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] => 1
{{1},{2,3}} => [1,3,2] => [1,3,2] => 0
{{1},{2},{3}} => [1,2,3] => [1,2,3] => 0
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Description
The number of edges in the reduced word graph of a signed permutation.
The reduced word graph of a signed permutation $\pi$ has the reduced words of $\pi$ as vertices and an edge between two reduced words if they differ by exactly one braid move.
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.