Identifier
Mp00170: Permutations —to signed permutation⟶ Signed permutations
Mp00245: Signed permutations —standardize⟶ Permutations
Images
[1] => [1] => [1]
[1,2] => [1,2] => [1,2]
[2,1] => [2,1] => [2,1]
[1,2,3] => [1,2,3] => [1,2,3]
[1,3,2] => [1,3,2] => [1,3,2]
[2,1,3] => [2,1,3] => [2,1,3]
[2,3,1] => [2,3,1] => [2,3,1]
[3,1,2] => [3,1,2] => [3,1,2]
[3,2,1] => [3,2,1] => [3,2,1]
[1,2,3,4] => [1,2,3,4] => [1,2,3,4]
[1,2,4,3] => [1,2,4,3] => [1,2,4,3]
[1,3,2,4] => [1,3,2,4] => [1,3,2,4]
[1,3,4,2] => [1,3,4,2] => [1,3,4,2]
[1,4,2,3] => [1,4,2,3] => [1,4,2,3]
[1,4,3,2] => [1,4,3,2] => [1,4,3,2]
[2,1,3,4] => [2,1,3,4] => [2,1,3,4]
[2,1,4,3] => [2,1,4,3] => [2,1,4,3]
[2,3,1,4] => [2,3,1,4] => [2,3,1,4]
[2,3,4,1] => [2,3,4,1] => [2,3,4,1]
[2,4,1,3] => [2,4,1,3] => [2,4,1,3]
[2,4,3,1] => [2,4,3,1] => [2,4,3,1]
[3,1,2,4] => [3,1,2,4] => [3,1,2,4]
[3,1,4,2] => [3,1,4,2] => [3,1,4,2]
[3,2,1,4] => [3,2,1,4] => [3,2,1,4]
[3,2,4,1] => [3,2,4,1] => [3,2,4,1]
[3,4,1,2] => [3,4,1,2] => [3,4,1,2]
[3,4,2,1] => [3,4,2,1] => [3,4,2,1]
[4,1,2,3] => [4,1,2,3] => [4,1,2,3]
[4,1,3,2] => [4,1,3,2] => [4,1,3,2]
[4,2,1,3] => [4,2,1,3] => [4,2,1,3]
[4,2,3,1] => [4,2,3,1] => [4,2,3,1]
[4,3,1,2] => [4,3,1,2] => [4,3,1,2]
[4,3,2,1] => [4,3,2,1] => [4,3,2,1]
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5]
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4]
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5]
[1,2,4,5,3] => [1,2,4,5,3] => [1,2,4,5,3]
[1,2,5,3,4] => [1,2,5,3,4] => [1,2,5,3,4]
[1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3]
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5]
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4]
[1,3,4,2,5] => [1,3,4,2,5] => [1,3,4,2,5]
[1,3,4,5,2] => [1,3,4,5,2] => [1,3,4,5,2]
[1,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4]
[1,3,5,4,2] => [1,3,5,4,2] => [1,3,5,4,2]
[1,4,2,3,5] => [1,4,2,3,5] => [1,4,2,3,5]
[1,4,2,5,3] => [1,4,2,5,3] => [1,4,2,5,3]
[1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5]
[1,4,3,5,2] => [1,4,3,5,2] => [1,4,3,5,2]
[1,4,5,2,3] => [1,4,5,2,3] => [1,4,5,2,3]
[1,4,5,3,2] => [1,4,5,3,2] => [1,4,5,3,2]
[1,5,2,3,4] => [1,5,2,3,4] => [1,5,2,3,4]
[1,5,2,4,3] => [1,5,2,4,3] => [1,5,2,4,3]
[1,5,3,2,4] => [1,5,3,2,4] => [1,5,3,2,4]
[1,5,3,4,2] => [1,5,3,4,2] => [1,5,3,4,2]
[1,5,4,2,3] => [1,5,4,2,3] => [1,5,4,2,3]
[1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2]
[2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5]
[2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4]
[2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5]
[2,1,4,5,3] => [2,1,4,5,3] => [2,1,4,5,3]
[2,1,5,3,4] => [2,1,5,3,4] => [2,1,5,3,4]
[2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3]
[2,3,1,4,5] => [2,3,1,4,5] => [2,3,1,4,5]
[2,3,1,5,4] => [2,3,1,5,4] => [2,3,1,5,4]
[2,3,4,1,5] => [2,3,4,1,5] => [2,3,4,1,5]
[2,3,4,5,1] => [2,3,4,5,1] => [2,3,4,5,1]
[2,3,5,1,4] => [2,3,5,1,4] => [2,3,5,1,4]
[2,3,5,4,1] => [2,3,5,4,1] => [2,3,5,4,1]
[2,4,1,3,5] => [2,4,1,3,5] => [2,4,1,3,5]
[2,4,1,5,3] => [2,4,1,5,3] => [2,4,1,5,3]
[2,4,3,1,5] => [2,4,3,1,5] => [2,4,3,1,5]
[2,4,3,5,1] => [2,4,3,5,1] => [2,4,3,5,1]
[2,4,5,1,3] => [2,4,5,1,3] => [2,4,5,1,3]
[2,4,5,3,1] => [2,4,5,3,1] => [2,4,5,3,1]
[2,5,1,3,4] => [2,5,1,3,4] => [2,5,1,3,4]
[2,5,1,4,3] => [2,5,1,4,3] => [2,5,1,4,3]
[2,5,3,1,4] => [2,5,3,1,4] => [2,5,3,1,4]
[2,5,3,4,1] => [2,5,3,4,1] => [2,5,3,4,1]
[2,5,4,1,3] => [2,5,4,1,3] => [2,5,4,1,3]
[2,5,4,3,1] => [2,5,4,3,1] => [2,5,4,3,1]
[3,1,2,4,5] => [3,1,2,4,5] => [3,1,2,4,5]
[3,1,2,5,4] => [3,1,2,5,4] => [3,1,2,5,4]
[3,1,4,2,5] => [3,1,4,2,5] => [3,1,4,2,5]
[3,1,4,5,2] => [3,1,4,5,2] => [3,1,4,5,2]
[3,1,5,2,4] => [3,1,5,2,4] => [3,1,5,2,4]
[3,1,5,4,2] => [3,1,5,4,2] => [3,1,5,4,2]
[3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5]
[3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4]
[3,2,4,1,5] => [3,2,4,1,5] => [3,2,4,1,5]
[3,2,4,5,1] => [3,2,4,5,1] => [3,2,4,5,1]
[3,2,5,1,4] => [3,2,5,1,4] => [3,2,5,1,4]
[3,2,5,4,1] => [3,2,5,4,1] => [3,2,5,4,1]
[3,4,1,2,5] => [3,4,1,2,5] => [3,4,1,2,5]
[3,4,1,5,2] => [3,4,1,5,2] => [3,4,1,5,2]
[3,4,2,1,5] => [3,4,2,1,5] => [3,4,2,1,5]
[3,4,2,5,1] => [3,4,2,5,1] => [3,4,2,5,1]
[3,4,5,1,2] => [3,4,5,1,2] => [3,4,5,1,2]
[3,4,5,2,1] => [3,4,5,2,1] => [3,4,5,2,1]
[3,5,1,2,4] => [3,5,1,2,4] => [3,5,1,2,4]
[3,5,1,4,2] => [3,5,1,4,2] => [3,5,1,4,2]
>>> Load all 153 entries. <<<
[3,5,2,1,4] => [3,5,2,1,4] => [3,5,2,1,4]
[3,5,2,4,1] => [3,5,2,4,1] => [3,5,2,4,1]
[3,5,4,1,2] => [3,5,4,1,2] => [3,5,4,1,2]
[3,5,4,2,1] => [3,5,4,2,1] => [3,5,4,2,1]
[4,1,2,3,5] => [4,1,2,3,5] => [4,1,2,3,5]
[4,1,2,5,3] => [4,1,2,5,3] => [4,1,2,5,3]
[4,1,3,2,5] => [4,1,3,2,5] => [4,1,3,2,5]
[4,1,3,5,2] => [4,1,3,5,2] => [4,1,3,5,2]
[4,1,5,2,3] => [4,1,5,2,3] => [4,1,5,2,3]
[4,1,5,3,2] => [4,1,5,3,2] => [4,1,5,3,2]
[4,2,1,3,5] => [4,2,1,3,5] => [4,2,1,3,5]
[4,2,1,5,3] => [4,2,1,5,3] => [4,2,1,5,3]
[4,2,3,1,5] => [4,2,3,1,5] => [4,2,3,1,5]
[4,2,3,5,1] => [4,2,3,5,1] => [4,2,3,5,1]
[4,2,5,1,3] => [4,2,5,1,3] => [4,2,5,1,3]
[4,2,5,3,1] => [4,2,5,3,1] => [4,2,5,3,1]
[4,3,1,2,5] => [4,3,1,2,5] => [4,3,1,2,5]
[4,3,1,5,2] => [4,3,1,5,2] => [4,3,1,5,2]
[4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5]
[4,3,2,5,1] => [4,3,2,5,1] => [4,3,2,5,1]
[4,3,5,1,2] => [4,3,5,1,2] => [4,3,5,1,2]
[4,3,5,2,1] => [4,3,5,2,1] => [4,3,5,2,1]
[4,5,1,2,3] => [4,5,1,2,3] => [4,5,1,2,3]
[4,5,1,3,2] => [4,5,1,3,2] => [4,5,1,3,2]
[4,5,2,1,3] => [4,5,2,1,3] => [4,5,2,1,3]
[4,5,2,3,1] => [4,5,2,3,1] => [4,5,2,3,1]
[4,5,3,1,2] => [4,5,3,1,2] => [4,5,3,1,2]
[4,5,3,2,1] => [4,5,3,2,1] => [4,5,3,2,1]
[5,1,2,3,4] => [5,1,2,3,4] => [5,1,2,3,4]
[5,1,2,4,3] => [5,1,2,4,3] => [5,1,2,4,3]
[5,1,3,2,4] => [5,1,3,2,4] => [5,1,3,2,4]
[5,1,3,4,2] => [5,1,3,4,2] => [5,1,3,4,2]
[5,1,4,2,3] => [5,1,4,2,3] => [5,1,4,2,3]
[5,1,4,3,2] => [5,1,4,3,2] => [5,1,4,3,2]
[5,2,1,3,4] => [5,2,1,3,4] => [5,2,1,3,4]
[5,2,1,4,3] => [5,2,1,4,3] => [5,2,1,4,3]
[5,2,3,1,4] => [5,2,3,1,4] => [5,2,3,1,4]
[5,2,3,4,1] => [5,2,3,4,1] => [5,2,3,4,1]
[5,2,4,1,3] => [5,2,4,1,3] => [5,2,4,1,3]
[5,2,4,3,1] => [5,2,4,3,1] => [5,2,4,3,1]
[5,3,1,2,4] => [5,3,1,2,4] => [5,3,1,2,4]
[5,3,1,4,2] => [5,3,1,4,2] => [5,3,1,4,2]
[5,3,2,1,4] => [5,3,2,1,4] => [5,3,2,1,4]
[5,3,2,4,1] => [5,3,2,4,1] => [5,3,2,4,1]
[5,3,4,1,2] => [5,3,4,1,2] => [5,3,4,1,2]
[5,3,4,2,1] => [5,3,4,2,1] => [5,3,4,2,1]
[5,4,1,2,3] => [5,4,1,2,3] => [5,4,1,2,3]
[5,4,1,3,2] => [5,4,1,3,2] => [5,4,1,3,2]
[5,4,2,1,3] => [5,4,2,1,3] => [5,4,2,1,3]
[5,4,2,3,1] => [5,4,2,3,1] => [5,4,2,3,1]
[5,4,3,1,2] => [5,4,3,1,2] => [5,4,3,1,2]
[5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1]
Map
to signed permutation
Description
The signed permutation with all signs positive.
Map
standardize
Description
Return the standardization of the signed permutation, where 1 is the smallest and -1 the largest element.
Let $\pi\in\mathfrak H_n$ be a signed permutation. Assuming the order $1 < \dots < n < -n < \dots < -1$, this map returns the permutation in $\mathfrak S_n$ which is order isomorphic to $\pi(1),\dots,\pi(n)$.