Identifier
-
Mp00163:
Signed permutations
—permutation⟶
Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001857: Signed permutations ⟶ ℤ
Values
[1] => [1] => [1] => [1] => 0
[-1] => [1] => [1] => [1] => 0
[1,2] => [1,2] => [2,1] => [2,1] => 0
[1,-2] => [1,2] => [2,1] => [2,1] => 0
[-1,2] => [1,2] => [2,1] => [2,1] => 0
[-1,-2] => [1,2] => [2,1] => [2,1] => 0
[2,1] => [2,1] => [1,2] => [1,2] => 0
[2,-1] => [2,1] => [1,2] => [1,2] => 0
[-2,1] => [2,1] => [1,2] => [1,2] => 0
[-2,-1] => [2,1] => [1,2] => [1,2] => 0
[1,2,3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[1,2,-3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[1,-2,3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[1,-2,-3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[-1,2,3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[-1,2,-3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[-1,-2,3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[-1,-2,-3] => [1,2,3] => [2,3,1] => [2,3,1] => 0
[1,3,2] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[1,3,-2] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[1,-3,2] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[1,-3,-2] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[-1,3,2] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[-1,3,-2] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[-1,-3,2] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[-1,-3,-2] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[2,1,3] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[2,1,-3] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[2,-1,3] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[2,-1,-3] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[-2,1,3] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[-2,1,-3] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[-2,-1,3] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[-2,-1,-3] => [2,1,3] => [1,3,2] => [1,3,2] => 0
[2,3,1] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[2,3,-1] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[2,-3,1] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[2,-3,-1] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[-2,3,1] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[-2,3,-1] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[-2,-3,1] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[-2,-3,-1] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[3,1,2] => [3,1,2] => [3,1,2] => [3,1,2] => 0
[3,1,-2] => [3,1,2] => [3,1,2] => [3,1,2] => 0
[3,-1,2] => [3,1,2] => [3,1,2] => [3,1,2] => 0
[3,-1,-2] => [3,1,2] => [3,1,2] => [3,1,2] => 0
[-3,1,2] => [3,1,2] => [3,1,2] => [3,1,2] => 0
[-3,1,-2] => [3,1,2] => [3,1,2] => [3,1,2] => 0
[-3,-1,2] => [3,1,2] => [3,1,2] => [3,1,2] => 0
[-3,-1,-2] => [3,1,2] => [3,1,2] => [3,1,2] => 0
[3,2,1] => [3,2,1] => [2,1,3] => [2,1,3] => 0
[3,2,-1] => [3,2,1] => [2,1,3] => [2,1,3] => 0
[3,-2,1] => [3,2,1] => [2,1,3] => [2,1,3] => 0
[3,-2,-1] => [3,2,1] => [2,1,3] => [2,1,3] => 0
[-3,2,1] => [3,2,1] => [2,1,3] => [2,1,3] => 0
[-3,2,-1] => [3,2,1] => [2,1,3] => [2,1,3] => 0
[-3,-2,1] => [3,2,1] => [2,1,3] => [2,1,3] => 0
[-3,-2,-1] => [3,2,1] => [2,1,3] => [2,1,3] => 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.
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
Inverse Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $c\pi^{-1}$ where $c = (1,\ldots,n)$ is the long cycle.
Map
to signed permutation
Description
The signed permutation with all signs positive.
Map
permutation
Description
The permutation obtained by forgetting the colours.
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