Identifier
Values
{{1}} => [1] => [1] => [-1] => 1
{{1,2}} => [2,1] => [2,1] => [-2,-1] => 1
{{1},{2}} => [1,2] => [1,2] => [-1,-2] => 1
{{1,2,3}} => [2,3,1] => [2,3,1] => [-2,-3,-1] => 2
{{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] => 1
{{1},{2,3}} => [1,3,2] => [1,3,2] => [-1,-3,-2] => 1
{{1},{2},{3}} => [1,2,3] => [1,2,3] => [-1,-2,-3] => 1
{{1,2,3,4}} => [2,3,4,1] => [2,3,4,1] => [-2,-3,-4,-1] => 5
{{1,2,3},{4}} => [2,3,1,4] => [2,3,1,4] => [-2,-3,-1,-4] => 2
{{1,2,4},{3}} => [2,4,3,1] => [2,4,3,1] => [-2,-4,-3,-1] => 3
{{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] => 1
{{1,3,4},{2}} => [3,2,4,1] => [3,2,4,1] => [-3,-2,-4,-1] => 3
{{1,3},{2,4}} => [3,4,1,2] => [3,4,1,2] => [-3,-4,-1,-2] => 3
{{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] => 1
{{1},{2,3,4}} => [1,3,4,2] => [1,3,4,2] => [-1,-3,-4,-2] => 2
{{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] => [4,2,3,1] => [-4,-2,-3,-1] => 2
{{1},{2,4},{3}} => [1,4,3,2] => [1,4,3,2] => [-1,-4,-3,-2] => 1
{{1},{2},{3,4}} => [1,2,4,3] => [1,2,4,3] => [-1,-2,-4,-3] => 1
{{1},{2},{3},{4}} => [1,2,3,4] => [1,2,3,4] => [-1,-2,-3,-4] => 1
{{1},{2,3,4,5}} => [1,3,4,5,2] => [1,3,4,5,2] => [-1,-3,-4,-5,-2] => 5
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [1,3,4,2,5] => [-1,-3,-4,-2,-5] => 2
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [1,3,5,4,2] => [-1,-3,-5,-4,-2] => 3
{{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] => 1
{{1},{2,4,5},{3}} => [1,4,3,5,2] => [1,4,3,5,2] => [-1,-4,-3,-5,-2] => 3
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [1,4,5,2,3] => [-1,-4,-5,-2,-3] => 3
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [1,4,3,2,5] => [-1,-4,-3,-2,-5] => 1
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [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] => [-1,-2,-4,-3,-5] => 1
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [1,5,3,4,2] => [-1,-5,-3,-4,-2] => 2
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [1,2,5,4,3] => [-1,-2,-5,-4,-3] => 1
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [1,2,3,5,4] => [-1,-2,-3,-5,-4] => 1
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [1,2,3,4,5] => [-1,-2,-3,-4,-5] => 1
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Description
The number of facets of a certain subword complex associated with the signed permutation.
Let $Q=[1,\dots,n,1,\dots,n,\dots,1,\dots,n]$ be the word of length $n^2$, and let $\pi$ be a signed permutation. Then this statistic yields the number of facets of the subword complex $\Delta(Q, \pi)$.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
bar
Description
Return the signed permutation with all signs reversed.
Map
to signed permutation
Description
The signed permutation with all signs positive.