edit this statistic or download as text // json
Identifier
Values
[1] => 1
[1,2] => 1
[2,1] => 1
[1,2,3] => 1
[1,3,2] => 3
[2,1,3] => 3
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 3
[1,2,3,4] => 1
[1,2,4,3] => 6
[1,3,2,4] => 6
[1,3,4,2] => 8
[1,4,2,3] => 8
[1,4,3,2] => 6
[2,1,3,4] => 6
[2,1,4,3] => 9
[2,3,1,4] => 8
[2,3,4,1] => 9
[2,4,1,3] => 9
[2,4,3,1] => 8
[3,1,2,4] => 8
[3,1,4,2] => 9
[3,2,1,4] => 6
[3,2,4,1] => 8
[3,4,1,2] => 9
[3,4,2,1] => 9
[4,1,2,3] => 9
[4,1,3,2] => 8
[4,2,1,3] => 8
[4,2,3,1] => 6
[4,3,1,2] => 9
[4,3,2,1] => 9
[1,2,3,4,5] => 1
[1,2,3,5,4] => 10
[1,2,4,3,5] => 10
[1,2,4,5,3] => 20
[1,2,5,3,4] => 20
[1,2,5,4,3] => 10
[1,3,2,4,5] => 10
[1,3,2,5,4] => 45
[1,3,4,2,5] => 20
[1,3,4,5,2] => 45
[1,3,5,2,4] => 45
[1,3,5,4,2] => 20
[1,4,2,3,5] => 20
[1,4,2,5,3] => 45
[1,4,3,2,5] => 10
[1,4,3,5,2] => 20
[1,4,5,2,3] => 45
[1,4,5,3,2] => 45
[1,5,2,3,4] => 45
[1,5,2,4,3] => 20
[1,5,3,2,4] => 20
[1,5,3,4,2] => 10
[1,5,4,2,3] => 45
[1,5,4,3,2] => 45
[2,1,3,4,5] => 10
[2,1,3,5,4] => 45
[2,1,4,3,5] => 45
[2,1,4,5,3] => 44
[2,1,5,3,4] => 44
[2,1,5,4,3] => 45
[2,3,1,4,5] => 20
[2,3,1,5,4] => 44
[2,3,4,1,5] => 45
[2,3,4,5,1] => 44
[2,3,5,1,4] => 44
[2,3,5,4,1] => 45
[2,4,1,3,5] => 45
[2,4,1,5,3] => 44
[2,4,3,1,5] => 20
[2,4,3,5,1] => 45
[2,4,5,1,3] => 44
[2,4,5,3,1] => 44
[2,5,1,3,4] => 44
[2,5,1,4,3] => 45
[2,5,3,1,4] => 45
[2,5,3,4,1] => 20
[2,5,4,1,3] => 44
[2,5,4,3,1] => 44
[3,1,2,4,5] => 20
[3,1,2,5,4] => 44
[3,1,4,2,5] => 45
[3,1,4,5,2] => 44
[3,1,5,2,4] => 44
[3,1,5,4,2] => 45
[3,2,1,4,5] => 10
[3,2,1,5,4] => 45
[3,2,4,1,5] => 20
[3,2,4,5,1] => 45
[3,2,5,1,4] => 45
[3,2,5,4,1] => 20
[3,4,1,2,5] => 45
[3,4,1,5,2] => 44
[3,4,2,1,5] => 45
[3,4,2,5,1] => 44
[3,4,5,1,2] => 44
[3,4,5,2,1] => 44
[3,5,1,2,4] => 44
[3,5,1,4,2] => 45
>>> Load all 1200 entries. <<<
[3,5,2,1,4] => 44
[3,5,2,4,1] => 45
[3,5,4,1,2] => 44
[3,5,4,2,1] => 44
[4,1,2,3,5] => 45
[4,1,2,5,3] => 44
[4,1,3,2,5] => 20
[4,1,3,5,2] => 45
[4,1,5,2,3] => 44
[4,1,5,3,2] => 44
[4,2,1,3,5] => 20
[4,2,1,5,3] => 45
[4,2,3,1,5] => 10
[4,2,3,5,1] => 20
[4,2,5,1,3] => 45
[4,2,5,3,1] => 45
[4,3,1,2,5] => 45
[4,3,1,5,2] => 44
[4,3,2,1,5] => 45
[4,3,2,5,1] => 44
[4,3,5,1,2] => 44
[4,3,5,2,1] => 44
[4,5,1,2,3] => 44
[4,5,1,3,2] => 44
[4,5,2,1,3] => 44
[4,5,2,3,1] => 44
[4,5,3,1,2] => 45
[4,5,3,2,1] => 45
[5,1,2,3,4] => 44
[5,1,2,4,3] => 45
[5,1,3,2,4] => 45
[5,1,3,4,2] => 20
[5,1,4,2,3] => 44
[5,1,4,3,2] => 44
[5,2,1,3,4] => 45
[5,2,1,4,3] => 20
[5,2,3,1,4] => 20
[5,2,3,4,1] => 10
[5,2,4,1,3] => 45
[5,2,4,3,1] => 45
[5,3,1,2,4] => 44
[5,3,1,4,2] => 45
[5,3,2,1,4] => 44
[5,3,2,4,1] => 45
[5,3,4,1,2] => 44
[5,3,4,2,1] => 44
[5,4,1,2,3] => 44
[5,4,1,3,2] => 44
[5,4,2,1,3] => 44
[5,4,2,3,1] => 44
[5,4,3,1,2] => 45
[5,4,3,2,1] => 45
[1,2,3,4,5,6] => 1
[1,2,3,4,6,5] => 15
[1,2,3,5,4,6] => 15
[1,2,3,5,6,4] => 40
[1,2,3,6,4,5] => 40
[1,2,3,6,5,4] => 15
[1,2,4,3,5,6] => 15
[1,2,4,3,6,5] => 135
[1,2,4,5,3,6] => 40
[1,2,4,5,6,3] => 135
[1,2,4,6,3,5] => 135
[1,2,4,6,5,3] => 40
[1,2,5,3,4,6] => 40
[1,2,5,3,6,4] => 135
[1,2,5,4,3,6] => 15
[1,2,5,4,6,3] => 40
[1,2,5,6,3,4] => 135
[1,2,5,6,4,3] => 135
[1,2,6,3,4,5] => 135
[1,2,6,3,5,4] => 40
[1,2,6,4,3,5] => 40
[1,2,6,4,5,3] => 15
[1,2,6,5,3,4] => 135
[1,2,6,5,4,3] => 135
[1,3,2,4,5,6] => 15
[1,3,2,4,6,5] => 135
[1,3,2,5,4,6] => 135
[1,3,2,5,6,4] => 264
[1,3,2,6,4,5] => 264
[1,3,2,6,5,4] => 135
[1,3,4,2,5,6] => 40
[1,3,4,2,6,5] => 264
[1,3,4,5,2,6] => 135
[1,3,4,5,6,2] => 264
[1,3,4,6,2,5] => 264
[1,3,4,6,5,2] => 135
[1,3,5,2,4,6] => 135
[1,3,5,2,6,4] => 264
[1,3,5,4,2,6] => 40
[1,3,5,4,6,2] => 135
[1,3,5,6,2,4] => 264
[1,3,5,6,4,2] => 264
[1,3,6,2,4,5] => 264
[1,3,6,2,5,4] => 135
[1,3,6,4,2,5] => 135
[1,3,6,4,5,2] => 40
[1,3,6,5,2,4] => 264
[1,3,6,5,4,2] => 264
[1,4,2,3,5,6] => 40
[1,4,2,3,6,5] => 264
[1,4,2,5,3,6] => 135
[1,4,2,5,6,3] => 264
[1,4,2,6,3,5] => 264
[1,4,2,6,5,3] => 135
[1,4,3,2,5,6] => 15
[1,4,3,2,6,5] => 135
[1,4,3,5,2,6] => 40
[1,4,3,5,6,2] => 135
[1,4,3,6,2,5] => 135
[1,4,3,6,5,2] => 40
[1,4,5,2,3,6] => 135
[1,4,5,2,6,3] => 264
[1,4,5,3,2,6] => 135
[1,4,5,3,6,2] => 264
[1,4,5,6,2,3] => 264
[1,4,5,6,3,2] => 264
[1,4,6,2,3,5] => 264
[1,4,6,2,5,3] => 135
[1,4,6,3,2,5] => 264
[1,4,6,3,5,2] => 135
[1,4,6,5,2,3] => 264
[1,4,6,5,3,2] => 264
[1,5,2,3,4,6] => 135
[1,5,2,3,6,4] => 264
[1,5,2,4,3,6] => 40
[1,5,2,4,6,3] => 135
[1,5,2,6,3,4] => 264
[1,5,2,6,4,3] => 264
[1,5,3,2,4,6] => 40
[1,5,3,2,6,4] => 135
[1,5,3,4,2,6] => 15
[1,5,3,4,6,2] => 40
[1,5,3,6,2,4] => 135
[1,5,3,6,4,2] => 135
[1,5,4,2,3,6] => 135
[1,5,4,2,6,3] => 264
[1,5,4,3,2,6] => 135
[1,5,4,3,6,2] => 264
[1,5,4,6,2,3] => 264
[1,5,4,6,3,2] => 264
[1,5,6,2,3,4] => 264
[1,5,6,2,4,3] => 264
[1,5,6,3,2,4] => 264
[1,5,6,3,4,2] => 264
[1,5,6,4,2,3] => 135
[1,5,6,4,3,2] => 135
[1,6,2,3,4,5] => 264
[1,6,2,3,5,4] => 135
[1,6,2,4,3,5] => 135
[1,6,2,4,5,3] => 40
[1,6,2,5,3,4] => 264
[1,6,2,5,4,3] => 264
[1,6,3,2,4,5] => 135
[1,6,3,2,5,4] => 40
[1,6,3,4,2,5] => 40
[1,6,3,4,5,2] => 15
[1,6,3,5,2,4] => 135
[1,6,3,5,4,2] => 135
[1,6,4,2,3,5] => 264
[1,6,4,2,5,3] => 135
[1,6,4,3,2,5] => 264
[1,6,4,3,5,2] => 135
[1,6,4,5,2,3] => 264
[1,6,4,5,3,2] => 264
[1,6,5,2,3,4] => 264
[1,6,5,2,4,3] => 264
[1,6,5,3,2,4] => 264
[1,6,5,3,4,2] => 264
[1,6,5,4,2,3] => 135
[1,6,5,4,3,2] => 135
[2,1,3,4,5,6] => 15
[2,1,3,4,6,5] => 135
[2,1,3,5,4,6] => 135
[2,1,3,5,6,4] => 264
[2,1,3,6,4,5] => 264
[2,1,3,6,5,4] => 135
[2,1,4,3,5,6] => 135
[2,1,4,3,6,5] => 265
[2,1,4,5,3,6] => 264
[2,1,4,5,6,3] => 265
[2,1,4,6,3,5] => 265
[2,1,4,6,5,3] => 264
[2,1,5,3,4,6] => 264
[2,1,5,3,6,4] => 265
[2,1,5,4,3,6] => 135
[2,1,5,4,6,3] => 264
[2,1,5,6,3,4] => 265
[2,1,5,6,4,3] => 265
[2,1,6,3,4,5] => 265
[2,1,6,3,5,4] => 264
[2,1,6,4,3,5] => 264
[2,1,6,4,5,3] => 135
[2,1,6,5,3,4] => 265
[2,1,6,5,4,3] => 265
[2,3,1,4,5,6] => 40
[2,3,1,4,6,5] => 264
[2,3,1,5,4,6] => 264
[2,3,1,5,6,4] => 265
[2,3,1,6,4,5] => 265
[2,3,1,6,5,4] => 264
[2,3,4,1,5,6] => 135
[2,3,4,1,6,5] => 265
[2,3,4,5,1,6] => 264
[2,3,4,5,6,1] => 265
[2,3,4,6,1,5] => 265
[2,3,4,6,5,1] => 264
[2,3,5,1,4,6] => 264
[2,3,5,1,6,4] => 265
[2,3,5,4,1,6] => 135
[2,3,5,4,6,1] => 264
[2,3,5,6,1,4] => 265
[2,3,5,6,4,1] => 265
[2,3,6,1,4,5] => 265
[2,3,6,1,5,4] => 264
[2,3,6,4,1,5] => 264
[2,3,6,4,5,1] => 135
[2,3,6,5,1,4] => 265
[2,3,6,5,4,1] => 265
[2,4,1,3,5,6] => 135
[2,4,1,3,6,5] => 265
[2,4,1,5,3,6] => 264
[2,4,1,5,6,3] => 265
[2,4,1,6,3,5] => 265
[2,4,1,6,5,3] => 264
[2,4,3,1,5,6] => 40
[2,4,3,1,6,5] => 264
[2,4,3,5,1,6] => 135
[2,4,3,5,6,1] => 264
[2,4,3,6,1,5] => 264
[2,4,3,6,5,1] => 135
[2,4,5,1,3,6] => 264
[2,4,5,1,6,3] => 265
[2,4,5,3,1,6] => 264
[2,4,5,3,6,1] => 265
[2,4,5,6,1,3] => 265
[2,4,5,6,3,1] => 265
[2,4,6,1,3,5] => 265
[2,4,6,1,5,3] => 264
[2,4,6,3,1,5] => 265
[2,4,6,3,5,1] => 264
[2,4,6,5,1,3] => 265
[2,4,6,5,3,1] => 265
[2,5,1,3,4,6] => 264
[2,5,1,3,6,4] => 265
[2,5,1,4,3,6] => 135
[2,5,1,4,6,3] => 264
[2,5,1,6,3,4] => 265
[2,5,1,6,4,3] => 265
[2,5,3,1,4,6] => 135
[2,5,3,1,6,4] => 264
[2,5,3,4,1,6] => 40
[2,5,3,4,6,1] => 135
[2,5,3,6,1,4] => 264
[2,5,3,6,4,1] => 264
[2,5,4,1,3,6] => 264
[2,5,4,1,6,3] => 265
[2,5,4,3,1,6] => 264
[2,5,4,3,6,1] => 265
[2,5,4,6,1,3] => 265
[2,5,4,6,3,1] => 265
[2,5,6,1,3,4] => 265
[2,5,6,1,4,3] => 265
[2,5,6,3,1,4] => 265
[2,5,6,3,4,1] => 265
[2,5,6,4,1,3] => 264
[2,5,6,4,3,1] => 264
[2,6,1,3,4,5] => 265
[2,6,1,3,5,4] => 264
[2,6,1,4,3,5] => 264
[2,6,1,4,5,3] => 135
[2,6,1,5,3,4] => 265
[2,6,1,5,4,3] => 265
[2,6,3,1,4,5] => 264
[2,6,3,1,5,4] => 135
[2,6,3,4,1,5] => 135
[2,6,3,4,5,1] => 40
[2,6,3,5,1,4] => 264
[2,6,3,5,4,1] => 264
[2,6,4,1,3,5] => 265
[2,6,4,1,5,3] => 264
[2,6,4,3,1,5] => 265
[2,6,4,3,5,1] => 264
[2,6,4,5,1,3] => 265
[2,6,4,5,3,1] => 265
[2,6,5,1,3,4] => 265
[2,6,5,1,4,3] => 265
[2,6,5,3,1,4] => 265
[2,6,5,3,4,1] => 265
[2,6,5,4,1,3] => 264
[2,6,5,4,3,1] => 264
[3,1,2,4,5,6] => 40
[3,1,2,4,6,5] => 264
[3,1,2,5,4,6] => 264
[3,1,2,5,6,4] => 265
[3,1,2,6,4,5] => 265
[3,1,2,6,5,4] => 264
[3,1,4,2,5,6] => 135
[3,1,4,2,6,5] => 265
[3,1,4,5,2,6] => 264
[3,1,4,5,6,2] => 265
[3,1,4,6,2,5] => 265
[3,1,4,6,5,2] => 264
[3,1,5,2,4,6] => 264
[3,1,5,2,6,4] => 265
[3,1,5,4,2,6] => 135
[3,1,5,4,6,2] => 264
[3,1,5,6,2,4] => 265
[3,1,5,6,4,2] => 265
[3,1,6,2,4,5] => 265
[3,1,6,2,5,4] => 264
[3,1,6,4,2,5] => 264
[3,1,6,4,5,2] => 135
[3,1,6,5,2,4] => 265
[3,1,6,5,4,2] => 265
[3,2,1,4,5,6] => 15
[3,2,1,4,6,5] => 135
[3,2,1,5,4,6] => 135
[3,2,1,5,6,4] => 264
[3,2,1,6,4,5] => 264
[3,2,1,6,5,4] => 135
[3,2,4,1,5,6] => 40
[3,2,4,1,6,5] => 264
[3,2,4,5,1,6] => 135
[3,2,4,5,6,1] => 264
[3,2,4,6,1,5] => 264
[3,2,4,6,5,1] => 135
[3,2,5,1,4,6] => 135
[3,2,5,1,6,4] => 264
[3,2,5,4,1,6] => 40
[3,2,5,4,6,1] => 135
[3,2,5,6,1,4] => 264
[3,2,5,6,4,1] => 264
[3,2,6,1,4,5] => 264
[3,2,6,1,5,4] => 135
[3,2,6,4,1,5] => 135
[3,2,6,4,5,1] => 40
[3,2,6,5,1,4] => 264
[3,2,6,5,4,1] => 264
[3,4,1,2,5,6] => 135
[3,4,1,2,6,5] => 265
[3,4,1,5,2,6] => 264
[3,4,1,5,6,2] => 265
[3,4,1,6,2,5] => 265
[3,4,1,6,5,2] => 264
[3,4,2,1,5,6] => 135
[3,4,2,1,6,5] => 265
[3,4,2,5,1,6] => 264
[3,4,2,5,6,1] => 265
[3,4,2,6,1,5] => 265
[3,4,2,6,5,1] => 264
[3,4,5,1,2,6] => 264
[3,4,5,1,6,2] => 265
[3,4,5,2,1,6] => 264
[3,4,5,2,6,1] => 265
[3,4,5,6,1,2] => 265
[3,4,5,6,2,1] => 265
[3,4,6,1,2,5] => 265
[3,4,6,1,5,2] => 264
[3,4,6,2,1,5] => 265
[3,4,6,2,5,1] => 264
[3,4,6,5,1,2] => 265
[3,4,6,5,2,1] => 265
[3,5,1,2,4,6] => 264
[3,5,1,2,6,4] => 265
[3,5,1,4,2,6] => 135
[3,5,1,4,6,2] => 264
[3,5,1,6,2,4] => 265
[3,5,1,6,4,2] => 265
[3,5,2,1,4,6] => 264
[3,5,2,1,6,4] => 265
[3,5,2,4,1,6] => 135
[3,5,2,4,6,1] => 264
[3,5,2,6,1,4] => 265
[3,5,2,6,4,1] => 265
[3,5,4,1,2,6] => 264
[3,5,4,1,6,2] => 265
[3,5,4,2,1,6] => 264
[3,5,4,2,6,1] => 265
[3,5,4,6,1,2] => 265
[3,5,4,6,2,1] => 265
[3,5,6,1,2,4] => 265
[3,5,6,1,4,2] => 265
[3,5,6,2,1,4] => 265
[3,5,6,2,4,1] => 265
[3,5,6,4,1,2] => 264
[3,5,6,4,2,1] => 264
[3,6,1,2,4,5] => 265
[3,6,1,2,5,4] => 264
[3,6,1,4,2,5] => 264
[3,6,1,4,5,2] => 135
[3,6,1,5,2,4] => 265
[3,6,1,5,4,2] => 265
[3,6,2,1,4,5] => 265
[3,6,2,1,5,4] => 264
[3,6,2,4,1,5] => 264
[3,6,2,4,5,1] => 135
[3,6,2,5,1,4] => 265
[3,6,2,5,4,1] => 265
[3,6,4,1,2,5] => 265
[3,6,4,1,5,2] => 264
[3,6,4,2,1,5] => 265
[3,6,4,2,5,1] => 264
[3,6,4,5,1,2] => 265
[3,6,4,5,2,1] => 265
[3,6,5,1,2,4] => 265
[3,6,5,1,4,2] => 265
[3,6,5,2,1,4] => 265
[3,6,5,2,4,1] => 265
[3,6,5,4,1,2] => 264
[3,6,5,4,2,1] => 264
[4,1,2,3,5,6] => 135
[4,1,2,3,6,5] => 265
[4,1,2,5,3,6] => 264
[4,1,2,5,6,3] => 265
[4,1,2,6,3,5] => 265
[4,1,2,6,5,3] => 264
[4,1,3,2,5,6] => 40
[4,1,3,2,6,5] => 264
[4,1,3,5,2,6] => 135
[4,1,3,5,6,2] => 264
[4,1,3,6,2,5] => 264
[4,1,3,6,5,2] => 135
[4,1,5,2,3,6] => 264
[4,1,5,2,6,3] => 265
[4,1,5,3,2,6] => 264
[4,1,5,3,6,2] => 265
[4,1,5,6,2,3] => 265
[4,1,5,6,3,2] => 265
[4,1,6,2,3,5] => 265
[4,1,6,2,5,3] => 264
[4,1,6,3,2,5] => 265
[4,1,6,3,5,2] => 264
[4,1,6,5,2,3] => 265
[4,1,6,5,3,2] => 265
[4,2,1,3,5,6] => 40
[4,2,1,3,6,5] => 264
[4,2,1,5,3,6] => 135
[4,2,1,5,6,3] => 264
[4,2,1,6,3,5] => 264
[4,2,1,6,5,3] => 135
[4,2,3,1,5,6] => 15
[4,2,3,1,6,5] => 135
[4,2,3,5,1,6] => 40
[4,2,3,5,6,1] => 135
[4,2,3,6,1,5] => 135
[4,2,3,6,5,1] => 40
[4,2,5,1,3,6] => 135
[4,2,5,1,6,3] => 264
[4,2,5,3,1,6] => 135
[4,2,5,3,6,1] => 264
[4,2,5,6,1,3] => 264
[4,2,5,6,3,1] => 264
[4,2,6,1,3,5] => 264
[4,2,6,1,5,3] => 135
[4,2,6,3,1,5] => 264
[4,2,6,3,5,1] => 135
[4,2,6,5,1,3] => 264
[4,2,6,5,3,1] => 264
[4,3,1,2,5,6] => 135
[4,3,1,2,6,5] => 265
[4,3,1,5,2,6] => 264
[4,3,1,5,6,2] => 265
[4,3,1,6,2,5] => 265
[4,3,1,6,5,2] => 264
[4,3,2,1,5,6] => 135
[4,3,2,1,6,5] => 265
[4,3,2,5,1,6] => 264
[4,3,2,5,6,1] => 265
[4,3,2,6,1,5] => 265
[4,3,2,6,5,1] => 264
[4,3,5,1,2,6] => 264
[4,3,5,1,6,2] => 265
[4,3,5,2,1,6] => 264
[4,3,5,2,6,1] => 265
[4,3,5,6,1,2] => 265
[4,3,5,6,2,1] => 265
[4,3,6,1,2,5] => 265
[4,3,6,1,5,2] => 264
[4,3,6,2,1,5] => 265
[4,3,6,2,5,1] => 264
[4,3,6,5,1,2] => 265
[4,3,6,5,2,1] => 265
[4,5,1,2,3,6] => 264
[4,5,1,2,6,3] => 265
[4,5,1,3,2,6] => 264
[4,5,1,3,6,2] => 265
[4,5,1,6,2,3] => 265
[4,5,1,6,3,2] => 265
[4,5,2,1,3,6] => 264
[4,5,2,1,6,3] => 265
[4,5,2,3,1,6] => 264
[4,5,2,3,6,1] => 265
[4,5,2,6,1,3] => 265
[4,5,2,6,3,1] => 265
[4,5,3,1,2,6] => 135
[4,5,3,1,6,2] => 264
[4,5,3,2,1,6] => 135
[4,5,3,2,6,1] => 264
[4,5,3,6,1,2] => 264
[4,5,3,6,2,1] => 264
[4,5,6,1,2,3] => 265
[4,5,6,1,3,2] => 265
[4,5,6,2,1,3] => 265
[4,5,6,2,3,1] => 265
[4,5,6,3,1,2] => 265
[4,5,6,3,2,1] => 265
[4,6,1,2,3,5] => 265
[4,6,1,2,5,3] => 264
[4,6,1,3,2,5] => 265
[4,6,1,3,5,2] => 264
[4,6,1,5,2,3] => 265
[4,6,1,5,3,2] => 265
[4,6,2,1,3,5] => 265
[4,6,2,1,5,3] => 264
[4,6,2,3,1,5] => 265
[4,6,2,3,5,1] => 264
[4,6,2,5,1,3] => 265
[4,6,2,5,3,1] => 265
[4,6,3,1,2,5] => 264
[4,6,3,1,5,2] => 135
[4,6,3,2,1,5] => 264
[4,6,3,2,5,1] => 135
[4,6,3,5,1,2] => 264
[4,6,3,5,2,1] => 264
[4,6,5,1,2,3] => 265
[4,6,5,1,3,2] => 265
[4,6,5,2,1,3] => 265
[4,6,5,2,3,1] => 265
[4,6,5,3,1,2] => 265
[4,6,5,3,2,1] => 265
[5,1,2,3,4,6] => 264
[5,1,2,3,6,4] => 265
[5,1,2,4,3,6] => 135
[5,1,2,4,6,3] => 264
[5,1,2,6,3,4] => 265
[5,1,2,6,4,3] => 265
[5,1,3,2,4,6] => 135
[5,1,3,2,6,4] => 264
[5,1,3,4,2,6] => 40
[5,1,3,4,6,2] => 135
[5,1,3,6,2,4] => 264
[5,1,3,6,4,2] => 264
[5,1,4,2,3,6] => 264
[5,1,4,2,6,3] => 265
[5,1,4,3,2,6] => 264
[5,1,4,3,6,2] => 265
[5,1,4,6,2,3] => 265
[5,1,4,6,3,2] => 265
[5,1,6,2,3,4] => 265
[5,1,6,2,4,3] => 265
[5,1,6,3,2,4] => 265
[5,1,6,3,4,2] => 265
[5,1,6,4,2,3] => 264
[5,1,6,4,3,2] => 264
[5,2,1,3,4,6] => 135
[5,2,1,3,6,4] => 264
[5,2,1,4,3,6] => 40
[5,2,1,4,6,3] => 135
[5,2,1,6,3,4] => 264
[5,2,1,6,4,3] => 264
[5,2,3,1,4,6] => 40
[5,2,3,1,6,4] => 135
[5,2,3,4,1,6] => 15
[5,2,3,4,6,1] => 40
[5,2,3,6,1,4] => 135
[5,2,3,6,4,1] => 135
[5,2,4,1,3,6] => 135
[5,2,4,1,6,3] => 264
[5,2,4,3,1,6] => 135
[5,2,4,3,6,1] => 264
[5,2,4,6,1,3] => 264
[5,2,4,6,3,1] => 264
[5,2,6,1,3,4] => 264
[5,2,6,1,4,3] => 264
[5,2,6,3,1,4] => 264
[5,2,6,3,4,1] => 264
[5,2,6,4,1,3] => 135
[5,2,6,4,3,1] => 135
[5,3,1,2,4,6] => 264
[5,3,1,2,6,4] => 265
[5,3,1,4,2,6] => 135
[5,3,1,4,6,2] => 264
[5,3,1,6,2,4] => 265
[5,3,1,6,4,2] => 265
[5,3,2,1,4,6] => 264
[5,3,2,1,6,4] => 265
[5,3,2,4,1,6] => 135
[5,3,2,4,6,1] => 264
[5,3,2,6,1,4] => 265
[5,3,2,6,4,1] => 265
[5,3,4,1,2,6] => 264
[5,3,4,1,6,2] => 265
[5,3,4,2,1,6] => 264
[5,3,4,2,6,1] => 265
[5,3,4,6,1,2] => 265
[5,3,4,6,2,1] => 265
[5,3,6,1,2,4] => 265
[5,3,6,1,4,2] => 265
[5,3,6,2,1,4] => 265
[5,3,6,2,4,1] => 265
[5,3,6,4,1,2] => 264
[5,3,6,4,2,1] => 264
[5,4,1,2,3,6] => 264
[5,4,1,2,6,3] => 265
[5,4,1,3,2,6] => 264
[5,4,1,3,6,2] => 265
[5,4,1,6,2,3] => 265
[5,4,1,6,3,2] => 265
[5,4,2,1,3,6] => 264
[5,4,2,1,6,3] => 265
[5,4,2,3,1,6] => 264
[5,4,2,3,6,1] => 265
[5,4,2,6,1,3] => 265
[5,4,2,6,3,1] => 265
[5,4,3,1,2,6] => 135
[5,4,3,1,6,2] => 264
[5,4,3,2,1,6] => 135
[5,4,3,2,6,1] => 264
[5,4,3,6,1,2] => 264
[5,4,3,6,2,1] => 264
[5,4,6,1,2,3] => 265
[5,4,6,1,3,2] => 265
[5,4,6,2,1,3] => 265
[5,4,6,2,3,1] => 265
[5,4,6,3,1,2] => 265
[5,4,6,3,2,1] => 265
[5,6,1,2,3,4] => 265
[5,6,1,2,4,3] => 265
[5,6,1,3,2,4] => 265
[5,6,1,3,4,2] => 265
[5,6,1,4,2,3] => 264
[5,6,1,4,3,2] => 264
[5,6,2,1,3,4] => 265
[5,6,2,1,4,3] => 265
[5,6,2,3,1,4] => 265
[5,6,2,3,4,1] => 265
[5,6,2,4,1,3] => 264
[5,6,2,4,3,1] => 264
[5,6,3,1,2,4] => 264
[5,6,3,1,4,2] => 264
[5,6,3,2,1,4] => 264
[5,6,3,2,4,1] => 264
[5,6,3,4,1,2] => 135
[5,6,3,4,2,1] => 135
[5,6,4,1,2,3] => 265
[5,6,4,1,3,2] => 265
[5,6,4,2,1,3] => 265
[5,6,4,2,3,1] => 265
[5,6,4,3,1,2] => 265
[5,6,4,3,2,1] => 265
[6,1,2,3,4,5] => 265
[6,1,2,3,5,4] => 264
[6,1,2,4,3,5] => 264
[6,1,2,4,5,3] => 135
[6,1,2,5,3,4] => 265
[6,1,2,5,4,3] => 265
[6,1,3,2,4,5] => 264
[6,1,3,2,5,4] => 135
[6,1,3,4,2,5] => 135
[6,1,3,4,5,2] => 40
[6,1,3,5,2,4] => 264
[6,1,3,5,4,2] => 264
[6,1,4,2,3,5] => 265
[6,1,4,2,5,3] => 264
[6,1,4,3,2,5] => 265
[6,1,4,3,5,2] => 264
[6,1,4,5,2,3] => 265
[6,1,4,5,3,2] => 265
[6,1,5,2,3,4] => 265
[6,1,5,2,4,3] => 265
[6,1,5,3,2,4] => 265
[6,1,5,3,4,2] => 265
[6,1,5,4,2,3] => 264
[6,1,5,4,3,2] => 264
[6,2,1,3,4,5] => 264
[6,2,1,3,5,4] => 135
[6,2,1,4,3,5] => 135
[6,2,1,4,5,3] => 40
[6,2,1,5,3,4] => 264
[6,2,1,5,4,3] => 264
[6,2,3,1,4,5] => 135
[6,2,3,1,5,4] => 40
[6,2,3,4,1,5] => 40
[6,2,3,4,5,1] => 15
[6,2,3,5,1,4] => 135
[6,2,3,5,4,1] => 135
[6,2,4,1,3,5] => 264
[6,2,4,1,5,3] => 135
[6,2,4,3,1,5] => 264
[6,2,4,3,5,1] => 135
[6,2,4,5,1,3] => 264
[6,2,4,5,3,1] => 264
[6,2,5,1,3,4] => 264
[6,2,5,1,4,3] => 264
[6,2,5,3,1,4] => 264
[6,2,5,3,4,1] => 264
[6,2,5,4,1,3] => 135
[6,2,5,4,3,1] => 135
[6,3,1,2,4,5] => 265
[6,3,1,2,5,4] => 264
[6,3,1,4,2,5] => 264
[6,3,1,4,5,2] => 135
[6,3,1,5,2,4] => 265
[6,3,1,5,4,2] => 265
[6,3,2,1,4,5] => 265
[6,3,2,1,5,4] => 264
[6,3,2,4,1,5] => 264
[6,3,2,4,5,1] => 135
[6,3,2,5,1,4] => 265
[6,3,2,5,4,1] => 265
[6,3,4,1,2,5] => 265
[6,3,4,1,5,2] => 264
[6,3,4,2,1,5] => 265
[6,3,4,2,5,1] => 264
[6,3,4,5,1,2] => 265
[6,3,4,5,2,1] => 265
[6,3,5,1,2,4] => 265
[6,3,5,1,4,2] => 265
[6,3,5,2,1,4] => 265
[6,3,5,2,4,1] => 265
[6,3,5,4,1,2] => 264
[6,3,5,4,2,1] => 264
[6,4,1,2,3,5] => 265
[6,4,1,2,5,3] => 264
[6,4,1,3,2,5] => 265
[6,4,1,3,5,2] => 264
[6,4,1,5,2,3] => 265
[6,4,1,5,3,2] => 265
[6,4,2,1,3,5] => 265
[6,4,2,1,5,3] => 264
[6,4,2,3,1,5] => 265
[6,4,2,3,5,1] => 264
[6,4,2,5,1,3] => 265
[6,4,2,5,3,1] => 265
[6,4,3,1,2,5] => 264
[6,4,3,1,5,2] => 135
[6,4,3,2,1,5] => 264
[6,4,3,2,5,1] => 135
[6,4,3,5,1,2] => 264
[6,4,3,5,2,1] => 264
[6,4,5,1,2,3] => 265
[6,4,5,1,3,2] => 265
[6,4,5,2,1,3] => 265
[6,4,5,2,3,1] => 265
[6,4,5,3,1,2] => 265
[6,4,5,3,2,1] => 265
[6,5,1,2,3,4] => 265
[6,5,1,2,4,3] => 265
[6,5,1,3,2,4] => 265
[6,5,1,3,4,2] => 265
[6,5,1,4,2,3] => 264
[6,5,1,4,3,2] => 264
[6,5,2,1,3,4] => 265
[6,5,2,1,4,3] => 265
[6,5,2,3,1,4] => 265
[6,5,2,3,4,1] => 265
[6,5,2,4,1,3] => 264
[6,5,2,4,3,1] => 264
[6,5,3,1,2,4] => 264
[6,5,3,1,4,2] => 264
[6,5,3,2,1,4] => 264
[6,5,3,2,4,1] => 264
[6,5,3,4,1,2] => 135
[6,5,3,4,2,1] => 135
[6,5,4,1,2,3] => 265
[6,5,4,1,3,2] => 265
[6,5,4,2,1,3] => 265
[6,5,4,2,3,1] => 265
[6,5,4,3,1,2] => 265
[6,5,4,3,2,1] => 265
[1,2,3,4,5,6,7] => 1
[1,2,3,4,5,7,6] => 21
[1,2,3,4,6,5,7] => 21
[1,2,3,4,6,7,5] => 70
[1,2,3,4,7,5,6] => 70
[1,2,3,4,7,6,5] => 21
[1,2,3,5,4,6,7] => 21
[1,2,3,5,4,7,6] => 315
[1,2,3,5,6,4,7] => 70
[1,2,3,5,6,7,4] => 315
[1,2,3,5,7,4,6] => 315
[1,2,3,5,7,6,4] => 70
[1,2,3,6,4,5,7] => 70
[1,2,3,6,4,7,5] => 315
[1,2,3,6,5,4,7] => 21
[1,2,3,6,5,7,4] => 70
[1,2,3,6,7,4,5] => 315
[1,2,3,6,7,5,4] => 315
[1,2,3,7,4,5,6] => 315
[1,2,3,7,4,6,5] => 70
[1,2,3,7,5,4,6] => 70
[1,2,3,7,5,6,4] => 21
[1,2,3,7,6,4,5] => 315
[1,2,3,7,6,5,4] => 315
[1,2,4,3,5,6,7] => 21
[1,2,4,3,5,7,6] => 315
[1,2,4,3,6,5,7] => 315
[1,2,4,3,6,7,5] => 924
[1,2,4,3,7,5,6] => 924
[1,2,4,3,7,6,5] => 315
[1,2,4,5,3,6,7] => 70
[1,2,4,5,3,7,6] => 924
[1,2,4,5,6,3,7] => 315
[1,2,4,5,6,7,3] => 924
[1,2,4,5,7,3,6] => 924
[1,2,4,5,7,6,3] => 315
[1,2,4,6,3,5,7] => 315
[1,2,4,6,3,7,5] => 924
[1,2,4,6,5,3,7] => 70
[1,2,4,6,5,7,3] => 315
[1,2,4,6,7,3,5] => 924
[1,2,4,6,7,5,3] => 924
[1,2,4,7,3,5,6] => 924
[1,2,4,7,3,6,5] => 315
[1,2,4,7,5,3,6] => 315
[1,2,4,7,5,6,3] => 70
[1,2,4,7,6,3,5] => 924
[1,2,4,7,6,5,3] => 924
[1,2,5,3,4,6,7] => 70
[1,2,5,3,4,7,6] => 924
[1,2,5,3,6,4,7] => 315
[1,2,5,3,6,7,4] => 924
[1,2,5,3,7,4,6] => 924
[1,2,5,3,7,6,4] => 315
[1,2,5,4,3,6,7] => 21
[1,2,5,4,3,7,6] => 315
[1,2,5,4,6,3,7] => 70
[1,2,5,4,6,7,3] => 315
[1,2,5,4,7,3,6] => 315
[1,2,5,4,7,6,3] => 70
[1,2,5,6,3,4,7] => 315
[1,2,5,6,3,7,4] => 924
[1,2,5,6,4,3,7] => 315
[1,2,5,6,4,7,3] => 924
[1,2,5,6,7,3,4] => 924
[1,2,5,6,7,4,3] => 924
[1,2,5,7,3,4,6] => 924
[1,2,5,7,3,6,4] => 315
[1,2,5,7,4,3,6] => 924
[1,2,5,7,4,6,3] => 315
[1,2,5,7,6,3,4] => 924
[1,2,5,7,6,4,3] => 924
[1,2,6,3,4,5,7] => 315
[1,2,6,3,4,7,5] => 924
[1,2,6,3,5,4,7] => 70
[1,2,6,3,5,7,4] => 315
[1,2,6,3,7,4,5] => 924
[1,2,6,3,7,5,4] => 924
[1,2,6,4,3,5,7] => 70
[1,2,6,4,3,7,5] => 315
[1,2,6,4,5,3,7] => 21
[1,2,6,4,5,7,3] => 70
[1,2,6,4,7,3,5] => 315
[1,2,6,4,7,5,3] => 315
[1,2,6,5,3,4,7] => 315
[1,2,6,5,3,7,4] => 924
[1,2,6,5,4,3,7] => 315
[1,2,6,5,4,7,3] => 924
[1,2,6,5,7,3,4] => 924
[1,2,6,5,7,4,3] => 924
[1,2,6,7,3,4,5] => 924
[1,2,6,7,3,5,4] => 924
[1,2,6,7,4,3,5] => 924
[1,2,6,7,4,5,3] => 924
[1,2,6,7,5,3,4] => 315
[1,2,6,7,5,4,3] => 315
[1,2,7,3,4,5,6] => 924
[1,2,7,3,4,6,5] => 315
[1,2,7,3,5,4,6] => 315
[1,2,7,3,5,6,4] => 70
[1,2,7,3,6,4,5] => 924
[1,2,7,3,6,5,4] => 924
[1,2,7,4,3,5,6] => 315
[1,2,7,4,3,6,5] => 70
[1,2,7,4,5,3,6] => 70
[1,2,7,4,5,6,3] => 21
[1,2,7,4,6,3,5] => 315
[1,2,7,4,6,5,3] => 315
[1,2,7,5,3,4,6] => 924
[1,2,7,5,3,6,4] => 315
[1,2,7,5,4,3,6] => 924
[1,2,7,5,4,6,3] => 315
[1,2,7,5,6,3,4] => 924
[1,2,7,5,6,4,3] => 924
[1,2,7,6,3,4,5] => 924
[1,2,7,6,3,5,4] => 924
[1,2,7,6,4,3,5] => 924
[1,2,7,6,4,5,3] => 924
[1,2,7,6,5,3,4] => 315
[1,2,7,6,5,4,3] => 315
[1,3,2,4,5,6,7] => 21
[1,3,2,4,5,7,6] => 315
[1,3,2,4,6,5,7] => 315
[1,3,2,4,6,7,5] => 924
[1,3,2,4,7,5,6] => 924
[1,3,2,4,7,6,5] => 315
[1,3,2,5,4,6,7] => 315
[1,3,2,5,4,7,6] => 1855
[1,3,2,5,6,4,7] => 924
[1,3,2,5,6,7,4] => 1855
[1,3,2,5,7,4,6] => 1855
[1,3,2,5,7,6,4] => 924
[1,3,2,6,4,5,7] => 924
[1,3,2,6,4,7,5] => 1855
[1,3,2,6,5,4,7] => 315
[1,3,2,6,5,7,4] => 924
[1,3,2,6,7,4,5] => 1855
[1,3,2,6,7,5,4] => 1855
[1,3,2,7,4,5,6] => 1855
[1,3,2,7,4,6,5] => 924
[1,3,2,7,5,4,6] => 924
[1,3,2,7,5,6,4] => 315
[1,3,2,7,6,4,5] => 1855
[1,3,2,7,6,5,4] => 1855
[1,3,4,2,5,6,7] => 70
[1,3,4,2,5,7,6] => 924
[1,3,4,2,6,5,7] => 924
[1,3,4,2,6,7,5] => 1855
[1,3,4,2,7,5,6] => 1855
[1,3,4,2,7,6,5] => 924
[1,3,4,5,2,6,7] => 315
[1,3,4,5,2,7,6] => 1855
[1,3,4,5,6,2,7] => 924
[1,3,4,5,6,7,2] => 1855
[1,3,4,5,7,2,6] => 1855
[1,3,4,5,7,6,2] => 924
[1,3,4,6,2,5,7] => 924
[1,3,4,6,2,7,5] => 1855
[1,3,4,6,5,2,7] => 315
[1,3,4,6,5,7,2] => 924
[1,3,4,6,7,2,5] => 1855
[1,3,4,6,7,5,2] => 1855
[1,3,4,7,2,5,6] => 1855
[1,3,4,7,2,6,5] => 924
[1,3,4,7,5,2,6] => 924
[1,3,4,7,5,6,2] => 315
[1,3,4,7,6,2,5] => 1855
[1,3,4,7,6,5,2] => 1855
[1,3,5,2,4,6,7] => 315
[1,3,5,2,4,7,6] => 1855
[1,3,5,2,6,4,7] => 924
[1,3,5,2,6,7,4] => 1855
[1,3,5,2,7,4,6] => 1855
[1,3,5,2,7,6,4] => 924
[1,3,5,4,2,6,7] => 70
[1,3,5,4,2,7,6] => 924
[1,3,5,4,6,2,7] => 315
[1,3,5,4,6,7,2] => 924
[1,3,5,4,7,2,6] => 924
[1,3,5,4,7,6,2] => 315
[1,3,5,6,2,4,7] => 924
[1,3,5,6,2,7,4] => 1855
[1,3,5,6,4,2,7] => 924
[1,3,5,6,4,7,2] => 1855
[1,3,5,6,7,2,4] => 1855
[1,3,5,6,7,4,2] => 1855
[1,3,5,7,2,4,6] => 1855
[1,3,5,7,2,6,4] => 924
[1,3,5,7,4,2,6] => 1855
[1,3,5,7,4,6,2] => 924
[1,3,5,7,6,2,4] => 1855
[1,3,5,7,6,4,2] => 1855
[1,3,6,2,4,5,7] => 924
[1,3,6,2,4,7,5] => 1855
[1,3,6,2,5,4,7] => 315
[1,3,6,2,5,7,4] => 924
[1,3,6,2,7,4,5] => 1855
[1,3,6,2,7,5,4] => 1855
[1,3,6,4,2,5,7] => 315
[1,3,6,4,2,7,5] => 924
[1,3,6,4,5,2,7] => 70
[1,3,6,4,5,7,2] => 315
[1,3,6,4,7,2,5] => 924
[1,3,6,4,7,5,2] => 924
[1,3,6,5,2,4,7] => 924
[1,3,6,5,2,7,4] => 1855
[1,3,6,5,4,2,7] => 924
[1,3,6,5,4,7,2] => 1855
[1,3,6,5,7,2,4] => 1855
[1,3,6,5,7,4,2] => 1855
[1,3,6,7,2,4,5] => 1855
[1,3,6,7,2,5,4] => 1855
[1,3,6,7,4,2,5] => 1855
[1,3,6,7,4,5,2] => 1855
[1,3,6,7,5,2,4] => 924
[1,3,6,7,5,4,2] => 924
[1,3,7,2,4,5,6] => 1855
[1,3,7,2,4,6,5] => 924
[1,3,7,2,5,4,6] => 924
[1,3,7,2,5,6,4] => 315
[1,3,7,2,6,4,5] => 1855
[1,3,7,2,6,5,4] => 1855
[1,3,7,4,2,5,6] => 924
[1,3,7,4,2,6,5] => 315
[1,3,7,4,5,2,6] => 315
[1,3,7,4,5,6,2] => 70
[1,3,7,4,6,2,5] => 924
[1,3,7,4,6,5,2] => 924
[1,3,7,5,2,4,6] => 1855
[1,3,7,5,2,6,4] => 924
[1,3,7,5,4,2,6] => 1855
[1,3,7,5,4,6,2] => 924
[1,3,7,5,6,2,4] => 1855
[1,3,7,5,6,4,2] => 1855
[1,3,7,6,2,4,5] => 1855
[1,3,7,6,2,5,4] => 1855
[1,3,7,6,4,2,5] => 1855
[1,3,7,6,4,5,2] => 1855
[1,3,7,6,5,2,4] => 924
[1,3,7,6,5,4,2] => 924
[1,4,2,3,5,6,7] => 70
[1,4,2,3,5,7,6] => 924
[1,4,2,3,6,5,7] => 924
[1,4,2,3,6,7,5] => 1855
[1,4,2,3,7,5,6] => 1855
[1,4,2,3,7,6,5] => 924
[1,4,2,5,3,6,7] => 315
[1,4,2,5,3,7,6] => 1855
[1,4,2,5,6,3,7] => 924
[1,4,2,5,6,7,3] => 1855
[1,4,2,5,7,3,6] => 1855
[1,4,2,5,7,6,3] => 924
[1,4,2,6,3,5,7] => 924
[1,4,2,6,3,7,5] => 1855
[1,4,2,6,5,3,7] => 315
[1,4,2,6,5,7,3] => 924
[1,4,2,6,7,3,5] => 1855
[1,4,2,6,7,5,3] => 1855
[1,4,2,7,3,5,6] => 1855
[1,4,2,7,3,6,5] => 924
[1,4,2,7,5,3,6] => 924
[1,4,2,7,5,6,3] => 315
[1,4,2,7,6,3,5] => 1855
[1,4,2,7,6,5,3] => 1855
[1,4,3,2,5,6,7] => 21
[1,4,3,2,5,7,6] => 315
[1,4,3,2,6,5,7] => 315
[1,4,3,2,6,7,5] => 924
[1,4,3,2,7,5,6] => 924
[1,4,3,2,7,6,5] => 315
[1,4,3,5,2,6,7] => 70
[1,4,3,5,2,7,6] => 924
[1,4,3,5,6,2,7] => 315
[1,4,3,5,6,7,2] => 924
[1,4,3,5,7,2,6] => 924
[1,4,3,5,7,6,2] => 315
[1,4,3,6,2,5,7] => 315
[1,4,3,6,2,7,5] => 924
[1,4,3,6,5,2,7] => 70
[1,4,3,6,5,7,2] => 315
[1,4,3,6,7,2,5] => 924
[1,4,3,6,7,5,2] => 924
[1,4,3,7,2,5,6] => 924
[1,4,3,7,2,6,5] => 315
[1,4,3,7,5,2,6] => 315
[1,4,3,7,5,6,2] => 70
[1,4,3,7,6,2,5] => 924
[1,4,3,7,6,5,2] => 924
[1,4,5,2,3,6,7] => 315
[1,4,5,2,3,7,6] => 1855
[1,4,5,2,6,3,7] => 924
[1,4,5,2,6,7,3] => 1855
[1,4,5,2,7,3,6] => 1855
[1,4,5,2,7,6,3] => 924
[1,4,5,3,2,6,7] => 315
[1,4,5,3,2,7,6] => 1855
[1,4,5,3,6,2,7] => 924
[1,4,5,3,6,7,2] => 1855
[1,4,5,3,7,2,6] => 1855
[1,4,5,3,7,6,2] => 924
[1,4,5,6,2,3,7] => 924
[1,4,5,6,2,7,3] => 1855
[1,4,5,6,3,2,7] => 924
[1,4,5,6,3,7,2] => 1855
[1,4,5,6,7,2,3] => 1855
[1,4,5,6,7,3,2] => 1855
[1,4,5,7,2,3,6] => 1855
[1,4,5,7,2,6,3] => 924
[1,4,5,7,3,2,6] => 1855
[1,4,5,7,3,6,2] => 924
[1,4,5,7,6,2,3] => 1855
[1,4,5,7,6,3,2] => 1855
[1,4,6,2,3,5,7] => 924
[1,4,6,2,3,7,5] => 1855
[1,4,6,2,5,3,7] => 315
[1,4,6,2,5,7,3] => 924
[1,4,6,2,7,3,5] => 1855
[1,4,6,2,7,5,3] => 1855
[1,4,6,3,2,5,7] => 924
[1,4,6,3,2,7,5] => 1855
[1,4,6,3,5,2,7] => 315
[1,4,6,3,5,7,2] => 924
[1,4,6,3,7,2,5] => 1855
[1,4,6,3,7,5,2] => 1855
[1,4,6,5,2,3,7] => 924
[1,4,6,5,2,7,3] => 1855
[1,4,6,5,3,2,7] => 924
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Description
The number of permutations such that the product with the permutation has the same number of fixed points.
More formally, given a permutation $\pi$, this is the number of permutations $\sigma$ such that $\pi$ and $\pi\sigma$ have the same number of fixed points.
Note that the number of permutations $\sigma$ such that $\pi$ and $\pi\sigma$ have the same cycle type is the size of the conjugacy class of $\pi$, St000690The size of the conjugacy class of a permutation..
References
[1] balli Number of Permutations? MathOverflow:144899
Code
def statistic(pi):
    m = pi.number_of_fixed_points()
    return sum(1 for tau in Permutations(pi.size()) if (pi*tau).number_of_fixed_points() == m)
Created
Apr 09, 2020 at 18:37 by Martin Rubey
Updated
Apr 09, 2020 at 18:37 by Martin Rubey