Identifier
Identifier
Values
[1] => 1
[1,2] => 1
[2,1] => 2
[1,2,3] => 1
[1,3,2] => 1
[2,1,3] => 2
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 3
[1,2,3,4] => 1
[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] => 2
[2,1,4,3] => 2
[2,3,1,4] => 2
[2,3,4,1] => 2
[2,4,1,3] => 2
[2,4,3,1] => 3
[3,1,2,4] => 2
[3,1,4,2] => 2
[3,2,1,4] => 3
[3,2,4,1] => 3
[3,4,1,2] => 2
[3,4,2,1] => 3
[4,1,2,3] => 2
[4,1,3,2] => 2
[4,2,1,3] => 3
[4,2,3,1] => 3
[4,3,1,2] => 3
[4,3,2,1] => 4
[1,2,3,4,5] => 1
[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] => 1
[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] => 2
[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] => 2
[2,3,1,5,4] => 2
[2,3,4,1,5] => 2
[2,3,4,5,1] => 2
[2,3,5,1,4] => 2
[2,3,5,4,1] => 3
[2,4,1,3,5] => 2
[2,4,1,5,3] => 2
[2,4,3,1,5] => 3
[2,4,3,5,1] => 3
[2,4,5,1,3] => 2
[2,4,5,3,1] => 3
[2,5,1,3,4] => 2
[2,5,1,4,3] => 2
[2,5,3,1,4] => 3
[2,5,3,4,1] => 3
[2,5,4,1,3] => 3
[2,5,4,3,1] => 4
[3,1,2,4,5] => 2
[3,1,2,5,4] => 2
[3,1,4,2,5] => 2
[3,1,4,5,2] => 2
[3,1,5,2,4] => 2
[3,1,5,4,2] => 2
[3,2,1,4,5] => 3
[3,2,1,5,4] => 3
[3,2,4,1,5] => 3
[3,2,4,5,1] => 3
[3,2,5,1,4] => 3
[3,2,5,4,1] => 3
[3,4,1,2,5] => 2
[3,4,1,5,2] => 2
[3,4,2,1,5] => 3
[3,4,2,5,1] => 3
[3,4,5,1,2] => 2
[3,4,5,2,1] => 3
[3,5,1,2,4] => 2
[3,5,1,4,2] => 2
[3,5,2,1,4] => 3
[3,5,2,4,1] => 3
[3,5,4,1,2] => 3
[3,5,4,2,1] => 4
[4,1,2,3,5] => 2
[4,1,2,5,3] => 2
[4,1,3,2,5] => 2
[4,1,3,5,2] => 2
[4,1,5,2,3] => 2
[4,1,5,3,2] => 2
[4,2,1,3,5] => 3
[4,2,1,5,3] => 3
[4,2,3,1,5] => 3
[4,2,3,5,1] => 3
[4,2,5,1,3] => 3
[4,2,5,3,1] => 3
[4,3,1,2,5] => 3
[4,3,1,5,2] => 3
[4,3,2,1,5] => 4
[4,3,2,5,1] => 4
[4,3,5,1,2] => 3
[4,3,5,2,1] => 4
[4,5,1,2,3] => 2
[4,5,1,3,2] => 2
[4,5,2,1,3] => 3
[4,5,2,3,1] => 3
[4,5,3,1,2] => 3
[4,5,3,2,1] => 4
[5,1,2,3,4] => 2
[5,1,2,4,3] => 2
[5,1,3,2,4] => 2
[5,1,3,4,2] => 2
[5,1,4,2,3] => 2
[5,1,4,3,2] => 2
[5,2,1,3,4] => 3
[5,2,1,4,3] => 3
[5,2,3,1,4] => 3
[5,2,3,4,1] => 3
[5,2,4,1,3] => 3
[5,2,4,3,1] => 4
[5,3,1,2,4] => 3
[5,3,1,4,2] => 3
[5,3,2,1,4] => 4
[5,3,2,4,1] => 4
[5,3,4,1,2] => 3
[5,3,4,2,1] => 4
[5,4,1,2,3] => 3
[5,4,1,3,2] => 3
[5,4,2,1,3] => 4
[5,4,2,3,1] => 4
[5,4,3,1,2] => 4
[5,4,3,2,1] => 5
[1,2,3,4,5,6] => 1
[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] => 1
[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] => 1
[1,3,2,5,4,6] => 1
[1,3,2,5,6,4] => 1
[1,3,2,6,4,5] => 1
[1,3,2,6,5,4] => 1
[1,3,4,2,5,6] => 1
[1,3,4,2,6,5] => 1
[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] => 1
[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] => 1
[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] => 2
[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] => 2
[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] => 2
[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] => 2
[2,3,4,1,6,5] => 2
[2,3,4,5,1,6] => 2
[2,3,4,5,6,1] => 2
[2,3,4,6,1,5] => 2
[2,3,4,6,5,1] => 3
[2,3,5,1,4,6] => 2
[2,3,5,1,6,4] => 2
[2,3,5,4,1,6] => 3
[2,3,5,4,6,1] => 3
[2,3,5,6,1,4] => 2
[2,3,5,6,4,1] => 3
[2,3,6,1,4,5] => 2
[2,3,6,1,5,4] => 2
[2,3,6,4,1,5] => 3
[2,3,6,4,5,1] => 3
[2,3,6,5,1,4] => 3
[2,3,6,5,4,1] => 4
[2,4,1,3,5,6] => 2
[2,4,1,3,6,5] => 2
[2,4,1,5,3,6] => 2
[2,4,1,5,6,3] => 2
[2,4,1,6,3,5] => 2
[2,4,1,6,5,3] => 2
[2,4,3,1,5,6] => 3
[2,4,3,1,6,5] => 3
[2,4,3,5,1,6] => 3
[2,4,3,5,6,1] => 3
[2,4,3,6,1,5] => 3
[2,4,3,6,5,1] => 3
[2,4,5,1,3,6] => 2
[2,4,5,1,6,3] => 2
[2,4,5,3,1,6] => 3
[2,4,5,3,6,1] => 3
[2,4,5,6,1,3] => 2
[2,4,5,6,3,1] => 3
[2,4,6,1,3,5] => 2
[2,4,6,1,5,3] => 2
[2,4,6,3,1,5] => 3
[2,4,6,3,5,1] => 3
[2,4,6,5,1,3] => 3
[2,4,6,5,3,1] => 4
[2,5,1,3,4,6] => 2
[2,5,1,3,6,4] => 2
[2,5,1,4,3,6] => 2
[2,5,1,4,6,3] => 2
[2,5,1,6,3,4] => 2
[2,5,1,6,4,3] => 2
[2,5,3,1,4,6] => 3
[2,5,3,1,6,4] => 3
[2,5,3,4,1,6] => 3
[2,5,3,4,6,1] => 3
[2,5,3,6,1,4] => 3
[2,5,3,6,4,1] => 3
[2,5,4,1,3,6] => 3
[2,5,4,1,6,3] => 3
[2,5,4,3,1,6] => 4
[2,5,4,3,6,1] => 4
[2,5,4,6,1,3] => 3
[2,5,4,6,3,1] => 4
[2,5,6,1,3,4] => 2
[2,5,6,1,4,3] => 2
[2,5,6,3,1,4] => 3
[2,5,6,3,4,1] => 3
[2,5,6,4,1,3] => 3
[2,5,6,4,3,1] => 4
[2,6,1,3,4,5] => 2
[2,6,1,3,5,4] => 2
[2,6,1,4,3,5] => 2
[2,6,1,4,5,3] => 2
[2,6,1,5,3,4] => 2
[2,6,1,5,4,3] => 2
[2,6,3,1,4,5] => 3
[2,6,3,1,5,4] => 3
[2,6,3,4,1,5] => 3
[2,6,3,4,5,1] => 3
[2,6,3,5,1,4] => 3
[2,6,3,5,4,1] => 4
[2,6,4,1,3,5] => 3
[2,6,4,1,5,3] => 3
[2,6,4,3,1,5] => 4
[2,6,4,3,5,1] => 4
[2,6,4,5,1,3] => 3
[2,6,4,5,3,1] => 4
[2,6,5,1,3,4] => 3
[2,6,5,1,4,3] => 3
[2,6,5,3,1,4] => 4
[2,6,5,3,4,1] => 4
[2,6,5,4,1,3] => 4
[2,6,5,4,3,1] => 5
[3,1,2,4,5,6] => 2
[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] => 2
[3,1,4,2,6,5] => 2
[3,1,4,5,2,6] => 2
[3,1,4,5,6,2] => 2
[3,1,4,6,2,5] => 2
[3,1,4,6,5,2] => 2
[3,1,5,2,4,6] => 2
[3,1,5,2,6,4] => 2
[3,1,5,4,2,6] => 2
[3,1,5,4,6,2] => 2
[3,1,5,6,2,4] => 2
[3,1,5,6,4,2] => 2
[3,1,6,2,4,5] => 2
[3,1,6,2,5,4] => 2
[3,1,6,4,2,5] => 2
[3,1,6,4,5,2] => 2
[3,1,6,5,2,4] => 2
[3,1,6,5,4,2] => 2
[3,2,1,4,5,6] => 3
[3,2,1,4,6,5] => 3
[3,2,1,5,4,6] => 3
[3,2,1,5,6,4] => 3
[3,2,1,6,4,5] => 3
[3,2,1,6,5,4] => 3
[3,2,4,1,5,6] => 3
[3,2,4,1,6,5] => 3
[3,2,4,5,1,6] => 3
[3,2,4,5,6,1] => 3
[3,2,4,6,1,5] => 3
[3,2,4,6,5,1] => 3
[3,2,5,1,4,6] => 3
[3,2,5,1,6,4] => 3
[3,2,5,4,1,6] => 3
[3,2,5,4,6,1] => 3
[3,2,5,6,1,4] => 3
[3,2,5,6,4,1] => 3
[3,2,6,1,4,5] => 3
[3,2,6,1,5,4] => 3
[3,2,6,4,1,5] => 3
[3,2,6,4,5,1] => 3
[3,2,6,5,1,4] => 3
[3,2,6,5,4,1] => 4
[3,4,1,2,5,6] => 2
[3,4,1,2,6,5] => 2
[3,4,1,5,2,6] => 2
[3,4,1,5,6,2] => 2
[3,4,1,6,2,5] => 2
[3,4,1,6,5,2] => 2
[3,4,2,1,5,6] => 3
[3,4,2,1,6,5] => 3
[3,4,2,5,1,6] => 3
[3,4,2,5,6,1] => 3
[3,4,2,6,1,5] => 3
[3,4,2,6,5,1] => 3
[3,4,5,1,2,6] => 2
[3,4,5,1,6,2] => 2
[3,4,5,2,1,6] => 3
[3,4,5,2,6,1] => 3
[3,4,5,6,1,2] => 2
[3,4,5,6,2,1] => 3
[3,4,6,1,2,5] => 2
[3,4,6,1,5,2] => 2
[3,4,6,2,1,5] => 3
[3,4,6,2,5,1] => 3
[3,4,6,5,1,2] => 3
[3,4,6,5,2,1] => 4
[3,5,1,2,4,6] => 2
[3,5,1,2,6,4] => 2
[3,5,1,4,2,6] => 2
[3,5,1,4,6,2] => 2
[3,5,1,6,2,4] => 2
[3,5,1,6,4,2] => 2
[3,5,2,1,4,6] => 3
[3,5,2,1,6,4] => 3
[3,5,2,4,1,6] => 3
[3,5,2,4,6,1] => 3
[3,5,2,6,1,4] => 3
[3,5,2,6,4,1] => 3
[3,5,4,1,2,6] => 3
[3,5,4,1,6,2] => 3
[3,5,4,2,1,6] => 4
[3,5,4,2,6,1] => 4
[3,5,4,6,1,2] => 3
[3,5,4,6,2,1] => 4
[3,5,6,1,2,4] => 2
[3,5,6,1,4,2] => 2
[3,5,6,2,1,4] => 3
[3,5,6,2,4,1] => 3
[3,5,6,4,1,2] => 3
[3,5,6,4,2,1] => 4
[3,6,1,2,4,5] => 2
[3,6,1,2,5,4] => 2
[3,6,1,4,2,5] => 2
[3,6,1,4,5,2] => 2
[3,6,1,5,2,4] => 2
[3,6,1,5,4,2] => 2
[3,6,2,1,4,5] => 3
[3,6,2,1,5,4] => 3
[3,6,2,4,1,5] => 3
[3,6,2,4,5,1] => 3
[3,6,2,5,1,4] => 3
[3,6,2,5,4,1] => 4
[3,6,4,1,2,5] => 3
[3,6,4,1,5,2] => 3
[3,6,4,2,1,5] => 4
[3,6,4,2,5,1] => 4
[3,6,4,5,1,2] => 3
[3,6,4,5,2,1] => 4
[3,6,5,1,2,4] => 3
[3,6,5,1,4,2] => 3
[3,6,5,2,1,4] => 4
[3,6,5,2,4,1] => 4
[3,6,5,4,1,2] => 4
[3,6,5,4,2,1] => 5
[4,1,2,3,5,6] => 2
[4,1,2,3,6,5] => 2
[4,1,2,5,3,6] => 2
[4,1,2,5,6,3] => 2
[4,1,2,6,3,5] => 2
[4,1,2,6,5,3] => 2
[4,1,3,2,5,6] => 2
[4,1,3,2,6,5] => 2
[4,1,3,5,2,6] => 2
[4,1,3,5,6,2] => 2
[4,1,3,6,2,5] => 2
[4,1,3,6,5,2] => 2
[4,1,5,2,3,6] => 2
[4,1,5,2,6,3] => 2
[4,1,5,3,2,6] => 2
[4,1,5,3,6,2] => 2
[4,1,5,6,2,3] => 2
[4,1,5,6,3,2] => 2
[4,1,6,2,3,5] => 2
[4,1,6,2,5,3] => 2
[4,1,6,3,2,5] => 2
[4,1,6,3,5,2] => 2
[4,1,6,5,2,3] => 2
[4,1,6,5,3,2] => 2
[4,2,1,3,5,6] => 3
[4,2,1,3,6,5] => 3
[4,2,1,5,3,6] => 3
[4,2,1,5,6,3] => 3
[4,2,1,6,3,5] => 3
[4,2,1,6,5,3] => 3
[4,2,3,1,5,6] => 3
[4,2,3,1,6,5] => 3
[4,2,3,5,1,6] => 3
[4,2,3,5,6,1] => 3
[4,2,3,6,1,5] => 3
[4,2,3,6,5,1] => 3
[4,2,5,1,3,6] => 3
[4,2,5,1,6,3] => 3
[4,2,5,3,1,6] => 3
[4,2,5,3,6,1] => 3
[4,2,5,6,1,3] => 3
[4,2,5,6,3,1] => 3
[4,2,6,1,3,5] => 3
[4,2,6,1,5,3] => 3
[4,2,6,3,1,5] => 3
[4,2,6,3,5,1] => 3
[4,2,6,5,1,3] => 3
[4,2,6,5,3,1] => 4
[4,3,1,2,5,6] => 3
[4,3,1,2,6,5] => 3
[4,3,1,5,2,6] => 3
[4,3,1,5,6,2] => 3
[4,3,1,6,2,5] => 3
[4,3,1,6,5,2] => 3
[4,3,2,1,5,6] => 4
[4,3,2,1,6,5] => 4
[4,3,2,5,1,6] => 4
[4,3,2,5,6,1] => 4
[4,3,2,6,1,5] => 4
[4,3,2,6,5,1] => 4
[4,3,5,1,2,6] => 3
[4,3,5,1,6,2] => 3
[4,3,5,2,1,6] => 4
[4,3,5,2,6,1] => 4
[4,3,5,6,1,2] => 3
[4,3,5,6,2,1] => 4
[4,3,6,1,2,5] => 3
[4,3,6,1,5,2] => 3
[4,3,6,2,1,5] => 4
[4,3,6,2,5,1] => 4
[4,3,6,5,1,2] => 3
[4,3,6,5,2,1] => 4
[4,5,1,2,3,6] => 2
[4,5,1,2,6,3] => 2
[4,5,1,3,2,6] => 2
[4,5,1,3,6,2] => 2
[4,5,1,6,2,3] => 2
[4,5,1,6,3,2] => 2
[4,5,2,1,3,6] => 3
[4,5,2,1,6,3] => 3
[4,5,2,3,1,6] => 3
[4,5,2,3,6,1] => 3
[4,5,2,6,1,3] => 3
[4,5,2,6,3,1] => 3
[4,5,3,1,2,6] => 3
[4,5,3,1,6,2] => 3
[4,5,3,2,1,6] => 4
[4,5,3,2,6,1] => 4
[4,5,3,6,1,2] => 3
[4,5,3,6,2,1] => 4
[4,5,6,1,2,3] => 2
[4,5,6,1,3,2] => 2
[4,5,6,2,1,3] => 3
[4,5,6,2,3,1] => 3
[4,5,6,3,1,2] => 3
[4,5,6,3,2,1] => 4
[4,6,1,2,3,5] => 2
[4,6,1,2,5,3] => 2
[4,6,1,3,2,5] => 2
[4,6,1,3,5,2] => 2
[4,6,1,5,2,3] => 2
[4,6,1,5,3,2] => 2
[4,6,2,1,3,5] => 3
[4,6,2,1,5,3] => 3
[4,6,2,3,1,5] => 3
[4,6,2,3,5,1] => 3
[4,6,2,5,1,3] => 3
[4,6,2,5,3,1] => 4
[4,6,3,1,2,5] => 3
[4,6,3,1,5,2] => 3
[4,6,3,2,1,5] => 4
[4,6,3,2,5,1] => 4
[4,6,3,5,1,2] => 3
[4,6,3,5,2,1] => 4
[4,6,5,1,2,3] => 3
[4,6,5,1,3,2] => 3
[4,6,5,2,1,3] => 4
[4,6,5,2,3,1] => 4
[4,6,5,3,1,2] => 4
[4,6,5,3,2,1] => 5
[5,1,2,3,4,6] => 2
[5,1,2,3,6,4] => 2
[5,1,2,4,3,6] => 2
[5,1,2,4,6,3] => 2
[5,1,2,6,3,4] => 2
[5,1,2,6,4,3] => 2
[5,1,3,2,4,6] => 2
[5,1,3,2,6,4] => 2
[5,1,3,4,2,6] => 2
[5,1,3,4,6,2] => 2
[5,1,3,6,2,4] => 2
[5,1,3,6,4,2] => 2
[5,1,4,2,3,6] => 2
[5,1,4,2,6,3] => 2
[5,1,4,3,2,6] => 2
[5,1,4,3,6,2] => 2
[5,1,4,6,2,3] => 2
[5,1,4,6,3,2] => 2
[5,1,6,2,3,4] => 2
[5,1,6,2,4,3] => 2
[5,1,6,3,2,4] => 2
[5,1,6,3,4,2] => 2
[5,1,6,4,2,3] => 2
[5,1,6,4,3,2] => 2
[5,2,1,3,4,6] => 3
[5,2,1,3,6,4] => 3
[5,2,1,4,3,6] => 3
[5,2,1,4,6,3] => 3
[5,2,1,6,3,4] => 3
[5,2,1,6,4,3] => 3
[5,2,3,1,4,6] => 3
[5,2,3,1,6,4] => 3
[5,2,3,4,1,6] => 3
[5,2,3,4,6,1] => 3
[5,2,3,6,1,4] => 3
[5,2,3,6,4,1] => 3
[5,2,4,1,3,6] => 3
[5,2,4,1,6,3] => 3
[5,2,4,3,1,6] => 4
[5,2,4,3,6,1] => 4
[5,2,4,6,1,3] => 3
[5,2,4,6,3,1] => 4
[5,2,6,1,3,4] => 3
[5,2,6,1,4,3] => 3
[5,2,6,3,1,4] => 3
[5,2,6,3,4,1] => 3
[5,2,6,4,1,3] => 3
[5,2,6,4,3,1] => 4
[5,3,1,2,4,6] => 3
[5,3,1,2,6,4] => 3
[5,3,1,4,2,6] => 3
[5,3,1,4,6,2] => 3
[5,3,1,6,2,4] => 3
[5,3,1,6,4,2] => 3
[5,3,2,1,4,6] => 4
[5,3,2,1,6,4] => 4
[5,3,2,4,1,6] => 4
[5,3,2,4,6,1] => 4
[5,3,2,6,1,4] => 4
[5,3,2,6,4,1] => 4
[5,3,4,1,2,6] => 3
[5,3,4,1,6,2] => 3
[5,3,4,2,1,6] => 4
[5,3,4,2,6,1] => 4
[5,3,4,6,1,2] => 3
[5,3,4,6,2,1] => 4
[5,3,6,1,2,4] => 3
[5,3,6,1,4,2] => 3
[5,3,6,2,1,4] => 4
[5,3,6,2,4,1] => 4
[5,3,6,4,1,2] => 3
[5,3,6,4,2,1] => 4
[5,4,1,2,3,6] => 3
[5,4,1,2,6,3] => 3
[5,4,1,3,2,6] => 3
[5,4,1,3,6,2] => 3
[5,4,1,6,2,3] => 3
[5,4,1,6,3,2] => 3
[5,4,2,1,3,6] => 4
[5,4,2,1,6,3] => 4
[5,4,2,3,1,6] => 4
[5,4,2,3,6,1] => 4
[5,4,2,6,1,3] => 4
[5,4,2,6,3,1] => 4
[5,4,3,1,2,6] => 4
[5,4,3,1,6,2] => 4
[5,4,3,2,1,6] => 5
[5,4,3,2,6,1] => 5
[5,4,3,6,1,2] => 4
[5,4,3,6,2,1] => 5
[5,4,6,1,2,3] => 3
[5,4,6,1,3,2] => 3
[5,4,6,2,1,3] => 4
[5,4,6,2,3,1] => 4
[5,4,6,3,1,2] => 4
[5,4,6,3,2,1] => 5
[5,6,1,2,3,4] => 2
[5,6,1,2,4,3] => 2
[5,6,1,3,2,4] => 2
[5,6,1,3,4,2] => 2
[5,6,1,4,2,3] => 2
[5,6,1,4,3,2] => 2
[5,6,2,1,3,4] => 3
[5,6,2,1,4,3] => 3
[5,6,2,3,1,4] => 3
[5,6,2,3,4,1] => 3
[5,6,2,4,1,3] => 3
[5,6,2,4,3,1] => 4
[5,6,3,1,2,4] => 3
[5,6,3,1,4,2] => 3
[5,6,3,2,1,4] => 4
[5,6,3,2,4,1] => 4
[5,6,3,4,1,2] => 3
[5,6,3,4,2,1] => 4
[5,6,4,1,2,3] => 3
[5,6,4,1,3,2] => 3
[5,6,4,2,1,3] => 4
[5,6,4,2,3,1] => 4
[5,6,4,3,1,2] => 4
[5,6,4,3,2,1] => 5
[6,1,2,3,4,5] => 2
[6,1,2,3,5,4] => 2
[6,1,2,4,3,5] => 2
[6,1,2,4,5,3] => 2
[6,1,2,5,3,4] => 2
[6,1,2,5,4,3] => 2
[6,1,3,2,4,5] => 2
[6,1,3,2,5,4] => 2
[6,1,3,4,2,5] => 2
[6,1,3,4,5,2] => 2
[6,1,3,5,2,4] => 2
[6,1,3,5,4,2] => 2
[6,1,4,2,3,5] => 2
[6,1,4,2,5,3] => 2
[6,1,4,3,2,5] => 2
[6,1,4,3,5,2] => 2
[6,1,4,5,2,3] => 2
[6,1,4,5,3,2] => 2
[6,1,5,2,3,4] => 2
[6,1,5,2,4,3] => 2
[6,1,5,3,2,4] => 2
[6,1,5,3,4,2] => 2
[6,1,5,4,2,3] => 2
[6,1,5,4,3,2] => 2
[6,2,1,3,4,5] => 3
[6,2,1,3,5,4] => 3
[6,2,1,4,3,5] => 3
[6,2,1,4,5,3] => 3
[6,2,1,5,3,4] => 3
[6,2,1,5,4,3] => 3
[6,2,3,1,4,5] => 3
[6,2,3,1,5,4] => 3
[6,2,3,4,1,5] => 3
[6,2,3,4,5,1] => 3
[6,2,3,5,1,4] => 3
[6,2,3,5,4,1] => 4
[6,2,4,1,3,5] => 3
[6,2,4,1,5,3] => 3
[6,2,4,3,1,5] => 4
[6,2,4,3,5,1] => 4
[6,2,4,5,1,3] => 3
[6,2,4,5,3,1] => 4
[6,2,5,1,3,4] => 3
[6,2,5,1,4,3] => 3
[6,2,5,3,1,4] => 4
[6,2,5,3,4,1] => 4
[6,2,5,4,1,3] => 4
[6,2,5,4,3,1] => 5
[6,3,1,2,4,5] => 3
[6,3,1,2,5,4] => 3
[6,3,1,4,2,5] => 3
[6,3,1,4,5,2] => 3
[6,3,1,5,2,4] => 3
[6,3,1,5,4,2] => 3
[6,3,2,1,4,5] => 4
[6,3,2,1,5,4] => 4
[6,3,2,4,1,5] => 4
[6,3,2,4,5,1] => 4
[6,3,2,5,1,4] => 4
[6,3,2,5,4,1] => 4
[6,3,4,1,2,5] => 3
[6,3,4,1,5,2] => 3
[6,3,4,2,1,5] => 4
[6,3,4,2,5,1] => 4
[6,3,4,5,1,2] => 3
[6,3,4,5,2,1] => 4
[6,3,5,1,2,4] => 3
[6,3,5,1,4,2] => 3
[6,3,5,2,1,4] => 4
[6,3,5,2,4,1] => 4
[6,3,5,4,1,2] => 4
[6,3,5,4,2,1] => 5
[6,4,1,2,3,5] => 3
[6,4,1,2,5,3] => 3
[6,4,1,3,2,5] => 3
[6,4,1,3,5,2] => 3
[6,4,1,5,2,3] => 3
[6,4,1,5,3,2] => 3
[6,4,2,1,3,5] => 4
[6,4,2,1,5,3] => 4
[6,4,2,3,1,5] => 4
[6,4,2,3,5,1] => 4
[6,4,2,5,1,3] => 4
[6,4,2,5,3,1] => 4
[6,4,3,1,2,5] => 4
[6,4,3,1,5,2] => 4
[6,4,3,2,1,5] => 5
[6,4,3,2,5,1] => 5
[6,4,3,5,1,2] => 4
[6,4,3,5,2,1] => 5
[6,4,5,1,2,3] => 3
[6,4,5,1,3,2] => 3
[6,4,5,2,1,3] => 4
[6,4,5,2,3,1] => 4
[6,4,5,3,1,2] => 4
[6,4,5,3,2,1] => 5
[6,5,1,2,3,4] => 3
[6,5,1,2,4,3] => 3
[6,5,1,3,2,4] => 3
[6,5,1,3,4,2] => 3
[6,5,1,4,2,3] => 3
[6,5,1,4,3,2] => 3
[6,5,2,1,3,4] => 4
[6,5,2,1,4,3] => 4
[6,5,2,3,1,4] => 4
[6,5,2,3,4,1] => 4
[6,5,2,4,1,3] => 4
[6,5,2,4,3,1] => 5
[6,5,3,1,2,4] => 4
[6,5,3,1,4,2] => 4
[6,5,3,2,1,4] => 5
[6,5,3,2,4,1] => 5
[6,5,3,4,1,2] => 4
[6,5,3,4,2,1] => 5
[6,5,4,1,2,3] => 4
[6,5,4,1,3,2] => 4
[6,5,4,2,1,3] => 5
[6,5,4,2,3,1] => 5
[6,5,4,3,1,2] => 5
[6,5,4,3,2,1] => 6
click to show generating function       
Description
The number of bumps occurring when Schensted-inserting the letter 1 of a permutation.
For a given permutation $\pi$, this is the index of the row containing $\pi^{-1}(1)$ of the recording tableau of $\pi$ (obtained by Mp00070Robinson-Schensted recording tableau).
Code
def statistic(pi):
    if pi:
        return 1+RSK(pi)[1].cells_containing(pi.index(1)+1)[0][0]
    # I am not sure of the value of the empty permutation. It might be 0.

Created
May 11, 2019 at 22:46 by Martin Rubey
Updated
May 12, 2019 at 09:36 by Martin Rubey