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Identifier
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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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.
Code
def statistic(pi):
    return pi.reduced_word_graph().size()
Created
Nov 27, 2022 at 20:18 by Martin Rubey
Updated
Nov 27, 2022 at 20:18 by Martin Rubey