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Statistic identifier: St001856

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Collection: Permutations

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Description: The number of edges in the reduced word graph of a permutation.

The reduced word graph of a 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
[1,2]       => 0
[2,1]       => 0
[1,2,3]     => 0
[1,3,2]     => 0
[2,1,3]     => 0
[2,3,1]     => 0
[3,1,2]     => 0
[3,2,1]     => 1
[1,2,3,4]   => 0
[1,2,4,3]   => 0
[1,3,2,4]   => 0
[1,3,4,2]   => 0
[1,4,2,3]   => 0
[1,4,3,2]   => 1
[2,1,3,4]   => 0
[2,1,4,3]   => 1
[2,3,1,4]   => 0
[2,3,4,1]   => 0
[2,4,1,3]   => 1
[2,4,3,1]   => 2
[3,1,2,4]   => 0
[3,1,4,2]   => 1
[3,2,1,4]   => 1
[3,2,4,1]   => 2
[3,4,1,2]   => 1
[3,4,2,1]   => 4
[4,1,2,3]   => 0
[4,1,3,2]   => 2
[4,2,1,3]   => 2
[4,2,3,1]   => 6
[4,3,1,2]   => 4
[4,3,2,1]   => 18
[1,2,3,4,5] => 0
[1,2,3,5,4] => 0
[1,2,4,3,5] => 0
[1,2,4,5,3] => 0
[1,2,5,3,4] => 0
[1,2,5,4,3] => 1
[1,3,2,4,5] => 0
[1,3,2,5,4] => 1
[1,3,4,2,5] => 0
[1,3,4,5,2] => 0
[1,3,5,2,4] => 1
[1,3,5,4,2] => 2
[1,4,2,3,5] => 0
[1,4,2,5,3] => 1
[1,4,3,2,5] => 1
[1,4,3,5,2] => 2
[1,4,5,2,3] => 1
[1,4,5,3,2] => 4
[1,5,2,3,4] => 0
[1,5,2,4,3] => 2
[1,5,3,2,4] => 2
[1,5,3,4,2] => 6
[1,5,4,2,3] => 4
[1,5,4,3,2] => 18
[2,1,3,4,5] => 0
[2,1,3,5,4] => 1
[2,1,4,3,5] => 1
[2,1,4,5,3] => 2
[2,1,5,3,4] => 2
[2,1,5,4,3] => 8
[2,3,1,4,5] => 0
[2,3,1,5,4] => 2
[2,3,4,1,5] => 0
[2,3,4,5,1] => 0
[2,3,5,1,4] => 2
[2,3,5,4,1] => 3
[2,4,1,3,5] => 1
[2,4,1,5,3] => 5
[2,4,3,1,5] => 2
[2,4,3,5,1] => 3
[2,4,5,1,3] => 5
[2,4,5,3,1] => 10
[2,5,1,3,4] => 2
[2,5,1,4,3] => 13
[2,5,3,1,4] => 6
[2,5,3,4,1] => 12
[2,5,4,1,3] => 21
[2,5,4,3,1] => 52
[3,1,2,4,5] => 0
[3,1,2,5,4] => 2
[3,1,4,2,5] => 1
[3,1,4,5,2] => 2
[3,1,5,2,4] => 5
[3,1,5,4,2] => 13
[3,2,1,4,5] => 1
[3,2,1,5,4] => 8
[3,2,4,1,5] => 2
[3,2,4,5,1] => 3
[3,2,5,1,4] => 13
[3,2,5,4,1] => 25
[3,4,1,2,5] => 1
[3,4,1,5,2] => 5
[3,4,2,1,5] => 4
[3,4,2,5,1] => 10
[3,4,5,1,2] => 5
[3,4,5,2,1] => 17
[3,5,1,2,4] => 5
[3,5,1,4,2] => 23
[3,5,2,1,4] => 21
[3,5,2,4,1] => 57
[3,5,4,1,2] => 31
[3,5,4,2,1] => 119
[4,1,2,3,5] => 0
[4,1,2,5,3] => 2
[4,1,3,2,5] => 2
[4,1,3,5,2] => 6
[4,1,5,2,3] => 5
[4,1,5,3,2] => 21
[4,2,1,3,5] => 2
[4,2,1,5,3] => 13
[4,2,3,1,5] => 6
[4,2,3,5,1] => 12
[4,2,5,1,3] => 23
[4,2,5,3,1] => 57
[4,3,1,2,5] => 4
[4,3,1,5,2] => 21
[4,3,2,1,5] => 18
[4,3,2,5,1] => 52
[4,3,5,1,2] => 31
[4,3,5,2,1] => 119
[4,5,1,2,3] => 5
[4,5,1,3,2] => 31
[4,5,2,1,3] => 31
[4,5,2,3,1] => 104
[4,5,3,1,2] => 68
[4,5,3,2,1] => 327
[5,1,2,3,4] => 0
[5,1,2,4,3] => 3
[5,1,3,2,4] => 3
[5,1,3,4,2] => 12
[5,1,4,2,3] => 10
[5,1,4,3,2] => 52
[5,2,1,3,4] => 3
[5,2,1,4,3] => 25
[5,2,3,1,4] => 12
[5,2,3,4,1] => 30
[5,2,4,1,3] => 57
[5,2,4,3,1] => 169
[5,3,1,2,4] => 10
[5,3,1,4,2] => 57
[5,3,2,1,4] => 52
[5,3,2,4,1] => 169
[5,3,4,1,2] => 104
[5,3,4,2,1] => 457
[5,4,1,2,3] => 17
[5,4,1,3,2] => 119
[5,4,2,1,3] => 119
[5,4,2,3,1] => 457
[5,4,3,1,2] => 327
[5,4,3,2,1] => 1770

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Created: Nov 27, 2022 at 20:18 by Martin Rubey

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Last Updated: Nov 27, 2022 at 20:18 by Martin Rubey