Identifier
Values
{{1,2}} => [2,1] => [2,1] => [2,1] => 1
{{1},{2}} => [1,2] => [1,2] => [1,2] => 0
{{1,2,3}} => [2,3,1] => [3,2,1] => [3,2,1] => 1
{{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] => 0
{{1,2,3,4}} => [2,3,4,1] => [4,2,3,1] => [4,2,3,1] => 1
{{1,2,3},{4}} => [2,3,1,4] => [3,2,1,4] => [3,2,1,4] => 1
{{1,2,4},{3}} => [2,4,3,1] => [4,3,2,1] => [4,3,2,1] => 1
{{1,2},{3,4}} => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 2
{{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] => [4,2,3,1] => [4,2,3,1] => 1
{{1,3},{2,4}} => [3,4,1,2] => [4,3,2,1] => [4,3,2,1] => 1
{{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] => [1,4,3,2] => [1,4,3,2] => 1
{{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] => [4,3,2,1] => [4,3,2,1] => 1
{{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] => 0
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Description
The number of factors of the Stanley symmetric function associated with a signed permutation.
Map
Demazure product with inverse
Description
This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
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.