Identifier
Values
{{1}} => [1] => [1] => [1] => 1
{{1,2}} => [2,1] => [1,2] => [1,2] => 2
{{1},{2}} => [1,2] => [2,1] => [2,1] => 1
{{1,2,3}} => [2,3,1] => [1,2,3] => [1,2,3] => 3
{{1,2},{3}} => [2,1,3] => [1,3,2] => [1,3,2] => 2
{{1,3},{2}} => [3,2,1] => [2,1,3] => [2,1,3] => 2
{{1},{2,3}} => [1,3,2] => [3,2,1] => [3,2,1] => 2
{{1},{2},{3}} => [1,2,3] => [2,3,1] => [2,3,1] => 2
{{1,2,3,4}} => [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 4
{{1,2,3},{4}} => [2,3,1,4] => [1,2,4,3] => [1,2,4,3] => 3
{{1,2,4},{3}} => [2,4,3,1] => [1,3,2,4] => [1,3,2,4] => 3
{{1,2},{3,4}} => [2,1,4,3] => [1,4,3,2] => [1,4,3,2] => 3
{{1,2},{3},{4}} => [2,1,3,4] => [1,3,4,2] => [1,3,4,2] => 3
{{1,3,4},{2}} => [3,2,4,1] => [2,1,3,4] => [2,1,3,4] => 3
{{1,3},{2,4}} => [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 1
{{1,3},{2},{4}} => [3,2,1,4] => [2,1,4,3] => [2,1,4,3] => 2
{{1,4},{2,3}} => [4,3,2,1] => [3,2,1,4] => [3,2,1,4] => 3
{{1},{2,3,4}} => [1,3,4,2] => [4,2,3,1] => [4,2,3,1] => 3
{{1},{2,3},{4}} => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => 3
{{1,4},{2},{3}} => [4,2,3,1] => [2,3,1,4] => [2,3,1,4] => 3
{{1},{2,4},{3}} => [1,4,3,2] => [4,3,2,1] => [4,3,2,1] => 2
{{1},{2},{3,4}} => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => 3
{{1},{2},{3},{4}} => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 3
{{1,2,3,4,5}} => [2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => 5
{{1,2,3,4},{5}} => [2,3,4,1,5] => [1,2,3,5,4] => [1,2,3,5,4] => 4
{{1,2,3,5},{4}} => [2,3,5,4,1] => [1,2,4,3,5] => [1,2,4,3,5] => 4
{{1,2,3},{4,5}} => [2,3,1,5,4] => [1,2,5,4,3] => [1,2,5,4,3] => 4
{{1,2,3},{4},{5}} => [2,3,1,4,5] => [1,2,4,5,3] => [1,2,4,5,3] => 4
{{1,2,4,5},{3}} => [2,4,3,5,1] => [1,3,2,4,5] => [1,3,2,4,5] => 4
{{1,2,4},{3,5}} => [2,4,5,1,3] => [1,5,2,3,4] => [1,5,2,3,4] => 2
{{1,2,4},{3},{5}} => [2,4,3,1,5] => [1,3,2,5,4] => [1,3,2,5,4] => 3
{{1,2,5},{3,4}} => [2,5,4,3,1] => [1,4,3,2,5] => [1,4,3,2,5] => 4
{{1,2},{3,4,5}} => [2,1,4,5,3] => [1,5,3,4,2] => [1,5,3,4,2] => 4
{{1,2},{3,4},{5}} => [2,1,4,3,5] => [1,4,3,5,2] => [1,4,3,5,2] => 4
{{1,2,5},{3},{4}} => [2,5,3,4,1] => [1,3,4,2,5] => [1,3,4,2,5] => 4
{{1,2},{3,5},{4}} => [2,1,5,4,3] => [1,5,4,3,2] => [1,5,4,3,2] => 3
{{1,2},{3},{4,5}} => [2,1,3,5,4] => [1,3,5,4,2] => [1,3,5,4,2] => 4
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => [1,3,4,5,2] => [1,3,4,5,2] => 4
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Description
The number of weak excedances of a signed permutation.
For a signed permutation $\pi\in\mathfrak H_n$, this is $\lvert\{i\in[n] \mid \pi(i) \geq i\}\rvert$.
Map
Inverse Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $c\pi^{-1}$ where $c = (1,\ldots,n)$ is the long cycle.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
to signed permutation
Description
The signed permutation with all signs positive.