Identifier
Values
[[1]] => [1] => [1] => [-1] => 1
[[1,2]] => [1,2] => [1,2] => [-2,1] => 1
[[1],[2]] => [2,1] => [2,1] => [1,-2] => 1
[[1,2,3]] => [1,2,3] => [1,2,3] => [-3,1,2] => 1
[[1,3],[2]] => [2,1,3] => [2,1,3] => [1,-3,2] => 1
[[1,2],[3]] => [3,1,2] => [3,1,2] => [2,-3,1] => 2
[[1],[2],[3]] => [3,2,1] => [3,2,1] => [1,2,-3] => 1
[[1,2,3,4]] => [1,2,3,4] => [1,2,3,4] => [-4,1,2,3] => 1
[[1,3,4],[2]] => [2,1,3,4] => [2,1,3,4] => [1,-4,2,3] => 1
[[1,2,4],[3]] => [3,1,2,4] => [3,1,2,4] => [2,-4,1,3] => 2
[[1,2,3],[4]] => [4,1,2,3] => [4,1,2,3] => [3,-4,1,2] => 2
[[1,3],[2,4]] => [2,4,1,3] => [2,4,1,3] => [3,1,-4,2] => 2
[[1,2],[3,4]] => [3,4,1,2] => [3,4,1,2] => [3,2,-4,1] => 3
[[1,4],[2],[3]] => [3,2,1,4] => [3,2,1,4] => [1,2,-4,3] => 1
[[1,3],[2],[4]] => [4,2,1,3] => [4,2,1,3] => [1,3,-4,2] => 2
[[1,2],[3],[4]] => [4,3,1,2] => [4,3,1,2] => [2,3,-4,1] => 2
[[1],[2],[3],[4]] => [4,3,2,1] => [4,3,2,1] => [1,2,3,-4] => 1
[[1,3,4,5],[2]] => [2,1,3,4,5] => [2,1,3,4,5] => [1,-5,2,3,4] => 1
[[1,4,5],[2],[3]] => [3,2,1,4,5] => [3,2,1,4,5] => [1,2,-5,3,4] => 1
[[1,3,5],[2],[4]] => [4,2,1,3,5] => [4,2,1,3,5] => [1,3,-5,2,4] => 2
[[1,3,4],[2],[5]] => [5,2,1,3,4] => [5,2,1,3,4] => [1,4,-5,2,3] => 2
[[1,4],[2,5],[3]] => [3,2,5,1,4] => [3,2,5,1,4] => [1,4,2,-5,3] => 2
[[1,3],[2,5],[4]] => [4,2,5,1,3] => [4,2,5,1,3] => [1,4,3,-5,2] => 3
[[1,5],[2],[3],[4]] => [4,3,2,1,5] => [4,3,2,1,5] => [1,2,3,-5,4] => 1
[[1,4],[2],[3],[5]] => [5,3,2,1,4] => [5,3,2,1,4] => [1,2,4,-5,3] => 2
[[1,3],[2],[4],[5]] => [5,4,2,1,3] => [5,4,2,1,3] => [1,3,4,-5,2] => 2
[[1],[2],[3],[4],[5]] => [5,4,3,2,1] => [5,4,3,2,1] => [1,2,3,4,-5] => 1
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Description
The number of right descents of a signed permutations.
An index is a right descent if it is a left descent of the inverse signed permutation.
Map
rowmotion
Description
The rowmotion of a signed permutation with respect to the sorting order.
The sorting order on signed permutations (with respect to the Coxeter element $-n, 1, 2,\dots, n-1$) is defined in [1].
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
to signed permutation
Description
The signed permutation with all signs positive.