- FindStat

Identifier

St001857: Signed permutations ⟶ ℤ

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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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.

Code

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

Created

Nov 27, 2022 at 20:32 by Martin Rubey

Updated

Nov 27, 2022 at 20:32 by Martin Rubey