Identifier
Values
{{1}} => [1] => [1] => [1] => 0
{{1,2}} => [2,1] => [2,1] => [2,1] => 0
{{1},{2}} => [1,2] => [1,2] => [1,2] => 0
{{1,2,3}} => [2,3,1] => [1,3,2] => [1,3,2] => 0
{{1,2},{3}} => [2,1,3] => [2,1,3] => [2,1,3] => 1
{{1,3},{2}} => [3,2,1] => [3,2,1] => [3,2,1] => 0
{{1},{2,3}} => [1,3,2] => [1,3,2] => [1,3,2] => 0
{{1},{2},{3}} => [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}} => [2,3,4,1] => [1,2,4,3] => [1,2,4,3] => 0
{{1,2,3},{4}} => [2,3,1,4] => [1,3,2,4] => [1,3,2,4] => 1
{{1,2,4},{3}} => [2,4,3,1] => [1,4,3,2] => [1,4,3,2] => 0
{{1,2},{3,4}} => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 1
{{1,2},{3},{4}} => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 2
{{1,3,4},{2}} => [3,2,4,1] => [2,1,4,3] => [2,1,4,3] => 1
{{1,3},{2,4}} => [3,4,1,2] => [2,4,1,3] => [2,4,1,3] => 0
{{1,3},{2},{4}} => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 1
{{1,4},{2,3}} => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 0
{{1},{2,3,4}} => [1,3,4,2] => [1,2,4,3] => [1,2,4,3] => 0
{{1},{2,3},{4}} => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1
{{1,4},{2},{3}} => [4,2,3,1] => [4,1,3,2] => [4,1,3,2] => 1
{{1},{2,4},{3}} => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 0
{{1},{2},{3,4}} => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 0
{{1},{2},{3},{4}} => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3,4,5}} => [2,3,4,5,1] => [1,2,3,5,4] => [1,2,3,5,4] => 0
{{1,2,3,4},{5}} => [2,3,4,1,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
{{1,2,3,5},{4}} => [2,3,5,4,1] => [1,2,5,4,3] => [1,2,5,4,3] => 0
{{1,2,3},{4,5}} => [2,3,1,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 1
{{1,2,3},{4},{5}} => [2,3,1,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 2
{{1,2,4,5},{3}} => [2,4,3,5,1] => [1,3,2,5,4] => [1,3,2,5,4] => 1
{{1,2,4},{3,5}} => [2,4,5,1,3] => [1,3,5,2,4] => [1,3,5,2,4] => 0
{{1,2,4},{3},{5}} => [2,4,3,1,5] => [1,4,3,2,5] => [1,4,3,2,5] => 1
{{1,2,5},{3,4}} => [2,5,4,3,1] => [1,5,4,3,2] => [1,5,4,3,2] => 0
{{1,2,5},{3},{4}} => [2,5,3,4,1] => [1,5,2,4,3] => [1,5,2,4,3] => 1
{{1,3,5},{2,4}} => [3,4,5,2,1] => [1,2,5,4,3] => [1,2,5,4,3] => 0
{{1,3},{2,4,5}} => [3,4,1,5,2] => [1,3,2,5,4] => [1,3,2,5,4] => 1
{{1},{2,3,4,5}} => [1,3,4,5,2] => [1,2,3,5,4] => [1,2,3,5,4] => 0
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [1,2,5,4,3] => [1,2,5,4,3] => 0
{{1},{2,3},{4,5}} => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 1
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 2
{{1},{2,4,5},{3}} => [1,4,3,5,2] => [1,3,2,5,4] => [1,3,2,5,4] => 1
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [1,3,5,2,4] => [1,3,5,2,4] => 0
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 1
{{1},{2,5},{3,4}} => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 0
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [1,2,3,5,4] => [1,2,3,5,4] => 0
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [1,5,2,4,3] => [1,5,2,4,3] => 1
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 0
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
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Description
The number of alignments of type NE of a signed permutation.
An alignment of type NE of a signed permutation $\pi\in\mathfrak H_n$ is a pair $1 \leq i, j\leq n$ such that $\pi(i) < i < j \leq \pi(j)$.
Map
Inverse fireworks map
Description
Sends a permutation to an inverse fireworks permutation.
A permutation $\sigma$ is inverse fireworks if its inverse avoids the vincular pattern $3-12$. The inverse fireworks map sends any permutation $\sigma$ to an inverse fireworks permutation that is below $\sigma$ in left weak order and has the same Rajchgot index St001759The Rajchgot index of a permutation..
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.