- 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

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

$F_{1} = 2$

$F_{2} = 7 + q$

$F_{3} = 15 + 11\ q + 6\ q^{2} + 2\ q^{3} + 2\ q^{4} + 4\ q^{5} + 2\ q^{7} + 2\ q^{10} + q^{13} + q^{17} + q^{22} + q^{60}$

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