edit this statistic or download as text // json
Identifier
Values
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 1
[1,2,3,4] => 0
[1,2,4,3] => 1
[1,3,2,4] => 1
[1,3,4,2] => 1
[1,4,2,3] => 1
[1,4,3,2] => 1
[2,1,3,4] => 1
[2,1,4,3] => 2
[2,3,1,4] => 1
[2,3,4,1] => 1
[2,4,1,3] => 1
[2,4,3,1] => 1
[3,1,2,4] => 1
[3,1,4,2] => 1
[3,2,1,4] => 1
[3,2,4,1] => 1
[3,4,1,2] => 1
[3,4,2,1] => 1
[4,1,2,3] => 1
[4,1,3,2] => 1
[4,2,1,3] => 1
[4,2,3,1] => 1
[4,3,1,2] => 1
[4,3,2,1] => 1
[1,2,3,4,5] => 0
[1,2,3,5,4] => 1
[1,2,4,3,5] => 1
[1,2,4,5,3] => 1
[1,2,5,3,4] => 1
[1,2,5,4,3] => 1
[1,3,2,4,5] => 1
[1,3,2,5,4] => 2
[1,3,4,2,5] => 1
[1,3,4,5,2] => 1
[1,3,5,2,4] => 1
[1,3,5,4,2] => 1
[1,4,2,3,5] => 1
[1,4,2,5,3] => 1
[1,4,3,2,5] => 1
[1,4,3,5,2] => 1
[1,4,5,2,3] => 1
[1,4,5,3,2] => 1
[1,5,2,3,4] => 1
[1,5,2,4,3] => 1
[1,5,3,2,4] => 1
[1,5,3,4,2] => 1
[1,5,4,2,3] => 1
[1,5,4,3,2] => 1
[2,1,3,4,5] => 1
[2,1,3,5,4] => 2
[2,1,4,3,5] => 2
[2,1,4,5,3] => 2
[2,1,5,3,4] => 2
[2,1,5,4,3] => 2
[2,3,1,4,5] => 1
[2,3,1,5,4] => 2
[2,3,4,1,5] => 1
[2,3,4,5,1] => 1
[2,3,5,1,4] => 1
[2,3,5,4,1] => 1
[2,4,1,3,5] => 1
[2,4,1,5,3] => 1
[2,4,3,1,5] => 1
[2,4,3,5,1] => 1
[2,4,5,1,3] => 1
[2,4,5,3,1] => 1
[2,5,1,3,4] => 1
[2,5,1,4,3] => 1
[2,5,3,1,4] => 1
[2,5,3,4,1] => 1
[2,5,4,1,3] => 1
[2,5,4,3,1] => 1
[3,1,2,4,5] => 1
[3,1,2,5,4] => 2
[3,1,4,2,5] => 1
[3,1,4,5,2] => 1
[3,1,5,2,4] => 1
[3,1,5,4,2] => 1
[3,2,1,4,5] => 1
[3,2,1,5,4] => 2
[3,2,4,1,5] => 1
[3,2,4,5,1] => 1
[3,2,5,1,4] => 1
[3,2,5,4,1] => 1
[3,4,1,2,5] => 1
[3,4,1,5,2] => 1
[3,4,2,1,5] => 1
[3,4,2,5,1] => 1
[3,4,5,1,2] => 1
[3,4,5,2,1] => 1
[3,5,1,2,4] => 1
[3,5,1,4,2] => 1
[3,5,2,1,4] => 1
>>> Load all 872 entries. <<<
[3,5,2,4,1] => 1
[3,5,4,1,2] => 1
[3,5,4,2,1] => 1
[4,1,2,3,5] => 1
[4,1,2,5,3] => 1
[4,1,3,2,5] => 1
[4,1,3,5,2] => 1
[4,1,5,2,3] => 1
[4,1,5,3,2] => 1
[4,2,1,3,5] => 1
[4,2,1,5,3] => 1
[4,2,3,1,5] => 1
[4,2,3,5,1] => 1
[4,2,5,1,3] => 1
[4,2,5,3,1] => 1
[4,3,1,2,5] => 1
[4,3,1,5,2] => 1
[4,3,2,1,5] => 1
[4,3,2,5,1] => 1
[4,3,5,1,2] => 1
[4,3,5,2,1] => 1
[4,5,1,2,3] => 1
[4,5,1,3,2] => 1
[4,5,2,1,3] => 1
[4,5,2,3,1] => 1
[4,5,3,1,2] => 1
[4,5,3,2,1] => 1
[5,1,2,3,4] => 1
[5,1,2,4,3] => 1
[5,1,3,2,4] => 1
[5,1,3,4,2] => 1
[5,1,4,2,3] => 1
[5,1,4,3,2] => 1
[5,2,1,3,4] => 1
[5,2,1,4,3] => 1
[5,2,3,1,4] => 1
[5,2,3,4,1] => 1
[5,2,4,1,3] => 1
[5,2,4,3,1] => 1
[5,3,1,2,4] => 1
[5,3,1,4,2] => 1
[5,3,2,1,4] => 1
[5,3,2,4,1] => 1
[5,3,4,1,2] => 1
[5,3,4,2,1] => 1
[5,4,1,2,3] => 1
[5,4,1,3,2] => 1
[5,4,2,1,3] => 1
[5,4,2,3,1] => 1
[5,4,3,1,2] => 1
[5,4,3,2,1] => 1
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 1
[1,2,3,5,4,6] => 1
[1,2,3,5,6,4] => 1
[1,2,3,6,4,5] => 1
[1,2,3,6,5,4] => 1
[1,2,4,3,5,6] => 1
[1,2,4,3,6,5] => 2
[1,2,4,5,3,6] => 1
[1,2,4,5,6,3] => 1
[1,2,4,6,3,5] => 1
[1,2,4,6,5,3] => 1
[1,2,5,3,4,6] => 1
[1,2,5,3,6,4] => 1
[1,2,5,4,3,6] => 1
[1,2,5,4,6,3] => 1
[1,2,5,6,3,4] => 1
[1,2,5,6,4,3] => 1
[1,2,6,3,4,5] => 1
[1,2,6,3,5,4] => 1
[1,2,6,4,3,5] => 1
[1,2,6,4,5,3] => 1
[1,2,6,5,3,4] => 1
[1,2,6,5,4,3] => 1
[1,3,2,4,5,6] => 1
[1,3,2,4,6,5] => 2
[1,3,2,5,4,6] => 2
[1,3,2,5,6,4] => 2
[1,3,2,6,4,5] => 2
[1,3,2,6,5,4] => 2
[1,3,4,2,5,6] => 1
[1,3,4,2,6,5] => 2
[1,3,4,5,2,6] => 1
[1,3,4,5,6,2] => 1
[1,3,4,6,2,5] => 1
[1,3,4,6,5,2] => 1
[1,3,5,2,4,6] => 1
[1,3,5,2,6,4] => 1
[1,3,5,4,2,6] => 1
[1,3,5,4,6,2] => 1
[1,3,5,6,2,4] => 1
[1,3,5,6,4,2] => 1
[1,3,6,2,4,5] => 1
[1,3,6,2,5,4] => 1
[1,3,6,4,2,5] => 1
[1,3,6,4,5,2] => 1
[1,3,6,5,2,4] => 1
[1,3,6,5,4,2] => 1
[1,4,2,3,5,6] => 1
[1,4,2,3,6,5] => 2
[1,4,2,5,3,6] => 1
[1,4,2,5,6,3] => 1
[1,4,2,6,3,5] => 1
[1,4,2,6,5,3] => 1
[1,4,3,2,5,6] => 1
[1,4,3,2,6,5] => 2
[1,4,3,5,2,6] => 1
[1,4,3,5,6,2] => 1
[1,4,3,6,2,5] => 1
[1,4,3,6,5,2] => 1
[1,4,5,2,3,6] => 1
[1,4,5,2,6,3] => 1
[1,4,5,3,2,6] => 1
[1,4,5,3,6,2] => 1
[1,4,5,6,2,3] => 1
[1,4,5,6,3,2] => 1
[1,4,6,2,3,5] => 1
[1,4,6,2,5,3] => 1
[1,4,6,3,2,5] => 1
[1,4,6,3,5,2] => 1
[1,4,6,5,2,3] => 1
[1,4,6,5,3,2] => 1
[1,5,2,3,4,6] => 1
[1,5,2,3,6,4] => 1
[1,5,2,4,3,6] => 1
[1,5,2,4,6,3] => 1
[1,5,2,6,3,4] => 1
[1,5,2,6,4,3] => 1
[1,5,3,2,4,6] => 1
[1,5,3,2,6,4] => 1
[1,5,3,4,2,6] => 1
[1,5,3,4,6,2] => 1
[1,5,3,6,2,4] => 1
[1,5,3,6,4,2] => 1
[1,5,4,2,3,6] => 1
[1,5,4,2,6,3] => 1
[1,5,4,3,2,6] => 1
[1,5,4,3,6,2] => 1
[1,5,4,6,2,3] => 1
[1,5,4,6,3,2] => 1
[1,5,6,2,3,4] => 1
[1,5,6,2,4,3] => 1
[1,5,6,3,2,4] => 1
[1,5,6,3,4,2] => 1
[1,5,6,4,2,3] => 1
[1,5,6,4,3,2] => 1
[1,6,2,3,4,5] => 1
[1,6,2,3,5,4] => 1
[1,6,2,4,3,5] => 1
[1,6,2,4,5,3] => 1
[1,6,2,5,3,4] => 1
[1,6,2,5,4,3] => 1
[1,6,3,2,4,5] => 1
[1,6,3,2,5,4] => 1
[1,6,3,4,2,5] => 1
[1,6,3,4,5,2] => 1
[1,6,3,5,2,4] => 1
[1,6,3,5,4,2] => 1
[1,6,4,2,3,5] => 1
[1,6,4,2,5,3] => 1
[1,6,4,3,2,5] => 1
[1,6,4,3,5,2] => 1
[1,6,4,5,2,3] => 1
[1,6,4,5,3,2] => 1
[1,6,5,2,3,4] => 1
[1,6,5,2,4,3] => 1
[1,6,5,3,2,4] => 1
[1,6,5,3,4,2] => 1
[1,6,5,4,2,3] => 1
[1,6,5,4,3,2] => 1
[2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => 2
[2,1,3,5,4,6] => 2
[2,1,3,5,6,4] => 2
[2,1,3,6,4,5] => 2
[2,1,3,6,5,4] => 2
[2,1,4,3,5,6] => 2
[2,1,4,3,6,5] => 3
[2,1,4,5,3,6] => 2
[2,1,4,5,6,3] => 2
[2,1,4,6,3,5] => 2
[2,1,4,6,5,3] => 2
[2,1,5,3,4,6] => 2
[2,1,5,3,6,4] => 2
[2,1,5,4,3,6] => 2
[2,1,5,4,6,3] => 2
[2,1,5,6,3,4] => 2
[2,1,5,6,4,3] => 2
[2,1,6,3,4,5] => 2
[2,1,6,3,5,4] => 2
[2,1,6,4,3,5] => 2
[2,1,6,4,5,3] => 2
[2,1,6,5,3,4] => 2
[2,1,6,5,4,3] => 2
[2,3,1,4,5,6] => 1
[2,3,1,4,6,5] => 2
[2,3,1,5,4,6] => 2
[2,3,1,5,6,4] => 2
[2,3,1,6,4,5] => 2
[2,3,1,6,5,4] => 2
[2,3,4,1,5,6] => 1
[2,3,4,1,6,5] => 2
[2,3,4,5,1,6] => 1
[2,3,4,5,6,1] => 1
[2,3,4,6,1,5] => 1
[2,3,4,6,5,1] => 1
[2,3,5,1,4,6] => 1
[2,3,5,1,6,4] => 1
[2,3,5,4,1,6] => 1
[2,3,5,4,6,1] => 1
[2,3,5,6,1,4] => 1
[2,3,5,6,4,1] => 1
[2,3,6,1,4,5] => 1
[2,3,6,1,5,4] => 1
[2,3,6,4,1,5] => 1
[2,3,6,4,5,1] => 1
[2,3,6,5,1,4] => 1
[2,3,6,5,4,1] => 1
[2,4,1,3,5,6] => 1
[2,4,1,3,6,5] => 2
[2,4,1,5,3,6] => 1
[2,4,1,5,6,3] => 1
[2,4,1,6,3,5] => 1
[2,4,1,6,5,3] => 1
[2,4,3,1,5,6] => 1
[2,4,3,1,6,5] => 2
[2,4,3,5,1,6] => 1
[2,4,3,5,6,1] => 1
[2,4,3,6,1,5] => 1
[2,4,3,6,5,1] => 1
[2,4,5,1,3,6] => 1
[2,4,5,1,6,3] => 1
[2,4,5,3,1,6] => 1
[2,4,5,3,6,1] => 1
[2,4,5,6,1,3] => 1
[2,4,5,6,3,1] => 1
[2,4,6,1,3,5] => 1
[2,4,6,1,5,3] => 1
[2,4,6,3,1,5] => 1
[2,4,6,3,5,1] => 1
[2,4,6,5,1,3] => 1
[2,4,6,5,3,1] => 1
[2,5,1,3,4,6] => 1
[2,5,1,3,6,4] => 1
[2,5,1,4,3,6] => 1
[2,5,1,4,6,3] => 1
[2,5,1,6,3,4] => 1
[2,5,1,6,4,3] => 1
[2,5,3,1,4,6] => 1
[2,5,3,1,6,4] => 1
[2,5,3,4,1,6] => 1
[2,5,3,4,6,1] => 1
[2,5,3,6,1,4] => 1
[2,5,3,6,4,1] => 1
[2,5,4,1,3,6] => 1
[2,5,4,1,6,3] => 1
[2,5,4,3,1,6] => 1
[2,5,4,3,6,1] => 1
[2,5,4,6,1,3] => 1
[2,5,4,6,3,1] => 1
[2,5,6,1,3,4] => 1
[2,5,6,1,4,3] => 1
[2,5,6,3,1,4] => 1
[2,5,6,3,4,1] => 1
[2,5,6,4,1,3] => 1
[2,5,6,4,3,1] => 1
[2,6,1,3,4,5] => 1
[2,6,1,3,5,4] => 1
[2,6,1,4,3,5] => 1
[2,6,1,4,5,3] => 1
[2,6,1,5,3,4] => 1
[2,6,1,5,4,3] => 1
[2,6,3,1,4,5] => 1
[2,6,3,1,5,4] => 1
[2,6,3,4,1,5] => 1
[2,6,3,4,5,1] => 1
[2,6,3,5,1,4] => 1
[2,6,3,5,4,1] => 1
[2,6,4,1,3,5] => 1
[2,6,4,1,5,3] => 1
[2,6,4,3,1,5] => 1
[2,6,4,3,5,1] => 1
[2,6,4,5,1,3] => 1
[2,6,4,5,3,1] => 1
[2,6,5,1,3,4] => 1
[2,6,5,1,4,3] => 1
[2,6,5,3,1,4] => 1
[2,6,5,3,4,1] => 1
[2,6,5,4,1,3] => 1
[2,6,5,4,3,1] => 1
[3,1,2,4,5,6] => 1
[3,1,2,4,6,5] => 2
[3,1,2,5,4,6] => 2
[3,1,2,5,6,4] => 2
[3,1,2,6,4,5] => 2
[3,1,2,6,5,4] => 2
[3,1,4,2,5,6] => 1
[3,1,4,2,6,5] => 2
[3,1,4,5,2,6] => 1
[3,1,4,5,6,2] => 1
[3,1,4,6,2,5] => 1
[3,1,4,6,5,2] => 1
[3,1,5,2,4,6] => 1
[3,1,5,2,6,4] => 1
[3,1,5,4,2,6] => 1
[3,1,5,4,6,2] => 1
[3,1,5,6,2,4] => 1
[3,1,5,6,4,2] => 1
[3,1,6,2,4,5] => 1
[3,1,6,2,5,4] => 1
[3,1,6,4,2,5] => 1
[3,1,6,4,5,2] => 1
[3,1,6,5,2,4] => 1
[3,1,6,5,4,2] => 1
[3,2,1,4,5,6] => 1
[3,2,1,4,6,5] => 2
[3,2,1,5,4,6] => 2
[3,2,1,5,6,4] => 2
[3,2,1,6,4,5] => 2
[3,2,1,6,5,4] => 2
[3,2,4,1,5,6] => 1
[3,2,4,1,6,5] => 2
[3,2,4,5,1,6] => 1
[3,2,4,5,6,1] => 1
[3,2,4,6,1,5] => 1
[3,2,4,6,5,1] => 1
[3,2,5,1,4,6] => 1
[3,2,5,1,6,4] => 1
[3,2,5,4,1,6] => 1
[3,2,5,4,6,1] => 1
[3,2,5,6,1,4] => 1
[3,2,5,6,4,1] => 1
[3,2,6,1,4,5] => 1
[3,2,6,1,5,4] => 1
[3,2,6,4,1,5] => 1
[3,2,6,4,5,1] => 1
[3,2,6,5,1,4] => 1
[3,2,6,5,4,1] => 1
[3,4,1,2,5,6] => 1
[3,4,1,2,6,5] => 2
[3,4,1,5,2,6] => 1
[3,4,1,5,6,2] => 1
[3,4,1,6,2,5] => 1
[3,4,1,6,5,2] => 1
[3,4,2,1,5,6] => 1
[3,4,2,1,6,5] => 2
[3,4,2,5,1,6] => 1
[3,4,2,5,6,1] => 1
[3,4,2,6,1,5] => 1
[3,4,2,6,5,1] => 1
[3,4,5,1,2,6] => 1
[3,4,5,1,6,2] => 1
[3,4,5,2,1,6] => 1
[3,4,5,2,6,1] => 1
[3,4,5,6,1,2] => 1
[3,4,5,6,2,1] => 1
[3,4,6,1,2,5] => 1
[3,4,6,1,5,2] => 1
[3,4,6,2,1,5] => 1
[3,4,6,2,5,1] => 1
[3,4,6,5,1,2] => 1
[3,4,6,5,2,1] => 1
[3,5,1,2,4,6] => 1
[3,5,1,2,6,4] => 1
[3,5,1,4,2,6] => 1
[3,5,1,4,6,2] => 1
[3,5,1,6,2,4] => 1
[3,5,1,6,4,2] => 1
[3,5,2,1,4,6] => 1
[3,5,2,1,6,4] => 1
[3,5,2,4,1,6] => 1
[3,5,2,4,6,1] => 1
[3,5,2,6,1,4] => 1
[3,5,2,6,4,1] => 1
[3,5,4,1,2,6] => 1
[3,5,4,1,6,2] => 1
[3,5,4,2,1,6] => 1
[3,5,4,2,6,1] => 1
[3,5,4,6,1,2] => 1
[3,5,4,6,2,1] => 1
[3,5,6,1,2,4] => 1
[3,5,6,1,4,2] => 1
[3,5,6,2,1,4] => 1
[3,5,6,2,4,1] => 1
[3,5,6,4,1,2] => 1
[3,5,6,4,2,1] => 1
[3,6,1,2,4,5] => 1
[3,6,1,2,5,4] => 1
[3,6,1,4,2,5] => 1
[3,6,1,4,5,2] => 1
[3,6,1,5,2,4] => 1
[3,6,1,5,4,2] => 1
[3,6,2,1,4,5] => 1
[3,6,2,1,5,4] => 1
[3,6,2,4,1,5] => 1
[3,6,2,4,5,1] => 1
[3,6,2,5,1,4] => 1
[3,6,2,5,4,1] => 1
[3,6,4,1,2,5] => 1
[3,6,4,1,5,2] => 1
[3,6,4,2,1,5] => 1
[3,6,4,2,5,1] => 1
[3,6,4,5,1,2] => 1
[3,6,4,5,2,1] => 1
[3,6,5,1,2,4] => 1
[3,6,5,1,4,2] => 1
[3,6,5,2,1,4] => 1
[3,6,5,2,4,1] => 1
[3,6,5,4,1,2] => 1
[3,6,5,4,2,1] => 1
[4,1,2,3,5,6] => 1
[4,1,2,3,6,5] => 2
[4,1,2,5,3,6] => 1
[4,1,2,5,6,3] => 1
[4,1,2,6,3,5] => 1
[4,1,2,6,5,3] => 1
[4,1,3,2,5,6] => 1
[4,1,3,2,6,5] => 2
[4,1,3,5,2,6] => 1
[4,1,3,5,6,2] => 1
[4,1,3,6,2,5] => 1
[4,1,3,6,5,2] => 1
[4,1,5,2,3,6] => 1
[4,1,5,2,6,3] => 1
[4,1,5,3,2,6] => 1
[4,1,5,3,6,2] => 1
[4,1,5,6,2,3] => 1
[4,1,5,6,3,2] => 1
[4,1,6,2,3,5] => 1
[4,1,6,2,5,3] => 1
[4,1,6,3,2,5] => 1
[4,1,6,3,5,2] => 1
[4,1,6,5,2,3] => 1
[4,1,6,5,3,2] => 1
[4,2,1,3,5,6] => 1
[4,2,1,3,6,5] => 2
[4,2,1,5,3,6] => 1
[4,2,1,5,6,3] => 1
[4,2,1,6,3,5] => 1
[4,2,1,6,5,3] => 1
[4,2,3,1,5,6] => 1
[4,2,3,1,6,5] => 2
[4,2,3,5,1,6] => 1
[4,2,3,5,6,1] => 1
[4,2,3,6,1,5] => 1
[4,2,3,6,5,1] => 1
[4,2,5,1,3,6] => 1
[4,2,5,1,6,3] => 1
[4,2,5,3,1,6] => 1
[4,2,5,3,6,1] => 1
[4,2,5,6,1,3] => 1
[4,2,5,6,3,1] => 1
[4,2,6,1,3,5] => 1
[4,2,6,1,5,3] => 1
[4,2,6,3,1,5] => 1
[4,2,6,3,5,1] => 1
[4,2,6,5,1,3] => 1
[4,2,6,5,3,1] => 1
[4,3,1,2,5,6] => 1
[4,3,1,2,6,5] => 2
[4,3,1,5,2,6] => 1
[4,3,1,5,6,2] => 1
[4,3,1,6,2,5] => 1
[4,3,1,6,5,2] => 1
[4,3,2,1,5,6] => 1
[4,3,2,1,6,5] => 2
[4,3,2,5,1,6] => 1
[4,3,2,5,6,1] => 1
[4,3,2,6,1,5] => 1
[4,3,2,6,5,1] => 1
[4,3,5,1,2,6] => 1
[4,3,5,1,6,2] => 1
[4,3,5,2,1,6] => 1
[4,3,5,2,6,1] => 1
[4,3,5,6,1,2] => 1
[4,3,5,6,2,1] => 1
[4,3,6,1,2,5] => 1
[4,3,6,1,5,2] => 1
[4,3,6,2,1,5] => 1
[4,3,6,2,5,1] => 1
[4,3,6,5,1,2] => 1
[4,3,6,5,2,1] => 1
[4,5,1,2,3,6] => 1
[4,5,1,2,6,3] => 1
[4,5,1,3,2,6] => 1
[4,5,1,3,6,2] => 1
[4,5,1,6,2,3] => 1
[4,5,1,6,3,2] => 1
[4,5,2,1,3,6] => 1
[4,5,2,1,6,3] => 1
[4,5,2,3,1,6] => 1
[4,5,2,3,6,1] => 1
[4,5,2,6,1,3] => 1
[4,5,2,6,3,1] => 1
[4,5,3,1,2,6] => 1
[4,5,3,1,6,2] => 1
[4,5,3,2,1,6] => 1
[4,5,3,2,6,1] => 1
[4,5,3,6,1,2] => 1
[4,5,3,6,2,1] => 1
[4,5,6,1,2,3] => 1
[4,5,6,1,3,2] => 1
[4,5,6,2,1,3] => 1
[4,5,6,2,3,1] => 1
[4,5,6,3,1,2] => 1
[4,5,6,3,2,1] => 1
[4,6,1,2,3,5] => 1
[4,6,1,2,5,3] => 1
[4,6,1,3,2,5] => 1
[4,6,1,3,5,2] => 1
[4,6,1,5,2,3] => 1
[4,6,1,5,3,2] => 1
[4,6,2,1,3,5] => 1
[4,6,2,1,5,3] => 1
[4,6,2,3,1,5] => 1
[4,6,2,3,5,1] => 1
[4,6,2,5,1,3] => 1
[4,6,2,5,3,1] => 1
[4,6,3,1,2,5] => 1
[4,6,3,1,5,2] => 1
[4,6,3,2,1,5] => 1
[4,6,3,2,5,1] => 1
[4,6,3,5,1,2] => 1
[4,6,3,5,2,1] => 1
[4,6,5,1,2,3] => 1
[4,6,5,1,3,2] => 1
[4,6,5,2,1,3] => 1
[4,6,5,2,3,1] => 1
[4,6,5,3,1,2] => 1
[4,6,5,3,2,1] => 1
[5,1,2,3,4,6] => 1
[5,1,2,3,6,4] => 1
[5,1,2,4,3,6] => 1
[5,1,2,4,6,3] => 1
[5,1,2,6,3,4] => 1
[5,1,2,6,4,3] => 1
[5,1,3,2,4,6] => 1
[5,1,3,2,6,4] => 1
[5,1,3,4,2,6] => 1
[5,1,3,4,6,2] => 1
[5,1,3,6,2,4] => 1
[5,1,3,6,4,2] => 1
[5,1,4,2,3,6] => 1
[5,1,4,2,6,3] => 1
[5,1,4,3,2,6] => 1
[5,1,4,3,6,2] => 1
[5,1,4,6,2,3] => 1
[5,1,4,6,3,2] => 1
[5,1,6,2,3,4] => 1
[5,1,6,2,4,3] => 1
[5,1,6,3,2,4] => 1
[5,1,6,3,4,2] => 1
[5,1,6,4,2,3] => 1
[5,1,6,4,3,2] => 1
[5,2,1,3,4,6] => 1
[5,2,1,3,6,4] => 1
[5,2,1,4,3,6] => 1
[5,2,1,4,6,3] => 1
[5,2,1,6,3,4] => 1
[5,2,1,6,4,3] => 1
[5,2,3,1,4,6] => 1
[5,2,3,1,6,4] => 1
[5,2,3,4,1,6] => 1
[5,2,3,4,6,1] => 1
[5,2,3,6,1,4] => 1
[5,2,3,6,4,1] => 1
[5,2,4,1,3,6] => 1
[5,2,4,1,6,3] => 1
[5,2,4,3,1,6] => 1
[5,2,4,3,6,1] => 1
[5,2,4,6,1,3] => 1
[5,2,4,6,3,1] => 1
[5,2,6,1,3,4] => 1
[5,2,6,1,4,3] => 1
[5,2,6,3,1,4] => 1
[5,2,6,3,4,1] => 1
[5,2,6,4,1,3] => 1
[5,2,6,4,3,1] => 1
[5,3,1,2,4,6] => 1
[5,3,1,2,6,4] => 1
[5,3,1,4,2,6] => 1
[5,3,1,4,6,2] => 1
[5,3,1,6,2,4] => 1
[5,3,1,6,4,2] => 1
[5,3,2,1,4,6] => 1
[5,3,2,1,6,4] => 1
[5,3,2,4,1,6] => 1
[5,3,2,4,6,1] => 1
[5,3,2,6,1,4] => 1
[5,3,2,6,4,1] => 1
[5,3,4,1,2,6] => 1
[5,3,4,1,6,2] => 1
[5,3,4,2,1,6] => 1
[5,3,4,2,6,1] => 1
[5,3,4,6,1,2] => 1
[5,3,4,6,2,1] => 1
[5,3,6,1,2,4] => 1
[5,3,6,1,4,2] => 1
[5,3,6,2,1,4] => 1
[5,3,6,2,4,1] => 1
[5,3,6,4,1,2] => 1
[5,3,6,4,2,1] => 1
[5,4,1,2,3,6] => 1
[5,4,1,2,6,3] => 1
[5,4,1,3,2,6] => 1
[5,4,1,3,6,2] => 1
[5,4,1,6,2,3] => 1
[5,4,1,6,3,2] => 1
[5,4,2,1,3,6] => 1
[5,4,2,1,6,3] => 1
[5,4,2,3,1,6] => 1
[5,4,2,3,6,1] => 1
[5,4,2,6,1,3] => 1
[5,4,2,6,3,1] => 1
[5,4,3,1,2,6] => 1
[5,4,3,1,6,2] => 1
[5,4,3,2,1,6] => 1
[5,4,3,2,6,1] => 1
[5,4,3,6,1,2] => 1
[5,4,3,6,2,1] => 1
[5,4,6,1,2,3] => 1
[5,4,6,1,3,2] => 1
[5,4,6,2,1,3] => 1
[5,4,6,2,3,1] => 1
[5,4,6,3,1,2] => 1
[5,4,6,3,2,1] => 1
[5,6,1,2,3,4] => 1
[5,6,1,2,4,3] => 1
[5,6,1,3,2,4] => 1
[5,6,1,3,4,2] => 1
[5,6,1,4,2,3] => 1
[5,6,1,4,3,2] => 1
[5,6,2,1,3,4] => 1
[5,6,2,1,4,3] => 1
[5,6,2,3,1,4] => 1
[5,6,2,3,4,1] => 1
[5,6,2,4,1,3] => 1
[5,6,2,4,3,1] => 1
[5,6,3,1,2,4] => 1
[5,6,3,1,4,2] => 1
[5,6,3,2,1,4] => 1
[5,6,3,2,4,1] => 1
[5,6,3,4,1,2] => 1
[5,6,3,4,2,1] => 1
[5,6,4,1,2,3] => 1
[5,6,4,1,3,2] => 1
[5,6,4,2,1,3] => 1
[5,6,4,2,3,1] => 1
[5,6,4,3,1,2] => 1
[5,6,4,3,2,1] => 1
[6,1,2,3,4,5] => 1
[6,1,2,3,5,4] => 1
[6,1,2,4,3,5] => 1
[6,1,2,4,5,3] => 1
[6,1,2,5,3,4] => 1
[6,1,2,5,4,3] => 1
[6,1,3,2,4,5] => 1
[6,1,3,2,5,4] => 1
[6,1,3,4,2,5] => 1
[6,1,3,4,5,2] => 1
[6,1,3,5,2,4] => 1
[6,1,3,5,4,2] => 1
[6,1,4,2,3,5] => 1
[6,1,4,2,5,3] => 1
[6,1,4,3,2,5] => 1
[6,1,4,3,5,2] => 1
[6,1,4,5,2,3] => 1
[6,1,4,5,3,2] => 1
[6,1,5,2,3,4] => 1
[6,1,5,2,4,3] => 1
[6,1,5,3,2,4] => 1
[6,1,5,3,4,2] => 1
[6,1,5,4,2,3] => 1
[6,1,5,4,3,2] => 1
[6,2,1,3,4,5] => 1
[6,2,1,3,5,4] => 1
[6,2,1,4,3,5] => 1
[6,2,1,4,5,3] => 1
[6,2,1,5,3,4] => 1
[6,2,1,5,4,3] => 1
[6,2,3,1,4,5] => 1
[6,2,3,1,5,4] => 1
[6,2,3,4,1,5] => 1
[6,2,3,4,5,1] => 1
[6,2,3,5,1,4] => 1
[6,2,3,5,4,1] => 1
[6,2,4,1,3,5] => 1
[6,2,4,1,5,3] => 1
[6,2,4,3,1,5] => 1
[6,2,4,3,5,1] => 1
[6,2,4,5,1,3] => 1
[6,2,4,5,3,1] => 1
[6,2,5,1,3,4] => 1
[6,2,5,1,4,3] => 1
[6,2,5,3,1,4] => 1
[6,2,5,3,4,1] => 1
[6,2,5,4,1,3] => 1
[6,2,5,4,3,1] => 1
[6,3,1,2,4,5] => 1
[6,3,1,2,5,4] => 1
[6,3,1,4,2,5] => 1
[6,3,1,4,5,2] => 1
[6,3,1,5,2,4] => 1
[6,3,1,5,4,2] => 1
[6,3,2,1,4,5] => 1
[6,3,2,1,5,4] => 1
[6,3,2,4,1,5] => 1
[6,3,2,4,5,1] => 1
[6,3,2,5,1,4] => 1
[6,3,2,5,4,1] => 1
[6,3,4,1,2,5] => 1
[6,3,4,1,5,2] => 1
[6,3,4,2,1,5] => 1
[6,3,4,2,5,1] => 1
[6,3,4,5,1,2] => 1
[6,3,4,5,2,1] => 1
[6,3,5,1,2,4] => 1
[6,3,5,1,4,2] => 1
[6,3,5,2,1,4] => 1
[6,3,5,2,4,1] => 1
[6,3,5,4,1,2] => 1
[6,3,5,4,2,1] => 1
[6,4,1,2,3,5] => 1
[6,4,1,2,5,3] => 1
[6,4,1,3,2,5] => 1
[6,4,1,3,5,2] => 1
[6,4,1,5,2,3] => 1
[6,4,1,5,3,2] => 1
[6,4,2,1,3,5] => 1
[6,4,2,1,5,3] => 1
[6,4,2,3,1,5] => 1
[6,4,2,3,5,1] => 1
[6,4,2,5,1,3] => 1
[6,4,2,5,3,1] => 1
[6,4,3,1,2,5] => 1
[6,4,3,1,5,2] => 1
[6,4,3,2,1,5] => 1
[6,4,3,2,5,1] => 1
[6,4,3,5,1,2] => 1
[6,4,3,5,2,1] => 1
[6,4,5,1,2,3] => 1
[6,4,5,1,3,2] => 1
[6,4,5,2,1,3] => 1
[6,4,5,2,3,1] => 1
[6,4,5,3,1,2] => 1
[6,4,5,3,2,1] => 1
[6,5,1,2,3,4] => 1
[6,5,1,2,4,3] => 1
[6,5,1,3,2,4] => 1
[6,5,1,3,4,2] => 1
[6,5,1,4,2,3] => 1
[6,5,1,4,3,2] => 1
[6,5,2,1,3,4] => 1
[6,5,2,1,4,3] => 1
[6,5,2,3,1,4] => 1
[6,5,2,3,4,1] => 1
[6,5,2,4,1,3] => 1
[6,5,2,4,3,1] => 1
[6,5,3,1,2,4] => 1
[6,5,3,1,4,2] => 1
[6,5,3,2,1,4] => 1
[6,5,3,2,4,1] => 1
[6,5,3,4,1,2] => 1
[6,5,3,4,2,1] => 1
[6,5,4,1,2,3] => 1
[6,5,4,1,3,2] => 1
[6,5,4,2,1,3] => 1
[6,5,4,2,3,1] => 1
[6,5,4,3,1,2] => 1
[6,5,4,3,2,1] => 1
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Description
The number of factors of the Stanley symmetric function associated with a permutation.
For example, the Stanley symmetric function of $\pi=321645$ equals
$20 m_{1,1,1,1,1} + 11 m_{2,1,1,1} + 6 m_{2,2,1} + 4 m_{3,1,1} + 2 m_{3,2} + m_{4,1} = (m_{1,1} + m_{2})(2 m_{1,1,1} + m_{2,1}).$
Code
def statistic(pi):
    return sum(m for _, m in pi.stanley_symmetric_function().factor())
Created
Nov 29, 2022 at 12:32 by Martin Rubey
Updated
Nov 29, 2022 at 12:32 by Martin Rubey