Identifier
Values
[+] => [1] => [1] => 0
[-] => [1] => [1] => 0
[+,+] => [1,2] => [1,2] => 0
[-,+] => [2,1] => [2,1] => 0
[+,-] => [1,2] => [1,2] => 0
[-,-] => [1,2] => [1,2] => 0
[2,1] => [1,2] => [1,2] => 0
[+,+,+] => [1,2,3] => [1,2,3] => 0
[-,+,+] => [2,3,1] => [2,3,1] => 0
[+,-,+] => [1,3,2] => [1,3,2] => 0
[+,+,-] => [1,2,3] => [1,2,3] => 0
[-,-,+] => [3,1,2] => [3,1,2] => 0
[-,+,-] => [2,1,3] => [2,1,3] => 0
[+,-,-] => [1,2,3] => [1,2,3] => 0
[-,-,-] => [1,2,3] => [1,2,3] => 0
[+,3,2] => [1,2,3] => [1,2,3] => 0
[-,3,2] => [2,1,3] => [2,1,3] => 0
[2,1,+] => [1,3,2] => [1,3,2] => 0
[2,1,-] => [1,2,3] => [1,2,3] => 0
[2,3,1] => [1,2,3] => [1,2,3] => 0
[3,1,2] => [1,2,3] => [1,2,3] => 0
[3,+,1] => [2,1,3] => [2,1,3] => 0
[3,-,1] => [1,3,2] => [1,3,2] => 0
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searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
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
lower permutation
Description
The lower bound in the Grassmann interval corresponding to the decorated permutation.
Let $I$ be the anti-exceedance set of a decorated permutation $w$. Let $v$ be the $k$-Grassmannian permutation determined by $v[k] = w^{-1}(I)$ and let $u$ be the permutation satisfying $u = wv$. Then $[u, v]$ is the Grassmann interval corresponding to $w$.
This map returns $u$.
Map
to signed permutation
Description
The signed permutation with all signs positive.