- FindStat

Identifier

St001856: Permutations ⟶ ℤ

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
                    

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

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