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Statistic identifier: St001857

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Collection: Signed permutations

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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.

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References: 

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Code:
def statistic(pi):
    return pi.reduced_word_graph().size()

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Statistic values:

[1]        => 0
[-1]       => 0
[1,2]      => 0
[1,-2]     => 0
[-1,2]     => 0
[-1,-2]    => 1
[2,1]      => 0
[2,-1]     => 0
[-2,1]     => 0
[-2,-1]    => 0
[1,2,3]    => 0
[1,2,-3]   => 0
[1,-2,3]   => 0
[1,-2,-3]  => 1
[-1,2,3]   => 0
[-1,2,-3]  => 3
[-1,-2,3]  => 17
[-1,-2,-3] => 60
[1,3,2]    => 0
[1,3,-2]   => 0
[1,-3,2]   => 0
[1,-3,-2]  => 0
[-1,3,2]   => 3
[-1,3,-2]  => 10
[-1,-3,2]  => 10
[-1,-3,-2] => 22
[2,1,3]    => 0
[2,1,-3]   => 1
[2,-1,3]   => 0
[2,-1,-3]  => 2
[-2,1,3]   => 0
[-2,1,-3]  => 2
[-2,-1,3]  => 5
[-2,-1,-3] => 13
[2,3,1]    => 0
[2,3,-1]   => 0
[2,-3,1]   => 1
[2,-3,-1]  => 1
[-2,3,1]   => 2
[-2,3,-1]  => 5
[-2,-3,1]  => 4
[-2,-3,-1] => 7
[3,1,2]    => 0
[3,1,-2]   => 1
[3,-1,2]   => 2
[3,-1,-2]  => 4
[-3,1,2]   => 0
[-3,1,-2]  => 1
[-3,-1,2]  => 5
[-3,-1,-2] => 7
[3,2,1]    => 1
[3,2,-1]   => 2
[3,-2,1]   => 1
[3,-2,-1]  => 1
[-3,2,1]   => 2
[-3,2,-1]  => 5
[-3,-2,1]  => 1
[-3,-2,-1] => 1

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Created: Nov 27, 2022 at 20:32 by Martin Rubey

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Last Updated: Nov 27, 2022 at 20:32 by Martin Rubey