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Identifier
Values
[1,2] => 0
[1,-2] => 1
[-1,2] => 1
[-1,-2] => 2
[2,1] => 1
[2,-1] => 2
[-2,1] => 2
[-2,-1] => 1
[1,2,3] => 0
[1,2,-3] => 1
[1,-2,3] => 1
[1,-2,-3] => 2
[-1,2,3] => 1
[-1,2,-3] => 1
[-1,-2,3] => 1
[-1,-2,-3] => 2
[1,3,2] => 1
[1,3,-2] => 2
[1,-3,2] => 2
[1,-3,-2] => 1
[-1,3,2] => 1
[-1,3,-2] => 1
[-1,-3,2] => 1
[-1,-3,-2] => 1
[2,1,3] => 1
[2,1,-3] => 2
[2,-1,3] => 2
[2,-1,-3] => 1
[-2,1,3] => 2
[-2,1,-3] => 1
[-2,-1,3] => 1
[-2,-1,-3] => 1
[2,3,1] => 2
[2,3,-1] => 1
[2,-3,1] => 1
[2,-3,-1] => 2
[-2,3,1] => 1
[-2,3,-1] => 2
[-2,-3,1] => 2
[-2,-3,-1] => 2
[3,1,2] => 2
[3,1,-2] => 1
[3,-1,2] => 1
[3,-1,-2] => 2
[-3,1,2] => 1
[-3,1,-2] => 2
[-3,-1,2] => 2
[-3,-1,-2] => 2
[3,2,1] => 1
[3,2,-1] => 4
[3,-2,1] => 2
[3,-2,-1] => 1
[-3,2,1] => 4
[-3,2,-1] => 3
[-3,-2,1] => 1
[-3,-2,-1] => 1
[1,2,3,4] => 0
[1,2,3,-4] => 1
[1,2,-3,4] => 1
[1,2,-3,-4] => 2
[1,-2,3,4] => 1
[1,-2,3,-4] => 1
[1,-2,-3,4] => 1
[1,-2,-3,-4] => 2
[-1,2,3,4] => 1
[-1,2,3,-4] => 1
[-1,2,-3,4] => 1
[-1,2,-3,-4] => 1
[-1,-2,3,4] => 1
[-1,-2,3,-4] => 1
[-1,-2,-3,4] => 1
[-1,-2,-3,-4] => 2
[1,2,4,3] => 1
[1,2,4,-3] => 2
[1,2,-4,3] => 2
[1,2,-4,-3] => 1
[1,-2,4,3] => 1
[1,-2,4,-3] => 1
[1,-2,-4,3] => 1
[1,-2,-4,-3] => 1
[-1,2,4,3] => 1
[-1,2,4,-3] => 1
[-1,2,-4,3] => 1
[-1,2,-4,-3] => 1
[-1,-2,4,3] => 1
[-1,-2,4,-3] => 1
[-1,-2,-4,3] => 1
[-1,-2,-4,-3] => 1
[1,3,2,4] => 1
[1,3,2,-4] => 2
[1,3,-2,4] => 2
[1,3,-2,-4] => 1
[1,-3,2,4] => 2
[1,-3,2,-4] => 1
[1,-3,-2,4] => 1
[1,-3,-2,-4] => 1
[-1,3,2,4] => 1
[-1,3,2,-4] => 1
[-1,3,-2,4] => 1
[-1,3,-2,-4] => 1
[-1,-3,2,4] => 1
>>> Load all 440 entries. <<<
[-1,-3,2,-4] => 1
[-1,-3,-2,4] => 1
[-1,-3,-2,-4] => 1
[1,3,4,2] => 2
[1,3,4,-2] => 1
[1,3,-4,2] => 1
[1,3,-4,-2] => 2
[1,-3,4,2] => 1
[1,-3,4,-2] => 2
[1,-3,-4,2] => 2
[1,-3,-4,-2] => 2
[-1,3,4,2] => 1
[-1,3,4,-2] => 1
[-1,3,-4,2] => 1
[-1,3,-4,-2] => 1
[-1,-3,4,2] => 1
[-1,-3,4,-2] => 1
[-1,-3,-4,2] => 1
[-1,-3,-4,-2] => 1
[1,4,2,3] => 2
[1,4,2,-3] => 1
[1,4,-2,3] => 1
[1,4,-2,-3] => 2
[1,-4,2,3] => 1
[1,-4,2,-3] => 2
[1,-4,-2,3] => 2
[1,-4,-2,-3] => 2
[-1,4,2,3] => 1
[-1,4,2,-3] => 1
[-1,4,-2,3] => 1
[-1,4,-2,-3] => 1
[-1,-4,2,3] => 1
[-1,-4,2,-3] => 1
[-1,-4,-2,3] => 1
[-1,-4,-2,-3] => 1
[1,4,3,2] => 1
[1,4,3,-2] => 4
[1,4,-3,2] => 2
[1,4,-3,-2] => 1
[1,-4,3,2] => 4
[1,-4,3,-2] => 3
[1,-4,-3,2] => 1
[1,-4,-3,-2] => 1
[-1,4,3,2] => 1
[-1,4,3,-2] => 1
[-1,4,-3,2] => 1
[-1,4,-3,-2] => 1
[-1,-4,3,2] => 1
[-1,-4,3,-2] => 1
[-1,-4,-3,2] => 1
[-1,-4,-3,-2] => 1
[2,1,3,4] => 1
[2,1,3,-4] => 2
[2,1,-3,4] => 2
[2,1,-3,-4] => 3
[2,-1,3,4] => 1
[2,-1,3,-4] => 1
[2,-1,-3,4] => 1
[2,-1,-3,-4] => 1
[-2,1,3,4] => 1
[-2,1,3,-4] => 1
[-2,1,-3,4] => 1
[-2,1,-3,-4] => 1
[-2,-1,3,4] => 1
[-2,-1,3,-4] => 1
[-2,-1,-3,4] => 1
[-2,-1,-3,-4] => 1
[2,1,4,3] => 2
[2,1,4,-3] => 3
[2,1,-4,3] => 3
[2,1,-4,-3] => 2
[2,-1,4,3] => 1
[2,-1,4,-3] => 2
[2,-1,-4,3] => 2
[2,-1,-4,-3] => 1
[-2,1,4,3] => 1
[-2,1,4,-3] => 2
[-2,1,-4,3] => 2
[-2,1,-4,-3] => 1
[-2,-1,4,3] => 1
[-2,-1,4,-3] => 1
[-2,-1,-4,3] => 1
[-2,-1,-4,-3] => 1
[2,3,1,4] => 2
[2,3,1,-4] => 3
[2,3,-1,4] => 1
[2,3,-1,-4] => 1
[2,-3,1,4] => 1
[2,-3,1,-4] => 1
[2,-3,-1,4] => 1
[2,-3,-1,-4] => 2
[-2,3,1,4] => 1
[-2,3,1,-4] => 2
[-2,3,-1,4] => 1
[-2,3,-1,-4] => 1
[-2,-3,1,4] => 1
[-2,-3,1,-4] => 1
[-2,-3,-1,4] => 1
[-2,-3,-1,-4] => 1
[2,3,4,1] => 1
[2,3,4,-1] => 2
[2,3,-4,1] => 4
[2,3,-4,-1] => 1
[2,-3,4,1] => 2
[2,-3,4,-1] => 2
[2,-3,-4,1] => 3
[2,-3,-4,-1] => 3
[-2,3,4,1] => 2
[-2,3,4,-1] => 1
[-2,3,-4,1] => 1
[-2,3,-4,-1] => 1
[-2,-3,4,1] => 1
[-2,-3,4,-1] => 2
[-2,-3,-4,1] => 2
[-2,-3,-4,-1] => 2
[2,4,1,3] => 1
[2,4,1,-3] => 2
[2,4,-1,3] => 1
[2,4,-1,-3] => 1
[2,-4,1,3] => 4
[2,-4,1,-3] => 1
[2,-4,-1,3] => 1
[2,-4,-1,-3] => 1
[-2,4,1,3] => 2
[-2,4,1,-3] => 1
[-2,4,-1,3] => 1
[-2,4,-1,-3] => 2
[-2,-4,1,3] => 1
[-2,-4,1,-3] => 1
[-2,-4,-1,3] => 2
[-2,-4,-1,-3] => 2
[2,4,3,1] => 4
[2,4,3,-1] => 1
[2,4,-3,1] => 3
[2,4,-3,-1] => 2
[2,-4,3,1] => 1
[2,-4,3,-1] => 2
[2,-4,-3,1] => 1
[2,-4,-3,-1] => 2
[-2,4,3,1] => 1
[-2,4,3,-1] => 1
[-2,4,-3,1] => 1
[-2,4,-3,-1] => 1
[-2,-4,3,1] => 1
[-2,-4,3,-1] => 1
[-2,-4,-3,1] => 1
[-2,-4,-3,-1] => 1
[3,1,2,4] => 2
[3,1,2,-4] => 3
[3,1,-2,4] => 1
[3,1,-2,-4] => 1
[3,-1,2,4] => 1
[3,-1,2,-4] => 2
[3,-1,-2,4] => 1
[3,-1,-2,-4] => 1
[-3,1,2,4] => 1
[-3,1,2,-4] => 1
[-3,1,-2,4] => 1
[-3,1,-2,-4] => 2
[-3,-1,2,4] => 1
[-3,-1,2,-4] => 1
[-3,-1,-2,4] => 1
[-3,-1,-2,-4] => 1
[3,1,4,2] => 1
[3,1,4,-2] => 4
[3,1,-4,2] => 2
[3,1,-4,-2] => 1
[3,-1,4,2] => 2
[3,-1,4,-2] => 1
[3,-1,-4,2] => 1
[3,-1,-4,-2] => 1
[-3,1,4,2] => 1
[-3,1,4,-2] => 1
[-3,1,-4,2] => 1
[-3,1,-4,-2] => 1
[-3,-1,4,2] => 1
[-3,-1,4,-2] => 2
[-3,-1,-4,2] => 2
[-3,-1,-4,-2] => 2
[3,2,1,4] => 1
[3,2,1,-4] => 2
[3,2,-1,4] => 1
[3,2,-1,-4] => 1
[3,-2,1,4] => 1
[3,-2,1,-4] => 1
[3,-2,-1,4] => 1
[3,-2,-1,-4] => 1
[-3,2,1,4] => 1
[-3,2,1,-4] => 1
[-3,2,-1,4] => 1
[-3,2,-1,-4] => 1
[-3,-2,1,4] => 1
[-3,-2,1,-4] => 1
[-3,-2,-1,4] => 1
[-3,-2,-1,-4] => 1
[3,2,4,1] => 4
[3,2,4,-1] => 1
[3,2,-4,1] => 1
[3,2,-4,-1] => 1
[3,-2,4,1] => 1
[3,-2,4,-1] => 1
[3,-2,-4,1] => 1
[3,-2,-4,-1] => 2
[-3,2,4,1] => 2
[-3,2,4,-1] => 1
[-3,2,-4,1] => 1
[-3,2,-4,-1] => 2
[-3,-2,4,1] => 1
[-3,-2,4,-1] => 1
[-3,-2,-4,1] => 1
[-3,-2,-4,-1] => 1
[3,4,1,2] => 2
[3,4,1,-2] => 3
[3,4,-1,2] => 1
[3,4,-1,-2] => 1
[3,-4,1,2] => 3
[3,-4,1,-2] => 2
[3,-4,-1,2] => 1
[3,-4,-1,-2] => 2
[-3,4,1,2] => 1
[-3,4,1,-2] => 1
[-3,4,-1,2] => 1
[-3,4,-1,-2] => 2
[-3,-4,1,2] => 1
[-3,-4,1,-2] => 2
[-3,-4,-1,2] => 2
[-3,-4,-1,-2] => 3
[3,4,2,1] => 3
[3,4,2,-1] => 2
[3,4,-2,1] => 2
[3,4,-2,-1] => 1
[3,-4,2,1] => 1
[3,-4,2,-1] => 1
[3,-4,-2,1] => 1
[3,-4,-2,-1] => 1
[-3,4,2,1] => 1
[-3,4,2,-1] => 1
[-3,4,-2,1] => 2
[-3,4,-2,-1] => 1
[-3,-4,2,1] => 1
[-3,-4,2,-1] => 3
[-3,-4,-2,1] => 1
[-3,-4,-2,-1] => 2
[4,1,2,3] => 1
[4,1,2,-3] => 4
[4,1,-2,3] => 2
[4,1,-2,-3] => 3
[4,-1,2,3] => 2
[4,-1,2,-3] => 1
[4,-1,-2,3] => 1
[4,-1,-2,-3] => 2
[-4,1,2,3] => 2
[-4,1,2,-3] => 1
[-4,1,-2,3] => 2
[-4,1,-2,-3] => 3
[-4,-1,2,3] => 1
[-4,-1,2,-3] => 1
[-4,-1,-2,3] => 2
[-4,-1,-2,-3] => 2
[4,1,3,2] => 4
[4,1,3,-2] => 1
[4,1,-3,2] => 3
[4,1,-3,-2] => 1
[4,-1,3,2] => 1
[4,-1,3,-2] => 1
[4,-1,-3,2] => 1
[4,-1,-3,-2] => 1
[-4,1,3,2] => 1
[-4,1,3,-2] => 2
[-4,1,-3,2] => 2
[-4,1,-3,-2] => 2
[-4,-1,3,2] => 1
[-4,-1,3,-2] => 1
[-4,-1,-3,2] => 1
[-4,-1,-3,-2] => 1
[4,2,1,3] => 4
[4,2,1,-3] => 1
[4,2,-1,3] => 2
[4,2,-1,-3] => 1
[4,-2,1,3] => 1
[4,-2,1,-3] => 1
[4,-2,-1,3] => 1
[4,-2,-1,-3] => 1
[-4,2,1,3] => 1
[-4,2,1,-3] => 1
[-4,2,-1,3] => 1
[-4,2,-1,-3] => 2
[-4,-2,1,3] => 1
[-4,-2,1,-3] => 2
[-4,-2,-1,3] => 1
[-4,-2,-1,-3] => 1
[4,2,3,1] => 1
[4,2,3,-1] => 2
[4,2,-3,1] => 1
[4,2,-3,-1] => 3
[4,-2,3,1] => 1
[4,-2,3,-1] => 1
[4,-2,-3,1] => 2
[4,-2,-3,-1] => 1
[-4,2,3,1] => 2
[-4,2,3,-1] => 1
[-4,2,-3,1] => 3
[-4,2,-3,-1] => 3
[-4,-2,3,1] => 1
[-4,-2,3,-1] => 1
[-4,-2,-3,1] => 1
[-4,-2,-3,-1] => 2
[4,3,1,2] => 3
[4,3,1,-2] => 1
[4,3,-1,2] => 1
[4,3,-1,-2] => 1
[4,-3,1,2] => 2
[4,-3,1,-2] => 1
[4,-3,-1,2] => 2
[4,-3,-1,-2] => 1
[-4,3,1,2] => 2
[-4,3,1,-2] => 1
[-4,3,-1,2] => 1
[-4,3,-1,-2] => 3
[-4,-3,1,2] => 1
[-4,-3,1,-2] => 1
[-4,-3,-1,2] => 1
[-4,-3,-1,-2] => 2
[4,3,2,1] => 1
[4,3,2,-1] => 3
[4,3,-2,1] => 3
[4,3,-2,-1] => 1
[4,-3,2,1] => 3
[4,-3,2,-1] => 1
[4,-3,-2,1] => 1
[4,-3,-2,-1] => 1
[-4,3,2,1] => 3
[-4,3,2,-1] => 2
[-4,3,-2,1] => 1
[-4,3,-2,-1] => 2
[-4,-3,2,1] => 1
[-4,-3,2,-1] => 2
[-4,-3,-2,1] => 1
[-4,-3,-2,-1] => 1
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Description
The number of factors of the Stanley symmetric function associated with a signed permutation.
Code
def statistic(pi):
    return sum(m for _, m in pi.stanley_symmetric_function().factor())
Created
Nov 29, 2022 at 13:58 by Martin Rubey
Updated
Nov 29, 2022 at 13:58 by Martin Rubey