edit this statistic or download as text // json
Identifier
Values
[1] => 1
[-1] => 1
[1,2] => 1
[1,-2] => 1
[-1,2] => 1
[-1,-2] => 3
[2,1] => 1
[2,-1] => 0
[-2,1] => 0
[-2,-1] => 1
[1,2,3] => 1
[1,2,-3] => 1
[1,-2,3] => 1
[1,-2,-3] => 3
[-1,2,3] => 1
[-1,2,-3] => 3
[-1,-2,3] => 5
[-1,-2,-3] => 13
[1,3,2] => 1
[1,3,-2] => 0
[1,-3,2] => 0
[1,-3,-2] => 1
[-1,3,2] => 1
[-1,3,-2] => 0
[-1,-3,2] => 0
[-1,-3,-2] => 1
[2,1,3] => 1
[2,1,-3] => 1
[2,-1,3] => 0
[2,-1,-3] => 0
[-2,1,3] => 0
[-2,1,-3] => 0
[-2,-1,3] => 3
[-2,-1,-3] => 3
[2,3,1] => 0
[2,3,-1] => 0
[2,-3,1] => 0
[2,-3,-1] => 0
[-2,3,1] => 0
[-2,3,-1] => 0
[-2,-3,1] => 0
[-2,-3,-1] => 0
[3,1,2] => 0
[3,1,-2] => 0
[3,-1,2] => 0
[3,-1,-2] => 0
[-3,1,2] => 0
[-3,1,-2] => 0
[-3,-1,2] => 0
[-3,-1,-2] => 0
[3,2,1] => 3
[3,2,-1] => 0
[3,-2,1] => 1
[3,-2,-1] => 0
[-3,2,1] => 0
[-3,2,-1] => 3
[-3,-2,1] => 0
[-3,-2,-1] => 1
[1,2,3,4] => 1
[1,2,3,-4] => 1
[1,2,-3,4] => 1
[1,2,-3,-4] => 3
[1,-2,3,4] => 1
[1,-2,3,-4] => 3
[1,-2,-3,4] => 5
[1,-2,-3,-4] => 13
[-1,2,3,4] => 1
[-1,2,3,-4] => 3
[-1,2,-3,4] => 5
[-1,2,-3,-4] => 13
[-1,-2,3,4] => 7
[-1,-2,3,-4] => 15
[-1,-2,-3,4] => 19
[-1,-2,-3,-4] => 85
[1,2,4,3] => 1
[1,2,4,-3] => 0
[1,2,-4,3] => 0
[1,2,-4,-3] => 1
[1,-2,4,3] => 1
[1,-2,4,-3] => 0
[1,-2,-4,3] => 0
[1,-2,-4,-3] => 1
[-1,2,4,3] => 1
[-1,2,4,-3] => 0
[-1,2,-4,3] => 0
[-1,2,-4,-3] => 1
[-1,-2,4,3] => 9
[-1,-2,4,-3] => 0
[-1,-2,-4,3] => 0
[-1,-2,-4,-3] => 9
[1,3,2,4] => 1
[1,3,2,-4] => 1
[1,3,-2,4] => 0
[1,3,-2,-4] => 0
[1,-3,2,4] => 0
[1,-3,2,-4] => 0
[1,-3,-2,4] => 3
[1,-3,-2,-4] => 3
[-1,3,2,4] => 1
[-1,3,2,-4] => 3
[-1,3,-2,4] => 0
>>> Load all 1200 entries. <<<
[-1,3,-2,-4] => 0
[-1,-3,2,4] => 0
[-1,-3,2,-4] => 0
[-1,-3,-2,4] => 3
[-1,-3,-2,-4] => 5
[1,3,4,2] => 0
[1,3,4,-2] => 0
[1,3,-4,2] => 0
[1,3,-4,-2] => 0
[1,-3,4,2] => 0
[1,-3,4,-2] => 0
[1,-3,-4,2] => 0
[1,-3,-4,-2] => 0
[-1,3,4,2] => 0
[-1,3,4,-2] => 0
[-1,3,-4,2] => 0
[-1,3,-4,-2] => 0
[-1,-3,4,2] => 0
[-1,-3,4,-2] => 0
[-1,-3,-4,2] => 0
[-1,-3,-4,-2] => 0
[1,4,2,3] => 0
[1,4,2,-3] => 0
[1,4,-2,3] => 0
[1,4,-2,-3] => 0
[1,-4,2,3] => 0
[1,-4,2,-3] => 0
[1,-4,-2,3] => 0
[1,-4,-2,-3] => 0
[-1,4,2,3] => 0
[-1,4,2,-3] => 0
[-1,4,-2,3] => 0
[-1,4,-2,-3] => 0
[-1,-4,2,3] => 0
[-1,-4,2,-3] => 0
[-1,-4,-2,3] => 0
[-1,-4,-2,-3] => 0
[1,4,3,2] => 3
[1,4,3,-2] => 0
[1,4,-3,2] => 1
[1,4,-3,-2] => 0
[1,-4,3,2] => 0
[1,-4,3,-2] => 3
[1,-4,-3,2] => 0
[1,-4,-3,-2] => 1
[-1,4,3,2] => 3
[-1,4,3,-2] => 0
[-1,4,-3,2] => 3
[-1,4,-3,-2] => 0
[-1,-4,3,2] => 0
[-1,-4,3,-2] => 3
[-1,-4,-3,2] => 0
[-1,-4,-3,-2] => 3
[2,1,3,4] => 1
[2,1,3,-4] => 1
[2,1,-3,4] => 1
[2,1,-3,-4] => 3
[2,-1,3,4] => 0
[2,-1,3,-4] => 0
[2,-1,-3,4] => 0
[2,-1,-3,-4] => 0
[-2,1,3,4] => 0
[-2,1,3,-4] => 0
[-2,1,-3,4] => 0
[-2,1,-3,-4] => 0
[-2,-1,3,4] => 5
[-2,-1,3,-4] => 5
[-2,-1,-3,4] => 5
[-2,-1,-3,-4] => 19
[2,1,4,3] => 1
[2,1,4,-3] => 0
[2,1,-4,3] => 0
[2,1,-4,-3] => 1
[2,-1,4,3] => 0
[2,-1,4,-3] => 0
[2,-1,-4,3] => 0
[2,-1,-4,-3] => 0
[-2,1,4,3] => 0
[-2,1,4,-3] => 0
[-2,1,-4,3] => 0
[-2,1,-4,-3] => 0
[-2,-1,4,3] => 7
[-2,-1,4,-3] => 0
[-2,-1,-4,3] => 0
[-2,-1,-4,-3] => 7
[2,3,1,4] => 0
[2,3,1,-4] => 0
[2,3,-1,4] => 0
[2,3,-1,-4] => 0
[2,-3,1,4] => 0
[2,-3,1,-4] => 0
[2,-3,-1,4] => 0
[2,-3,-1,-4] => 0
[-2,3,1,4] => 0
[-2,3,1,-4] => 0
[-2,3,-1,4] => 0
[-2,3,-1,-4] => 0
[-2,-3,1,4] => 0
[-2,-3,1,-4] => 0
[-2,-3,-1,4] => 0
[-2,-3,-1,-4] => 0
[2,3,4,1] => 0
[2,3,4,-1] => 0
[2,3,-4,1] => 0
[2,3,-4,-1] => 0
[2,-3,4,1] => 0
[2,-3,4,-1] => 0
[2,-3,-4,1] => 0
[2,-3,-4,-1] => 0
[-2,3,4,1] => 0
[-2,3,4,-1] => 0
[-2,3,-4,1] => 0
[-2,3,-4,-1] => 0
[-2,-3,4,1] => 0
[-2,-3,4,-1] => 0
[-2,-3,-4,1] => 0
[-2,-3,-4,-1] => 0
[2,4,1,3] => 0
[2,4,1,-3] => 0
[2,4,-1,3] => 0
[2,4,-1,-3] => 0
[2,-4,1,3] => 0
[2,-4,1,-3] => 0
[2,-4,-1,3] => 0
[2,-4,-1,-3] => 0
[-2,4,1,3] => 0
[-2,4,1,-3] => 0
[-2,4,-1,3] => 0
[-2,4,-1,-3] => 0
[-2,-4,1,3] => 0
[-2,-4,1,-3] => 0
[-2,-4,-1,3] => 0
[-2,-4,-1,-3] => 0
[2,4,3,1] => 0
[2,4,3,-1] => 0
[2,4,-3,1] => 0
[2,4,-3,-1] => 0
[2,-4,3,1] => 0
[2,-4,3,-1] => 0
[2,-4,-3,1] => 0
[2,-4,-3,-1] => 0
[-2,4,3,1] => 0
[-2,4,3,-1] => 0
[-2,4,-3,1] => 0
[-2,4,-3,-1] => 0
[-2,-4,3,1] => 0
[-2,-4,3,-1] => 0
[-2,-4,-3,1] => 0
[-2,-4,-3,-1] => 0
[3,1,2,4] => 0
[3,1,2,-4] => 0
[3,1,-2,4] => 0
[3,1,-2,-4] => 0
[3,-1,2,4] => 0
[3,-1,2,-4] => 0
[3,-1,-2,4] => 0
[3,-1,-2,-4] => 0
[-3,1,2,4] => 0
[-3,1,2,-4] => 0
[-3,1,-2,4] => 0
[-3,1,-2,-4] => 0
[-3,-1,2,4] => 0
[-3,-1,2,-4] => 0
[-3,-1,-2,4] => 0
[-3,-1,-2,-4] => 0
[3,1,4,2] => 0
[3,1,4,-2] => 0
[3,1,-4,2] => 0
[3,1,-4,-2] => 0
[3,-1,4,2] => 0
[3,-1,4,-2] => 0
[3,-1,-4,2] => 0
[3,-1,-4,-2] => 0
[-3,1,4,2] => 0
[-3,1,4,-2] => 0
[-3,1,-4,2] => 0
[-3,1,-4,-2] => 0
[-3,-1,4,2] => 0
[-3,-1,4,-2] => 0
[-3,-1,-4,2] => 0
[-3,-1,-4,-2] => 0
[3,2,1,4] => 3
[3,2,1,-4] => 3
[3,2,-1,4] => 0
[3,2,-1,-4] => 0
[3,-2,1,4] => 1
[3,-2,1,-4] => 3
[3,-2,-1,4] => 0
[3,-2,-1,-4] => 0
[-3,2,1,4] => 0
[-3,2,1,-4] => 0
[-3,2,-1,4] => 5
[-3,2,-1,-4] => 5
[-3,-2,1,4] => 0
[-3,-2,1,-4] => 0
[-3,-2,-1,4] => 3
[-3,-2,-1,-4] => 5
[3,2,4,1] => 0
[3,2,4,-1] => 0
[3,2,-4,1] => 0
[3,2,-4,-1] => 0
[3,-2,4,1] => 0
[3,-2,4,-1] => 0
[3,-2,-4,1] => 0
[3,-2,-4,-1] => 0
[-3,2,4,1] => 0
[-3,2,4,-1] => 0
[-3,2,-4,1] => 0
[-3,2,-4,-1] => 0
[-3,-2,4,1] => 0
[-3,-2,4,-1] => 0
[-3,-2,-4,1] => 0
[-3,-2,-4,-1] => 0
[3,4,1,2] => 1
[3,4,1,-2] => 0
[3,4,-1,2] => 0
[3,4,-1,-2] => 0
[3,-4,1,2] => 0
[3,-4,1,-2] => 1
[3,-4,-1,2] => 0
[3,-4,-1,-2] => 0
[-3,4,1,2] => 0
[-3,4,1,-2] => 0
[-3,4,-1,2] => 7
[-3,4,-1,-2] => 0
[-3,-4,1,2] => 0
[-3,-4,1,-2] => 0
[-3,-4,-1,2] => 0
[-3,-4,-1,-2] => 7
[3,4,2,1] => 0
[3,4,2,-1] => 0
[3,4,-2,1] => 0
[3,4,-2,-1] => 0
[3,-4,2,1] => 0
[3,-4,2,-1] => 0
[3,-4,-2,1] => 0
[3,-4,-2,-1] => 0
[-3,4,2,1] => 0
[-3,4,2,-1] => 0
[-3,4,-2,1] => 0
[-3,4,-2,-1] => 0
[-3,-4,2,1] => 0
[-3,-4,2,-1] => 0
[-3,-4,-2,1] => 0
[-3,-4,-2,-1] => 0
[4,1,2,3] => 0
[4,1,2,-3] => 0
[4,1,-2,3] => 0
[4,1,-2,-3] => 0
[4,-1,2,3] => 0
[4,-1,2,-3] => 0
[4,-1,-2,3] => 0
[4,-1,-2,-3] => 0
[-4,1,2,3] => 0
[-4,1,2,-3] => 0
[-4,1,-2,3] => 0
[-4,1,-2,-3] => 0
[-4,-1,2,3] => 0
[-4,-1,2,-3] => 0
[-4,-1,-2,3] => 0
[-4,-1,-2,-3] => 0
[4,1,3,2] => 0
[4,1,3,-2] => 0
[4,1,-3,2] => 0
[4,1,-3,-2] => 0
[4,-1,3,2] => 0
[4,-1,3,-2] => 0
[4,-1,-3,2] => 0
[4,-1,-3,-2] => 0
[-4,1,3,2] => 0
[-4,1,3,-2] => 0
[-4,1,-3,2] => 0
[-4,1,-3,-2] => 0
[-4,-1,3,2] => 0
[-4,-1,3,-2] => 0
[-4,-1,-3,2] => 0
[-4,-1,-3,-2] => 0
[4,2,1,3] => 0
[4,2,1,-3] => 0
[4,2,-1,3] => 0
[4,2,-1,-3] => 0
[4,-2,1,3] => 0
[4,-2,1,-3] => 0
[4,-2,-1,3] => 0
[4,-2,-1,-3] => 0
[-4,2,1,3] => 0
[-4,2,1,-3] => 0
[-4,2,-1,3] => 0
[-4,2,-1,-3] => 0
[-4,-2,1,3] => 0
[-4,-2,1,-3] => 0
[-4,-2,-1,3] => 0
[-4,-2,-1,-3] => 0
[4,2,3,1] => 5
[4,2,3,-1] => 0
[4,2,-3,1] => 3
[4,2,-3,-1] => 0
[4,-2,3,1] => 3
[4,-2,3,-1] => 0
[4,-2,-3,1] => 3
[4,-2,-3,-1] => 0
[-4,2,3,1] => 0
[-4,2,3,-1] => 5
[-4,2,-3,1] => 0
[-4,2,-3,-1] => 3
[-4,-2,3,1] => 0
[-4,-2,3,-1] => 3
[-4,-2,-3,1] => 0
[-4,-2,-3,-1] => 3
[4,3,1,2] => 0
[4,3,1,-2] => 0
[4,3,-1,2] => 0
[4,3,-1,-2] => 0
[4,-3,1,2] => 0
[4,-3,1,-2] => 0
[4,-3,-1,2] => 0
[4,-3,-1,-2] => 0
[-4,3,1,2] => 0
[-4,3,1,-2] => 0
[-4,3,-1,2] => 0
[-4,3,-1,-2] => 0
[-4,-3,1,2] => 0
[-4,-3,1,-2] => 0
[-4,-3,-1,2] => 0
[-4,-3,-1,-2] => 0
[4,3,2,1] => 7
[4,3,2,-1] => 0
[4,3,-2,1] => 0
[4,3,-2,-1] => 0
[4,-3,2,1] => 0
[4,-3,2,-1] => 0
[4,-3,-2,1] => 1
[4,-3,-2,-1] => 0
[-4,3,2,1] => 0
[-4,3,2,-1] => 7
[-4,3,-2,1] => 0
[-4,3,-2,-1] => 0
[-4,-3,2,1] => 0
[-4,-3,2,-1] => 0
[-4,-3,-2,1] => 0
[-4,-3,-2,-1] => 1
[1,2,3,4,5] => 1
[1,2,3,4,-5] => 1
[1,2,3,-4,5] => 1
[1,2,3,-4,-5] => 3
[1,2,-3,4,5] => 1
[1,2,-3,4,-5] => 3
[1,2,-3,-4,5] => 5
[1,2,-3,-4,-5] => 13
[1,-2,3,4,5] => 1
[1,-2,3,4,-5] => 3
[1,-2,3,-4,5] => 5
[1,-2,3,-4,-5] => 13
[1,-2,-3,4,5] => 7
[1,-2,-3,4,-5] => 15
[1,-2,-3,-4,5] => 19
[1,-2,-3,-4,-5] => 85
[-1,2,3,4,5] => 1
[-1,2,3,4,-5] => 3
[-1,2,3,-4,5] => 5
[-1,2,3,-4,-5] => 13
[-1,2,-3,4,5] => 7
[-1,2,-3,4,-5] => 15
[-1,2,-3,-4,5] => 19
[-1,2,-3,-4,-5] => 85
[-1,-2,3,4,5] => 9
[-1,-2,3,4,-5] => 17
[-1,-2,3,-4,5] => 21
[-1,-2,3,-4,-5] => 91
[-1,-2,-3,4,5] => 25
[-1,-2,-3,4,-5] => 103
[-1,-2,-3,-4,5] => 169
[-1,-2,-3,-4,-5] => 681
[1,2,3,5,4] => 1
[1,2,3,5,-4] => 0
[1,2,3,-5,4] => 0
[1,2,3,-5,-4] => 1
[1,2,-3,5,4] => 1
[1,2,-3,5,-4] => 0
[1,2,-3,-5,4] => 0
[1,2,-3,-5,-4] => 1
[1,-2,3,5,4] => 1
[1,-2,3,5,-4] => 0
[1,-2,3,-5,4] => 0
[1,-2,3,-5,-4] => 1
[1,-2,-3,5,4] => 9
[1,-2,-3,5,-4] => 0
[1,-2,-3,-5,4] => 0
[1,-2,-3,-5,-4] => 9
[-1,2,3,5,4] => 1
[-1,2,3,5,-4] => 0
[-1,2,3,-5,4] => 0
[-1,2,3,-5,-4] => 1
[-1,2,-3,5,4] => 9
[-1,2,-3,5,-4] => 0
[-1,2,-3,-5,4] => 0
[-1,2,-3,-5,-4] => 9
[-1,-2,3,5,4] => 11
[-1,-2,3,5,-4] => 0
[-1,-2,3,-5,4] => 0
[-1,-2,3,-5,-4] => 11
[-1,-2,-3,5,4] => 31
[-1,-2,-3,5,-4] => 0
[-1,-2,-3,-5,4] => 0
[-1,-2,-3,-5,-4] => 31
[1,2,4,3,5] => 1
[1,2,4,3,-5] => 1
[1,2,4,-3,5] => 0
[1,2,4,-3,-5] => 0
[1,2,-4,3,5] => 0
[1,2,-4,3,-5] => 0
[1,2,-4,-3,5] => 3
[1,2,-4,-3,-5] => 3
[1,-2,4,3,5] => 1
[1,-2,4,3,-5] => 3
[1,-2,4,-3,5] => 0
[1,-2,4,-3,-5] => 0
[1,-2,-4,3,5] => 0
[1,-2,-4,3,-5] => 0
[1,-2,-4,-3,5] => 3
[1,-2,-4,-3,-5] => 5
[-1,2,4,3,5] => 1
[-1,2,4,3,-5] => 3
[-1,2,4,-3,5] => 0
[-1,2,4,-3,-5] => 0
[-1,2,-4,3,5] => 0
[-1,2,-4,3,-5] => 0
[-1,2,-4,-3,5] => 3
[-1,2,-4,-3,-5] => 5
[-1,-2,4,3,5] => 11
[-1,-2,4,3,-5] => 19
[-1,-2,4,-3,5] => 0
[-1,-2,4,-3,-5] => 0
[-1,-2,-4,3,5] => 0
[-1,-2,-4,3,-5] => 0
[-1,-2,-4,-3,5] => 41
[-1,-2,-4,-3,-5] => 49
[1,2,4,5,3] => 0
[1,2,4,5,-3] => 0
[1,2,4,-5,3] => 0
[1,2,4,-5,-3] => 0
[1,2,-4,5,3] => 0
[1,2,-4,5,-3] => 0
[1,2,-4,-5,3] => 0
[1,2,-4,-5,-3] => 0
[1,-2,4,5,3] => 0
[1,-2,4,5,-3] => 0
[1,-2,4,-5,3] => 0
[1,-2,4,-5,-3] => 0
[1,-2,-4,5,3] => 0
[1,-2,-4,5,-3] => 0
[1,-2,-4,-5,3] => 0
[1,-2,-4,-5,-3] => 0
[-1,2,4,5,3] => 0
[-1,2,4,5,-3] => 0
[-1,2,4,-5,3] => 0
[-1,2,4,-5,-3] => 0
[-1,2,-4,5,3] => 0
[-1,2,-4,5,-3] => 0
[-1,2,-4,-5,3] => 0
[-1,2,-4,-5,-3] => 0
[-1,-2,4,5,3] => 0
[-1,-2,4,5,-3] => 0
[-1,-2,4,-5,3] => 0
[-1,-2,4,-5,-3] => 0
[-1,-2,-4,5,3] => 0
[-1,-2,-4,5,-3] => 0
[-1,-2,-4,-5,3] => 0
[-1,-2,-4,-5,-3] => 0
[1,2,5,3,4] => 0
[1,2,5,3,-4] => 0
[1,2,5,-3,4] => 0
[1,2,5,-3,-4] => 0
[1,2,-5,3,4] => 0
[1,2,-5,3,-4] => 0
[1,2,-5,-3,4] => 0
[1,2,-5,-3,-4] => 0
[1,-2,5,3,4] => 0
[1,-2,5,3,-4] => 0
[1,-2,5,-3,4] => 0
[1,-2,5,-3,-4] => 0
[1,-2,-5,3,4] => 0
[1,-2,-5,3,-4] => 0
[1,-2,-5,-3,4] => 0
[1,-2,-5,-3,-4] => 0
[-1,2,5,3,4] => 0
[-1,2,5,3,-4] => 0
[-1,2,5,-3,4] => 0
[-1,2,5,-3,-4] => 0
[-1,2,-5,3,4] => 0
[-1,2,-5,3,-4] => 0
[-1,2,-5,-3,4] => 0
[-1,2,-5,-3,-4] => 0
[-1,-2,5,3,4] => 0
[-1,-2,5,3,-4] => 0
[-1,-2,5,-3,4] => 0
[-1,-2,5,-3,-4] => 0
[-1,-2,-5,3,4] => 0
[-1,-2,-5,3,-4] => 0
[-1,-2,-5,-3,4] => 0
[-1,-2,-5,-3,-4] => 0
[1,2,5,4,3] => 3
[1,2,5,4,-3] => 0
[1,2,5,-4,3] => 1
[1,2,5,-4,-3] => 0
[1,2,-5,4,3] => 0
[1,2,-5,4,-3] => 3
[1,2,-5,-4,3] => 0
[1,2,-5,-4,-3] => 1
[1,-2,5,4,3] => 3
[1,-2,5,4,-3] => 0
[1,-2,5,-4,3] => 3
[1,-2,5,-4,-3] => 0
[1,-2,-5,4,3] => 0
[1,-2,-5,4,-3] => 3
[1,-2,-5,-4,3] => 0
[1,-2,-5,-4,-3] => 3
[-1,2,5,4,3] => 3
[-1,2,5,4,-3] => 0
[-1,2,5,-4,3] => 3
[-1,2,5,-4,-3] => 0
[-1,2,-5,4,3] => 0
[-1,2,-5,4,-3] => 3
[-1,2,-5,-4,3] => 0
[-1,2,-5,-4,-3] => 3
[-1,-2,5,4,3] => 41
[-1,-2,5,4,-3] => 0
[-1,-2,5,-4,3] => 19
[-1,-2,5,-4,-3] => 0
[-1,-2,-5,4,3] => 0
[-1,-2,-5,4,-3] => 41
[-1,-2,-5,-4,3] => 0
[-1,-2,-5,-4,-3] => 19
[1,3,2,4,5] => 1
[1,3,2,4,-5] => 1
[1,3,2,-4,5] => 1
[1,3,2,-4,-5] => 3
[1,3,-2,4,5] => 0
[1,3,-2,4,-5] => 0
[1,3,-2,-4,5] => 0
[1,3,-2,-4,-5] => 0
[1,-3,2,4,5] => 0
[1,-3,2,4,-5] => 0
[1,-3,2,-4,5] => 0
[1,-3,2,-4,-5] => 0
[1,-3,-2,4,5] => 5
[1,-3,-2,4,-5] => 5
[1,-3,-2,-4,5] => 5
[1,-3,-2,-4,-5] => 19
[-1,3,2,4,5] => 1
[-1,3,2,4,-5] => 3
[-1,3,2,-4,5] => 5
[-1,3,2,-4,-5] => 13
[-1,3,-2,4,5] => 0
[-1,3,-2,4,-5] => 0
[-1,3,-2,-4,5] => 0
[-1,3,-2,-4,-5] => 0
[-1,-3,2,4,5] => 0
[-1,-3,2,4,-5] => 0
[-1,-3,2,-4,5] => 0
[-1,-3,2,-4,-5] => 0
[-1,-3,-2,4,5] => 5
[-1,-3,-2,4,-5] => 11
[-1,-3,-2,-4,5] => 13
[-1,-3,-2,-4,-5] => 37
[1,3,2,5,4] => 1
[1,3,2,5,-4] => 0
[1,3,2,-5,4] => 0
[1,3,2,-5,-4] => 1
[1,3,-2,5,4] => 0
[1,3,-2,5,-4] => 0
[1,3,-2,-5,4] => 0
[1,3,-2,-5,-4] => 0
[1,-3,2,5,4] => 0
[1,-3,2,5,-4] => 0
[1,-3,2,-5,4] => 0
[1,-3,2,-5,-4] => 0
[1,-3,-2,5,4] => 7
[1,-3,-2,5,-4] => 0
[1,-3,-2,-5,4] => 0
[1,-3,-2,-5,-4] => 7
[-1,3,2,5,4] => 1
[-1,3,2,5,-4] => 0
[-1,3,2,-5,4] => 0
[-1,3,2,-5,-4] => 1
[-1,3,-2,5,4] => 0
[-1,3,-2,5,-4] => 0
[-1,3,-2,-5,4] => 0
[-1,3,-2,-5,-4] => 0
[-1,-3,2,5,4] => 0
[-1,-3,2,5,-4] => 0
[-1,-3,2,-5,4] => 0
[-1,-3,2,-5,-4] => 0
[-1,-3,-2,5,4] => 7
[-1,-3,-2,5,-4] => 0
[-1,-3,-2,-5,4] => 0
[-1,-3,-2,-5,-4] => 7
[1,3,4,2,5] => 0
[1,3,4,2,-5] => 0
[1,3,4,-2,5] => 0
[1,3,4,-2,-5] => 0
[1,3,-4,2,5] => 0
[1,3,-4,2,-5] => 0
[1,3,-4,-2,5] => 0
[1,3,-4,-2,-5] => 0
[1,-3,4,2,5] => 0
[1,-3,4,2,-5] => 0
[1,-3,4,-2,5] => 0
[1,-3,4,-2,-5] => 0
[1,-3,-4,2,5] => 0
[1,-3,-4,2,-5] => 0
[1,-3,-4,-2,5] => 0
[1,-3,-4,-2,-5] => 0
[-1,3,4,2,5] => 0
[-1,3,4,2,-5] => 0
[-1,3,4,-2,5] => 0
[-1,3,4,-2,-5] => 0
[-1,3,-4,2,5] => 0
[-1,3,-4,2,-5] => 0
[-1,3,-4,-2,5] => 0
[-1,3,-4,-2,-5] => 0
[-1,-3,4,2,5] => 0
[-1,-3,4,2,-5] => 0
[-1,-3,4,-2,5] => 0
[-1,-3,4,-2,-5] => 0
[-1,-3,-4,2,5] => 0
[-1,-3,-4,2,-5] => 0
[-1,-3,-4,-2,5] => 0
[-1,-3,-4,-2,-5] => 0
[1,3,4,5,2] => 0
[1,3,4,5,-2] => 0
[1,3,4,-5,2] => 0
[1,3,4,-5,-2] => 0
[1,3,-4,5,2] => 0
[1,3,-4,5,-2] => 0
[1,3,-4,-5,2] => 0
[1,3,-4,-5,-2] => 0
[1,-3,4,5,2] => 0
[1,-3,4,5,-2] => 0
[1,-3,4,-5,2] => 0
[1,-3,4,-5,-2] => 0
[1,-3,-4,5,2] => 0
[1,-3,-4,5,-2] => 0
[1,-3,-4,-5,2] => 0
[1,-3,-4,-5,-2] => 0
[-1,3,4,5,2] => 0
[-1,3,4,5,-2] => 0
[-1,3,4,-5,2] => 0
[-1,3,4,-5,-2] => 0
[-1,3,-4,5,2] => 0
[-1,3,-4,5,-2] => 0
[-1,3,-4,-5,2] => 0
[-1,3,-4,-5,-2] => 0
[-1,-3,4,5,2] => 0
[-1,-3,4,5,-2] => 0
[-1,-3,4,-5,2] => 0
[-1,-3,4,-5,-2] => 0
[-1,-3,-4,5,2] => 0
[-1,-3,-4,5,-2] => 0
[-1,-3,-4,-5,2] => 0
[-1,-3,-4,-5,-2] => 0
[1,3,5,2,4] => 0
[1,3,5,2,-4] => 0
[1,3,5,-2,4] => 0
[1,3,5,-2,-4] => 0
[1,3,-5,2,4] => 0
[1,3,-5,2,-4] => 0
[1,3,-5,-2,4] => 0
[1,3,-5,-2,-4] => 0
[1,-3,5,2,4] => 0
[1,-3,5,2,-4] => 0
[1,-3,5,-2,4] => 0
[1,-3,5,-2,-4] => 0
[1,-3,-5,2,4] => 0
[1,-3,-5,2,-4] => 0
[1,-3,-5,-2,4] => 0
[1,-3,-5,-2,-4] => 0
[-1,3,5,2,4] => 0
[-1,3,5,2,-4] => 0
[-1,3,5,-2,4] => 0
[-1,3,5,-2,-4] => 0
[-1,3,-5,2,4] => 0
[-1,3,-5,2,-4] => 0
[-1,3,-5,-2,4] => 0
[-1,3,-5,-2,-4] => 0
[-1,-3,5,2,4] => 0
[-1,-3,5,2,-4] => 0
[-1,-3,5,-2,4] => 0
[-1,-3,5,-2,-4] => 0
[-1,-3,-5,2,4] => 0
[-1,-3,-5,2,-4] => 0
[-1,-3,-5,-2,4] => 0
[-1,-3,-5,-2,-4] => 0
[1,3,5,4,2] => 0
[1,3,5,4,-2] => 0
[1,3,5,-4,2] => 0
[1,3,5,-4,-2] => 0
[1,3,-5,4,2] => 0
[1,3,-5,4,-2] => 0
[1,3,-5,-4,2] => 0
[1,3,-5,-4,-2] => 0
[1,-3,5,4,2] => 0
[1,-3,5,4,-2] => 0
[1,-3,5,-4,2] => 0
[1,-3,5,-4,-2] => 0
[1,-3,-5,4,2] => 0
[1,-3,-5,4,-2] => 0
[1,-3,-5,-4,2] => 0
[1,-3,-5,-4,-2] => 0
[-1,3,5,4,2] => 0
[-1,3,5,4,-2] => 0
[-1,3,5,-4,2] => 0
[-1,3,5,-4,-2] => 0
[-1,3,-5,4,2] => 0
[-1,3,-5,4,-2] => 0
[-1,3,-5,-4,2] => 0
[-1,3,-5,-4,-2] => 0
[-1,-3,5,4,2] => 0
[-1,-3,5,4,-2] => 0
[-1,-3,5,-4,2] => 0
[-1,-3,5,-4,-2] => 0
[-1,-3,-5,4,2] => 0
[-1,-3,-5,4,-2] => 0
[-1,-3,-5,-4,2] => 0
[-1,-3,-5,-4,-2] => 0
[1,4,2,3,5] => 0
[1,4,2,3,-5] => 0
[1,4,2,-3,5] => 0
[1,4,2,-3,-5] => 0
[1,4,-2,3,5] => 0
[1,4,-2,3,-5] => 0
[1,4,-2,-3,5] => 0
[1,4,-2,-3,-5] => 0
[1,-4,2,3,5] => 0
[1,-4,2,3,-5] => 0
[1,-4,2,-3,5] => 0
[1,-4,2,-3,-5] => 0
[1,-4,-2,3,5] => 0
[1,-4,-2,3,-5] => 0
[1,-4,-2,-3,5] => 0
[1,-4,-2,-3,-5] => 0
[-1,4,2,3,5] => 0
[-1,4,2,3,-5] => 0
[-1,4,2,-3,5] => 0
[-1,4,2,-3,-5] => 0
[-1,4,-2,3,5] => 0
[-1,4,-2,3,-5] => 0
[-1,4,-2,-3,5] => 0
[-1,4,-2,-3,-5] => 0
[-1,-4,2,3,5] => 0
[-1,-4,2,3,-5] => 0
[-1,-4,2,-3,5] => 0
[-1,-4,2,-3,-5] => 0
[-1,-4,-2,3,5] => 0
[-1,-4,-2,3,-5] => 0
[-1,-4,-2,-3,5] => 0
[-1,-4,-2,-3,-5] => 0
[1,4,2,5,3] => 0
[1,4,2,5,-3] => 0
[1,4,2,-5,3] => 0
[1,4,2,-5,-3] => 0
[1,4,-2,5,3] => 0
[1,4,-2,5,-3] => 0
[1,4,-2,-5,3] => 0
[1,4,-2,-5,-3] => 0
[1,-4,2,5,3] => 0
[1,-4,2,5,-3] => 0
[1,-4,2,-5,3] => 0
[1,-4,2,-5,-3] => 0
[1,-4,-2,5,3] => 0
[1,-4,-2,5,-3] => 0
[1,-4,-2,-5,3] => 0
[1,-4,-2,-5,-3] => 0
[-1,4,2,5,3] => 0
[-1,4,2,5,-3] => 0
[-1,4,2,-5,3] => 0
[-1,4,2,-5,-3] => 0
[-1,4,-2,5,3] => 0
[-1,4,-2,5,-3] => 0
[-1,4,-2,-5,3] => 0
[-1,4,-2,-5,-3] => 0
[-1,-4,2,5,3] => 0
[-1,-4,2,5,-3] => 0
[-1,-4,2,-5,3] => 0
[-1,-4,2,-5,-3] => 0
[-1,-4,-2,5,3] => 0
[-1,-4,-2,5,-3] => 0
[-1,-4,-2,-5,3] => 0
[-1,-4,-2,-5,-3] => 0
[1,4,3,2,5] => 3
[1,4,3,2,-5] => 3
[1,4,3,-2,5] => 0
[1,4,3,-2,-5] => 0
[1,4,-3,2,5] => 1
[1,4,-3,2,-5] => 3
[1,4,-3,-2,5] => 0
[1,4,-3,-2,-5] => 0
[1,-4,3,2,5] => 0
[1,-4,3,2,-5] => 0
[1,-4,3,-2,5] => 5
[1,-4,3,-2,-5] => 5
[1,-4,-3,2,5] => 0
[1,-4,-3,2,-5] => 0
[1,-4,-3,-2,5] => 3
[1,-4,-3,-2,-5] => 5
[-1,4,3,2,5] => 3
[-1,4,3,2,-5] => 9
[-1,4,3,-2,5] => 0
[-1,4,3,-2,-5] => 0
[-1,4,-3,2,5] => 5
[-1,4,-3,2,-5] => 13
[-1,4,-3,-2,5] => 0
[-1,4,-3,-2,-5] => 0
[-1,-4,3,2,5] => 0
[-1,-4,3,2,-5] => 0
[-1,-4,3,-2,5] => 5
[-1,-4,3,-2,-5] => 11
[-1,-4,-3,2,5] => 0
[-1,-4,-3,2,-5] => 0
[-1,-4,-3,-2,5] => 11
[-1,-4,-3,-2,-5] => 19
[1,4,3,5,2] => 0
[1,4,3,5,-2] => 0
[1,4,3,-5,2] => 0
[1,4,3,-5,-2] => 0
[1,4,-3,5,2] => 0
[1,4,-3,5,-2] => 0
[1,4,-3,-5,2] => 0
[1,4,-3,-5,-2] => 0
[1,-4,3,5,2] => 0
[1,-4,3,5,-2] => 0
[1,-4,3,-5,2] => 0
[1,-4,3,-5,-2] => 0
[1,-4,-3,5,2] => 0
[1,-4,-3,5,-2] => 0
[1,-4,-3,-5,2] => 0
[1,-4,-3,-5,-2] => 0
[-1,4,3,5,2] => 0
[-1,4,3,5,-2] => 0
[-1,4,3,-5,2] => 0
[-1,4,3,-5,-2] => 0
[-1,4,-3,5,2] => 0
[-1,4,-3,5,-2] => 0
[-1,4,-3,-5,2] => 0
[-1,4,-3,-5,-2] => 0
[-1,-4,3,5,2] => 0
[-1,-4,3,5,-2] => 0
[-1,-4,3,-5,2] => 0
[-1,-4,3,-5,-2] => 0
[-1,-4,-3,5,2] => 0
[-1,-4,-3,5,-2] => 0
[-1,-4,-3,-5,2] => 0
[-1,-4,-3,-5,-2] => 0
[1,4,5,2,3] => 1
[1,4,5,2,-3] => 0
[1,4,5,-2,3] => 0
[1,4,5,-2,-3] => 0
[1,4,-5,2,3] => 0
[1,4,-5,2,-3] => 1
[1,4,-5,-2,3] => 0
[1,4,-5,-2,-3] => 0
[1,-4,5,2,3] => 0
[1,-4,5,2,-3] => 0
[1,-4,5,-2,3] => 7
[1,-4,5,-2,-3] => 0
[1,-4,-5,2,3] => 0
[1,-4,-5,2,-3] => 0
[1,-4,-5,-2,3] => 0
[1,-4,-5,-2,-3] => 7
[-1,4,5,2,3] => 1
[-1,4,5,2,-3] => 0
[-1,4,5,-2,3] => 0
[-1,4,5,-2,-3] => 0
[-1,4,-5,2,3] => 0
[-1,4,-5,2,-3] => 1
[-1,4,-5,-2,3] => 0
[-1,4,-5,-2,-3] => 0
[-1,-4,5,2,3] => 0
[-1,-4,5,2,-3] => 0
[-1,-4,5,-2,3] => 7
[-1,-4,5,-2,-3] => 0
[-1,-4,-5,2,3] => 0
[-1,-4,-5,2,-3] => 0
[-1,-4,-5,-2,3] => 0
[-1,-4,-5,-2,-3] => 7
[1,4,5,3,2] => 0
[1,4,5,3,-2] => 0
[1,4,5,-3,2] => 0
[1,4,5,-3,-2] => 0
[1,4,-5,3,2] => 0
[1,4,-5,3,-2] => 0
[1,4,-5,-3,2] => 0
[1,4,-5,-3,-2] => 0
[1,-4,5,3,2] => 0
[1,-4,5,3,-2] => 0
[1,-4,5,-3,2] => 0
[1,-4,5,-3,-2] => 0
[1,-4,-5,3,2] => 0
[1,-4,-5,3,-2] => 0
[1,-4,-5,-3,2] => 0
[1,-4,-5,-3,-2] => 0
[-1,4,5,3,2] => 0
[-1,4,5,3,-2] => 0
[-1,4,5,-3,2] => 0
[-1,4,5,-3,-2] => 0
[-1,4,-5,3,2] => 0
[-1,4,-5,3,-2] => 0
[-1,4,-5,-3,2] => 0
[-1,4,-5,-3,-2] => 0
[-1,-4,5,3,2] => 0
[-1,-4,5,3,-2] => 0
[-1,-4,5,-3,2] => 0
[-1,-4,5,-3,-2] => 0
[-1,-4,-5,3,2] => 0
[-1,-4,-5,3,-2] => 0
[-1,-4,-5,-3,2] => 0
[-1,-4,-5,-3,-2] => 0
[1,5,2,3,4] => 0
[1,5,2,3,-4] => 0
[1,5,2,-3,4] => 0
[1,5,2,-3,-4] => 0
[1,5,-2,3,4] => 0
[1,5,-2,3,-4] => 0
[1,5,-2,-3,4] => 0
[1,5,-2,-3,-4] => 0
[1,-5,2,3,4] => 0
[1,-5,2,3,-4] => 0
[1,-5,2,-3,4] => 0
[1,-5,2,-3,-4] => 0
[1,-5,-2,3,4] => 0
[1,-5,-2,3,-4] => 0
[1,-5,-2,-3,4] => 0
[1,-5,-2,-3,-4] => 0
[-1,5,2,3,4] => 0
[-1,5,2,3,-4] => 0
[-1,5,2,-3,4] => 0
[-1,5,2,-3,-4] => 0
[-1,5,-2,3,4] => 0
[-1,5,-2,3,-4] => 0
[-1,5,-2,-3,4] => 0
[-1,5,-2,-3,-4] => 0
[-1,-5,2,3,4] => 0
[-1,-5,2,3,-4] => 0
[-1,-5,2,-3,4] => 0
[-1,-5,2,-3,-4] => 0
[-1,-5,-2,3,4] => 0
[-1,-5,-2,3,-4] => 0
[-1,-5,-2,-3,4] => 0
[-1,-5,-2,-3,-4] => 0
[1,5,2,4,3] => 0
[1,5,2,4,-3] => 0
[1,5,2,-4,3] => 0
[1,5,2,-4,-3] => 0
[1,5,-2,4,3] => 0
[1,5,-2,4,-3] => 0
[1,5,-2,-4,3] => 0
[1,5,-2,-4,-3] => 0
[1,-5,2,4,3] => 0
[1,-5,2,4,-3] => 0
[1,-5,2,-4,3] => 0
[1,-5,2,-4,-3] => 0
[1,-5,-2,4,3] => 0
[1,-5,-2,4,-3] => 0
[1,-5,-2,-4,3] => 0
[1,-5,-2,-4,-3] => 0
[-1,5,2,4,3] => 0
[-1,5,2,4,-3] => 0
[-1,5,2,-4,3] => 0
[-1,5,2,-4,-3] => 0
[-1,5,-2,4,3] => 0
[-1,5,-2,4,-3] => 0
[-1,5,-2,-4,3] => 0
[-1,5,-2,-4,-3] => 0
[-1,-5,2,4,3] => 0
[-1,-5,2,4,-3] => 0
[-1,-5,2,-4,3] => 0
[-1,-5,2,-4,-3] => 0
[-1,-5,-2,4,3] => 0
[-1,-5,-2,4,-3] => 0
[-1,-5,-2,-4,3] => 0
[-1,-5,-2,-4,-3] => 0
[1,5,3,2,4] => 0
[1,5,3,2,-4] => 0
[1,5,3,-2,4] => 0
[1,5,3,-2,-4] => 0
[1,5,-3,2,4] => 0
[1,5,-3,2,-4] => 0
[1,5,-3,-2,4] => 0
[1,5,-3,-2,-4] => 0
[1,-5,3,2,4] => 0
[1,-5,3,2,-4] => 0
[1,-5,3,-2,4] => 0
[1,-5,3,-2,-4] => 0
[1,-5,-3,2,4] => 0
[1,-5,-3,2,-4] => 0
[1,-5,-3,-2,4] => 0
[1,-5,-3,-2,-4] => 0
[-1,5,3,2,4] => 0
[-1,5,3,2,-4] => 0
[-1,5,3,-2,4] => 0
[-1,5,3,-2,-4] => 0
[-1,5,-3,2,4] => 0
[-1,5,-3,2,-4] => 0
[-1,5,-3,-2,4] => 0
[-1,5,-3,-2,-4] => 0
[-1,-5,3,2,4] => 0
[-1,-5,3,2,-4] => 0
[-1,-5,3,-2,4] => 0
[-1,-5,3,-2,-4] => 0
[-1,-5,-3,2,4] => 0
[-1,-5,-3,2,-4] => 0
[-1,-5,-3,-2,4] => 0
[-1,-5,-3,-2,-4] => 0
[1,5,3,4,2] => 5
[1,5,3,4,-2] => 0
[1,5,3,-4,2] => 3
[1,5,3,-4,-2] => 0
[1,5,-3,4,2] => 3
[1,5,-3,4,-2] => 0
[1,5,-3,-4,2] => 3
[1,5,-3,-4,-2] => 0
[1,-5,3,4,2] => 0
[1,-5,3,4,-2] => 5
[1,-5,3,-4,2] => 0
[1,-5,3,-4,-2] => 3
[1,-5,-3,4,2] => 0
[1,-5,-3,4,-2] => 3
[1,-5,-3,-4,2] => 0
[1,-5,-3,-4,-2] => 3
[-1,5,3,4,2] => 5
[-1,5,3,4,-2] => 0
[-1,5,3,-4,2] => 9
[-1,5,3,-4,-2] => 0
[-1,5,-3,4,2] => 11
[-1,5,-3,4,-2] => 0
[-1,5,-3,-4,2] => 13
[-1,5,-3,-4,-2] => 0
[-1,-5,3,4,2] => 0
[-1,-5,3,4,-2] => 5
[-1,-5,3,-4,2] => 0
[-1,-5,3,-4,-2] => 9
[-1,-5,-3,4,2] => 0
[-1,-5,-3,4,-2] => 11
[-1,-5,-3,-4,2] => 0
[-1,-5,-3,-4,-2] => 13
[1,5,4,2,3] => 0
[1,5,4,2,-3] => 0
[1,5,4,-2,3] => 0
[1,5,4,-2,-3] => 0
[1,5,-4,2,3] => 0
[1,5,-4,2,-3] => 0
[1,5,-4,-2,3] => 0
[1,5,-4,-2,-3] => 0
[1,-5,4,2,3] => 0
[1,-5,4,2,-3] => 0
[1,-5,4,-2,3] => 0
[1,-5,4,-2,-3] => 0
[1,-5,-4,2,3] => 0
[1,-5,-4,2,-3] => 0
[1,-5,-4,-2,3] => 0
[1,-5,-4,-2,-3] => 0
[-1,5,4,2,3] => 0
[-1,5,4,2,-3] => 0
[-1,5,4,-2,3] => 0
[-1,5,4,-2,-3] => 0
[-1,5,-4,2,3] => 0
[-1,5,-4,2,-3] => 0
[-1,5,-4,-2,3] => 0
[-1,5,-4,-2,-3] => 0
[-1,-5,4,2,3] => 0
[-1,-5,4,2,-3] => 0
[-1,-5,4,-2,3] => 0
[-1,-5,4,-2,-3] => 0
[-1,-5,-4,2,3] => 0
[-1,-5,-4,2,-3] => 0
[-1,-5,-4,-2,3] => 0
[-1,-5,-4,-2,-3] => 0
[1,5,4,3,2] => 7
[1,5,4,3,-2] => 0
[1,5,4,-3,2] => 0
[1,5,4,-3,-2] => 0
[1,5,-4,3,2] => 0
[1,5,-4,3,-2] => 0
[1,5,-4,-3,2] => 1
[1,5,-4,-3,-2] => 0
[1,-5,4,3,2] => 0
[1,-5,4,3,-2] => 7
[1,-5,4,-3,2] => 0
[1,-5,4,-3,-2] => 0
[1,-5,-4,3,2] => 0
[1,-5,-4,3,-2] => 0
[1,-5,-4,-3,2] => 0
[1,-5,-4,-3,-2] => 1
[-1,5,4,3,2] => 7
[-1,5,4,3,-2] => 0
[-1,5,4,-3,2] => 0
[-1,5,4,-3,-2] => 0
[-1,5,-4,3,2] => 0
[-1,5,-4,3,-2] => 0
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Description
The number of Hecke atoms of a signed permutation.
For a signed permutation $z\in\mathfrak H_n$, this is the cardinality of the set
$$ \{ w\in\mathfrak H_n | w^{-1} \star w = z\}, $$
where $\star$ denotes the Demazure product. Note that $w\mapsto w^{-1}\star w$ is a surjection onto the set of involutions.
References
[1] Hamaker, Z., Marberg, E. Atoms for signed permutations arXiv:1802.09805
Code
def statistic(z):
    return len(set(w for w in SignedPermutations(len(z)) if w.inverse().apply_demazure_product(w) == z))
Created
Nov 26, 2022 at 12:09 by Martin Rubey
Updated
Nov 26, 2022 at 12:09 by Martin Rubey