Identifier
Values
{{1}} => [1] => [1] => 0
{{1,2}} => [2,1] => [2,1] => 0
{{1},{2}} => [1,2] => [1,2] => 0
{{1,2,3}} => [2,3,1] => [2,3,1] => 0
{{1,2},{3}} => [2,1,3] => [2,1,3] => 0
{{1,3},{2}} => [3,2,1] => [3,2,1] => 0
{{1},{2,3}} => [1,3,2] => [1,3,2] => 1
{{1},{2},{3}} => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}} => [2,3,4,1] => [2,3,4,1] => 0
{{1,2,3},{4}} => [2,3,1,4] => [2,3,1,4] => 0
{{1,2,4},{3}} => [2,4,3,1] => [2,4,3,1] => 0
{{1,2},{3,4}} => [2,1,4,3] => [2,1,4,3] => 1
{{1,2},{3},{4}} => [2,1,3,4] => [2,1,3,4] => 0
{{1,3,4},{2}} => [3,2,4,1] => [3,2,4,1] => 0
{{1,3},{2,4}} => [3,4,1,2] => [3,4,1,2] => 0
{{1,3},{2},{4}} => [3,2,1,4] => [3,2,1,4] => 0
{{1,4},{2,3}} => [4,3,2,1] => [4,3,2,1] => 0
{{1},{2,3,4}} => [1,3,4,2] => [1,3,4,2] => 1
{{1},{2,3},{4}} => [1,3,2,4] => [1,3,2,4] => 1
{{1,4},{2},{3}} => [4,2,3,1] => [4,2,3,1] => 0
{{1},{2,4},{3}} => [1,4,3,2] => [1,4,3,2] => 1
{{1},{2},{3,4}} => [1,2,4,3] => [1,2,4,3] => 2
{{1},{2},{3},{4}} => [1,2,3,4] => [1,2,3,4] => 0
{{1},{2,3,4,5}} => [1,3,4,5,2] => [1,3,4,5,2] => 1
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [1,3,4,2,5] => 1
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [1,3,5,4,2] => 1
{{1},{2,3},{4,5}} => [1,3,2,5,4] => [1,3,2,5,4] => 3
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [1,3,2,4,5] => 1
{{1},{2,4,5},{3}} => [1,4,3,5,2] => [1,4,3,5,2] => 1
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [1,4,5,2,3] => 2
{{1},{2,4},{3},{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] => 2
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [1,2,4,5,3] => 2
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [1,2,4,3,5] => 2
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [1,5,3,4,2] => 1
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [1,2,5,4,3] => 2
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [1,2,3,5,4] => 3
{{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 EN of a signed permutation.
An alignment of type EN of a signed permutation π∈Hn is a pair −n≤i≤j≤n, i,j≠0, such that one of the following conditions hold:
  • $-i < 0 < -\pi(i) < \pi(j) < j$
  • $i \leq\pi(i) < \pi(j) < j$.
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.