
[6,2,5,3,4,1] => [6,2,5,3,4,1] => [-1,3,5,6,4,2] => [-1,6,2,5,3,4] => 100000
[6,2,5,4,3,1] => [6,2,5,4,3,1] => [-1,3,6,5,4,2] => [-1,6,2,5,4,3] => 100000
[6,3,2,4,5,1] => [6,3,2,4,5,1] => [-1,4,3,5,6,2] => [-1,6,3,2,4,5] => 100000
[6,3,2,5,4,1] => [6,3,2,5,4,1] => [-1,4,3,6,5,2] => [-1,6,3,2,5,4] => 100000
[6,3,4,2,5,1] => [6,3,4,2,5,1] => [-1,5,3,4,6,2] => [-1,6,3,4,2,5] => 100000
[6,3,4,5,2,1] => [6,3,4,5,2,1] => [-1,6,3,4,5,2] => [-1,6,3,4,5,2] => 100000
[6,3,5,1,2,4] => [6,3,5,1,2,4] => [5,6,3,-1,4,2] => [-4,6,3,5,1,2] => 100000
[6,3,5,4,2,1] => [6,3,5,4,2,1] => [-1,6,3,5,4,2] => [-1,6,3,5,4,2] => 100000
[6,4,2,3,5,1] => [6,4,2,3,5,1] => [-1,4,5,3,6,2] => [-1,6,4,2,3,5] => 100000
[6,4,3,2,5,1] => [6,4,3,2,5,1] => [-1,5,4,3,6,2] => [-1,6,4,3,2,5] => 100000
[6,4,3,5,2,1] => [6,4,3,5,2,1] => [-1,6,4,3,5,2] => [-1,6,4,3,5,2] => 100000
[6,4,5,2,3,1] => [6,4,5,2,3,1] => [-1,5,6,3,4,2] => [-1,6,4,5,2,3] => 100000
[6,4,5,3,2,1] => [6,4,5,3,2,1] => [-1,6,5,3,4,2] => [-1,6,4,5,3,2] => 100000
[6,5,2,3,4,1] => [6,5,2,3,4,1] => [-1,4,5,6,3,2] => [-1,6,5,2,3,4] => 100000
[6,5,2,4,3,1] => [6,5,2,4,3,1] => [-1,4,6,5,3,2] => [-1,6,5,2,4,3] => 100000
[6,5,3,2,4,1] => [6,5,3,2,4,1] => [-1,5,4,6,3,2] => [-1,6,5,3,2,4] => 100000
[6,5,3,4,2,1] => [6,5,3,4,2,1] => [-1,6,4,5,3,2] => [-1,6,5,3,4,2] => 100000
[6,5,4,2,3,1] => [6,5,4,2,3,1] => [-1,5,6,4,3,2] => [-1,6,5,4,2,3] => 100000
[6,5,4,3,2,1] => [6,5,4,3,2,1] => [-1,6,5,4,3,2] => [-1,6,5,4,3,2] => 100000
[2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => [-1,2,3,4,5,6,7] => [-1,2,3,4,5,6,7] => 1000000
[7,3,1,2,4,5,6] => [7,3,1,2,4,5,6] => [4,5,3,6,7,-1,2] => [-6,7,3,1,2,4,5] => 1000000
[7,6,1,2,3,4,5] => [7,6,1,2,3,4,5] => [4,5,6,7,-1,3,2] => [-5,7,6,1,2,3,4] => 1000000
[8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [-1,8,7,6,5,4,3,2] => [-1,8,7,6,5,4,3,2] => 10000000
Map
to signed permutation
Description
The signed permutation with all signs positive.
Map
Kreweras complement
Description
The Kreweras complement of a signed permutation.
This is the signed permutation $\pi^{-1}c$ where $c = (1,\ldots,n,-1,-2,\dots,-n)$ is the long cycle.
The order of the Kreweras complement on signed permutations of $\{\pm 1,\dots, \pm n\}$ is $2n$.
Map
inverse
Description
The inverse 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 $\pi(i) > 0$.