Identifier
Identifier
Values
[1,2] => 2
[2,1] => 2
[1,2,3] => 3
[1,3,2] => 2
[2,1,3] => 2
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 3
[1,2,3,4] => 4
[1,2,4,3] => 4
[1,3,2,4] => 2
[1,3,4,2] => 2
[1,4,2,3] => 2
[1,4,3,2] => 3
[2,1,3,4] => 4
[2,1,4,3] => 4
[2,3,1,4] => 2
[2,3,4,1] => 3
[2,4,1,3] => 0
[2,4,3,1] => 2
[3,1,2,4] => 2
[3,1,4,2] => 0
[3,2,1,4] => 3
[3,2,4,1] => 2
[3,4,1,2] => 4
[3,4,2,1] => 4
[4,1,2,3] => 3
[4,1,3,2] => 2
[4,2,1,3] => 2
[4,2,3,1] => 2
[4,3,1,2] => 4
[4,3,2,1] => 4
[1,2,3,4,5] => 5
[1,2,3,5,4] => 5
[1,2,4,3,5] => 4
[1,2,4,5,3] => 4
[1,2,5,3,4] => 4
[1,2,5,4,3] => 5
[1,3,2,4,5] => 4
[1,3,2,5,4] => 4
[1,3,4,2,5] => 2
[1,3,4,5,2] => 3
[1,3,5,2,4] => 0
[1,3,5,4,2] => 2
[1,4,2,3,5] => 2
[1,4,2,5,3] => 0
[1,4,3,2,5] => 3
[1,4,3,5,2] => 2
[1,4,5,2,3] => 4
[1,4,5,3,2] => 4
[1,5,2,3,4] => 3
[1,5,2,4,3] => 2
[1,5,3,2,4] => 2
[1,5,3,4,2] => 2
[1,5,4,2,3] => 4
[1,5,4,3,2] => 4
[2,1,3,4,5] => 5
[2,1,3,5,4] => 4
[2,1,4,3,5] => 4
[2,1,4,5,3] => 4
[2,1,5,3,4] => 4
[2,1,5,4,3] => 5
[2,3,1,4,5] => 4
[2,3,1,5,4] => 4
[2,3,4,1,5] => 3
[2,3,4,5,1] => 4
[2,3,5,1,4] => 2
[2,3,5,4,1] => 4
[2,4,1,3,5] => 0
[2,4,1,5,3] => 0
[2,4,3,1,5] => 2
[2,4,3,5,1] => 2
[2,4,5,1,3] => 2
[2,4,5,3,1] => 2
[2,5,1,3,4] => 2
[2,5,1,4,3] => 2
[2,5,3,1,4] => 0
[2,5,3,4,1] => 2
[2,5,4,1,3] => 2
[2,5,4,3,1] => 3
[3,1,2,4,5] => 4
[3,1,2,5,4] => 4
[3,1,4,2,5] => 0
[3,1,4,5,2] => 2
[3,1,5,2,4] => 0
[3,1,5,4,2] => 2
[3,2,1,4,5] => 5
[3,2,1,5,4] => 5
[3,2,4,1,5] => 2
[3,2,4,5,1] => 4
[3,2,5,1,4] => 2
[3,2,5,4,1] => 4
[3,4,1,2,5] => 4
[3,4,1,5,2] => 2
[3,4,2,1,5] => 4
[3,4,2,5,1] => 2
[3,4,5,1,2] => 5
[3,4,5,2,1] => 5
[3,5,1,2,4] => 2
[3,5,1,4,2] => 0
[3,5,2,1,4] => 2
[3,5,2,4,1] => 0
[3,5,4,1,2] => 4
[3,5,4,2,1] => 4
[4,1,2,3,5] => 3
[4,1,2,5,3] => 2
[4,1,3,2,5] => 2
[4,1,3,5,2] => 0
[4,1,5,2,3] => 2
[4,1,5,3,2] => 2
[4,2,1,3,5] => 2
[4,2,1,5,3] => 2
[4,2,3,1,5] => 2
[4,2,3,5,1] => 2
[4,2,5,1,3] => 0
[4,2,5,3,1] => 0
[4,3,1,2,5] => 4
[4,3,1,5,2] => 2
[4,3,2,1,5] => 4
[4,3,2,5,1] => 3
[4,3,5,1,2] => 4
[4,3,5,2,1] => 4
[4,5,1,2,3] => 5
[4,5,1,3,2] => 4
[4,5,2,1,3] => 4
[4,5,2,3,1] => 4
[4,5,3,1,2] => 4
[4,5,3,2,1] => 5
[5,1,2,3,4] => 4
[5,1,2,4,3] => 4
[5,1,3,2,4] => 2
[5,1,3,4,2] => 2
[5,1,4,2,3] => 2
[5,1,4,3,2] => 3
[5,2,1,3,4] => 4
[5,2,1,4,3] => 4
[5,2,3,1,4] => 2
[5,2,3,4,1] => 3
[5,2,4,1,3] => 0
[5,2,4,3,1] => 2
[5,3,1,2,4] => 2
[5,3,1,4,2] => 0
[5,3,2,1,4] => 3
[5,3,2,4,1] => 2
[5,3,4,1,2] => 4
[5,3,4,2,1] => 4
[5,4,1,2,3] => 5
[5,4,1,3,2] => 4
[5,4,2,1,3] => 4
[5,4,2,3,1] => 4
[5,4,3,1,2] => 5
[5,4,3,2,1] => 5
[1,2,3,4,5,6] => 6
[1,2,3,4,6,5] => 6
[1,2,3,5,4,6] => 5
[1,2,3,5,6,4] => 5
[1,2,3,6,4,5] => 5
[1,2,3,6,5,4] => 6
[1,2,4,3,5,6] => 6
[1,2,4,3,6,5] => 6
[1,2,4,5,3,6] => 4
[1,2,4,5,6,3] => 5
[1,2,4,6,3,5] => 2
[1,2,4,6,5,3] => 4
[1,2,5,3,4,6] => 4
[1,2,5,3,6,4] => 2
[1,2,5,4,3,6] => 5
[1,2,5,4,6,3] => 4
[1,2,5,6,3,4] => 6
[1,2,5,6,4,3] => 6
[1,2,6,3,4,5] => 5
[1,2,6,3,5,4] => 4
[1,2,6,4,3,5] => 4
[1,2,6,4,5,3] => 4
[1,2,6,5,3,4] => 6
[1,2,6,5,4,3] => 6
[1,3,2,4,5,6] => 5
[1,3,2,4,6,5] => 4
[1,3,2,5,4,6] => 4
[1,3,2,5,6,4] => 4
[1,3,2,6,4,5] => 4
[1,3,2,6,5,4] => 5
[1,3,4,2,5,6] => 4
[1,3,4,2,6,5] => 4
[1,3,4,5,2,6] => 3
[1,3,4,5,6,2] => 4
[1,3,4,6,2,5] => 2
[1,3,4,6,5,2] => 4
[1,3,5,2,4,6] => 0
[1,3,5,2,6,4] => 0
[1,3,5,4,2,6] => 2
[1,3,5,4,6,2] => 2
[1,3,5,6,2,4] => 2
[1,3,5,6,4,2] => 2
[1,3,6,2,4,5] => 2
[1,3,6,2,5,4] => 2
[1,3,6,4,2,5] => 0
[1,3,6,4,5,2] => 2
[1,3,6,5,2,4] => 2
[1,3,6,5,4,2] => 3
[1,4,2,3,5,6] => 4
[1,4,2,3,6,5] => 4
[1,4,2,5,3,6] => 0
[1,4,2,5,6,3] => 2
[1,4,2,6,3,5] => 0
[1,4,2,6,5,3] => 2
[1,4,3,2,5,6] => 5
[1,4,3,2,6,5] => 5
[1,4,3,5,2,6] => 2
[1,4,3,5,6,2] => 4
[1,4,3,6,2,5] => 2
[1,4,3,6,5,2] => 4
[1,4,5,2,3,6] => 4
[1,4,5,2,6,3] => 2
[1,4,5,3,2,6] => 4
[1,4,5,3,6,2] => 2
[1,4,5,6,2,3] => 5
[1,4,5,6,3,2] => 5
[1,4,6,2,3,5] => 2
[1,4,6,2,5,3] => 0
[1,4,6,3,2,5] => 2
[1,4,6,3,5,2] => 0
[1,4,6,5,2,3] => 4
[1,4,6,5,3,2] => 4
[1,5,2,3,4,6] => 3
[1,5,2,3,6,4] => 2
[1,5,2,4,3,6] => 2
[1,5,2,4,6,3] => 0
[1,5,2,6,3,4] => 2
[1,5,2,6,4,3] => 2
[1,5,3,2,4,6] => 2
[1,5,3,2,6,4] => 2
[1,5,3,4,2,6] => 2
[1,5,3,4,6,2] => 2
[1,5,3,6,2,4] => 0
[1,5,3,6,4,2] => 0
[1,5,4,2,3,6] => 4
[1,5,4,2,6,3] => 2
[1,5,4,3,2,6] => 4
[1,5,4,3,6,2] => 3
[1,5,4,6,2,3] => 4
[1,5,4,6,3,2] => 4
[1,5,6,2,3,4] => 5
[1,5,6,2,4,3] => 4
[1,5,6,3,2,4] => 4
[1,5,6,3,4,2] => 4
[1,5,6,4,2,3] => 4
[1,5,6,4,3,2] => 5
[1,6,2,3,4,5] => 4
[1,6,2,3,5,4] => 4
[1,6,2,4,3,5] => 2
[1,6,2,4,5,3] => 2
[1,6,2,5,3,4] => 2
[1,6,2,5,4,3] => 3
[1,6,3,2,4,5] => 4
[1,6,3,2,5,4] => 4
[1,6,3,4,2,5] => 2
[1,6,3,4,5,2] => 3
[1,6,3,5,2,4] => 0
[1,6,3,5,4,2] => 2
[1,6,4,2,3,5] => 2
[1,6,4,2,5,3] => 0
[1,6,4,3,2,5] => 3
[1,6,4,3,5,2] => 2
[1,6,4,5,2,3] => 4
[1,6,4,5,3,2] => 4
[1,6,5,2,3,4] => 5
[1,6,5,2,4,3] => 4
[1,6,5,3,2,4] => 4
[1,6,5,3,4,2] => 4
[1,6,5,4,2,3] => 5
[1,6,5,4,3,2] => 5
[2,1,3,4,5,6] => 6
[2,1,3,4,6,5] => 6
[2,1,3,5,4,6] => 4
[2,1,3,5,6,4] => 4
[2,1,3,6,4,5] => 4
[2,1,3,6,5,4] => 5
[2,1,4,3,5,6] => 6
[2,1,4,3,6,5] => 6
[2,1,4,5,3,6] => 4
[2,1,4,5,6,3] => 5
[2,1,4,6,3,5] => 2
[2,1,4,6,5,3] => 4
[2,1,5,3,4,6] => 4
[2,1,5,3,6,4] => 2
[2,1,5,4,3,6] => 5
[2,1,5,4,6,3] => 4
[2,1,5,6,3,4] => 6
[2,1,5,6,4,3] => 6
[2,1,6,3,4,5] => 5
[2,1,6,3,5,4] => 4
[2,1,6,4,3,5] => 4
[2,1,6,4,5,3] => 4
[2,1,6,5,3,4] => 6
[2,1,6,5,4,3] => 6
[2,3,1,4,5,6] => 5
[2,3,1,4,6,5] => 4
[2,3,1,5,4,6] => 4
[2,3,1,5,6,4] => 4
[2,3,1,6,4,5] => 4
[2,3,1,6,5,4] => 5
[2,3,4,1,5,6] => 5
[2,3,4,1,6,5] => 5
[2,3,4,5,1,6] => 4
[2,3,4,5,6,1] => 5
[2,3,4,6,1,5] => 3
[2,3,4,6,5,1] => 5
[2,3,5,1,4,6] => 2
[2,3,5,1,6,4] => 2
[2,3,5,4,1,6] => 4
[2,3,5,4,6,1] => 4
[2,3,5,6,1,4] => 4
[2,3,5,6,4,1] => 4
[2,3,6,1,4,5] => 4
[2,3,6,1,5,4] => 4
[2,3,6,4,1,5] => 2
[2,3,6,4,5,1] => 4
[2,3,6,5,1,4] => 4
[2,3,6,5,4,1] => 5
[2,4,1,3,5,6] => 2
[2,4,1,3,6,5] => 2
[2,4,1,5,3,6] => 0
[2,4,1,5,6,3] => 2
[2,4,1,6,3,5] => 0
[2,4,1,6,5,3] => 2
[2,4,3,1,5,6] => 4
[2,4,3,1,6,5] => 4
[2,4,3,5,1,6] => 2
[2,4,3,5,6,1] => 4
[2,4,3,6,1,5] => 2
[2,4,3,6,5,1] => 4
[2,4,5,1,3,6] => 2
[2,4,5,1,6,3] => 2
[2,4,5,3,1,6] => 2
[2,4,5,3,6,1] => 2
[2,4,5,6,1,3] => 3
[2,4,5,6,3,1] => 3
[2,4,6,1,3,5] => 0
[2,4,6,1,5,3] => 0
[2,4,6,3,1,5] => 0
[2,4,6,3,5,1] => 0
[2,4,6,5,1,3] => 2
[2,4,6,5,3,1] => 2
[2,5,1,3,4,6] => 2
[2,5,1,3,6,4] => 0
[2,5,1,4,3,6] => 2
[2,5,1,4,6,3] => 0
[2,5,1,6,3,4] => 2
[2,5,1,6,4,3] => 2
[2,5,3,1,4,6] => 0
[2,5,3,1,6,4] => 0
[2,5,3,4,1,6] => 2
[2,5,3,4,6,1] => 2
[2,5,3,6,1,4] => 0
[2,5,3,6,4,1] => 0
[2,5,4,1,3,6] => 2
[2,5,4,1,6,3] => 2
[2,5,4,3,1,6] => 3
[2,5,4,3,6,1] => 3
[2,5,4,6,1,3] => 2
[2,5,4,6,3,1] => 2
[2,5,6,1,3,4] => 4
[2,5,6,1,4,3] => 4
[2,5,6,3,1,4] => 2
[2,5,6,3,4,1] => 4
[2,5,6,4,1,3] => 2
[2,5,6,4,3,1] => 4
[2,6,1,3,4,5] => 3
[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] => 3
[2,6,3,1,4,5] => 2
[2,6,3,1,5,4] => 2
[2,6,3,4,1,5] => 2
[2,6,3,4,5,1] => 3
[2,6,3,5,1,4] => 0
[2,6,3,5,4,1] => 2
[2,6,4,1,3,5] => 0
[2,6,4,1,5,3] => 0
[2,6,4,3,1,5] => 2
[2,6,4,3,5,1] => 2
[2,6,4,5,1,3] => 2
[2,6,4,5,3,1] => 2
[2,6,5,1,3,4] => 4
[2,6,5,1,4,3] => 4
[2,6,5,3,1,4] => 2
[2,6,5,3,4,1] => 4
[2,6,5,4,1,3] => 3
[2,6,5,4,3,1] => 4
[3,1,2,4,5,6] => 5
[3,1,2,4,6,5] => 4
[3,1,2,5,4,6] => 4
[3,1,2,5,6,4] => 4
[3,1,2,6,4,5] => 4
[3,1,2,6,5,4] => 5
[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] => 3
[3,1,4,6,2,5] => 0
[3,1,4,6,5,2] => 2
[3,1,5,2,4,6] => 0
[3,1,5,2,6,4] => 0
[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] => 0
[3,1,6,4,5,2] => 2
[3,1,6,5,2,4] => 2
[3,1,6,5,4,2] => 3
[3,2,1,4,5,6] => 6
[3,2,1,4,6,5] => 5
[3,2,1,5,4,6] => 5
[3,2,1,5,6,4] => 5
[3,2,1,6,4,5] => 5
[3,2,1,6,5,4] => 6
[3,2,4,1,5,6] => 4
[3,2,4,1,6,5] => 4
[3,2,4,5,1,6] => 4
[3,2,4,5,6,1] => 5
[3,2,4,6,1,5] => 2
[3,2,4,6,5,1] => 4
[3,2,5,1,4,6] => 2
[3,2,5,1,6,4] => 2
[3,2,5,4,1,6] => 4
[3,2,5,4,6,1] => 4
[3,2,5,6,1,4] => 4
[3,2,5,6,4,1] => 4
[3,2,6,1,4,5] => 4
[3,2,6,1,5,4] => 4
[3,2,6,4,1,5] => 2
[3,2,6,4,5,1] => 4
[3,2,6,5,1,4] => 4
[3,2,6,5,4,1] => 5
[3,4,1,2,5,6] => 6
[3,4,1,2,6,5] => 6
[3,4,1,5,2,6] => 2
[3,4,1,5,6,2] => 4
[3,4,1,6,2,5] => 2
[3,4,1,6,5,2] => 4
[3,4,2,1,5,6] => 6
[3,4,2,1,6,5] => 6
[3,4,2,5,1,6] => 2
[3,4,2,5,6,1] => 4
[3,4,2,6,1,5] => 2
[3,4,2,6,5,1] => 4
[3,4,5,1,2,6] => 5
[3,4,5,1,6,2] => 3
[3,4,5,2,1,6] => 5
[3,4,5,2,6,1] => 3
[3,4,5,6,1,2] => 6
[3,4,5,6,2,1] => 6
[3,4,6,1,2,5] => 4
[3,4,6,1,5,2] => 2
[3,4,6,2,1,5] => 4
[3,4,6,2,5,1] => 2
[3,4,6,5,1,2] => 6
[3,4,6,5,2,1] => 6
[3,5,1,2,4,6] => 2
[3,5,1,2,6,4] => 2
[3,5,1,4,2,6] => 0
[3,5,1,4,6,2] => 0
[3,5,1,6,2,4] => 0
[3,5,1,6,4,2] => 0
[3,5,2,1,4,6] => 2
[3,5,2,1,6,4] => 2
[3,5,2,4,1,6] => 0
[3,5,2,4,6,1] => 0
[3,5,2,6,1,4] => 0
[3,5,2,6,4,1] => 0
[3,5,4,1,2,6] => 4
[3,5,4,1,6,2] => 2
[3,5,4,2,1,6] => 4
[3,5,4,2,6,1] => 2
[3,5,4,6,1,2] => 4
[3,5,4,6,2,1] => 4
[3,5,6,1,2,4] => 4
[3,5,6,1,4,2] => 2
[3,5,6,2,1,4] => 4
[3,5,6,2,4,1] => 2
[3,5,6,4,1,2] => 4
[3,5,6,4,2,1] => 4
[3,6,1,2,4,5] => 4
[3,6,1,2,5,4] => 4
[3,6,1,4,2,5] => 0
[3,6,1,4,5,2] => 2
[3,6,1,5,2,4] => 0
[3,6,1,5,4,2] => 2
[3,6,2,1,4,5] => 4
[3,6,2,1,5,4] => 4
[3,6,2,4,1,5] => 0
[3,6,2,4,5,1] => 2
[3,6,2,5,1,4] => 0
[3,6,2,5,4,1] => 2
[3,6,4,1,2,5] => 2
[3,6,4,1,5,2] => 0
[3,6,4,2,1,5] => 2
[3,6,4,2,5,1] => 0
[3,6,4,5,1,2] => 4
[3,6,4,5,2,1] => 4
[3,6,5,1,2,4] => 4
[3,6,5,1,4,2] => 2
[3,6,5,2,1,4] => 4
[3,6,5,2,4,1] => 2
[3,6,5,4,1,2] => 5
[3,6,5,4,2,1] => 5
[4,1,2,3,5,6] => 5
[4,1,2,3,6,5] => 5
[4,1,2,5,3,6] => 2
[4,1,2,5,6,3] => 4
[4,1,2,6,3,5] => 2
[4,1,2,6,5,3] => 4
[4,1,3,2,5,6] => 4
[4,1,3,2,6,5] => 4
[4,1,3,5,2,6] => 0
[4,1,3,5,6,2] => 2
[4,1,3,6,2,5] => 0
[4,1,3,6,5,2] => 2
[4,1,5,2,3,6] => 2
[4,1,5,2,6,3] => 0
[4,1,5,3,2,6] => 2
[4,1,5,3,6,2] => 0
[4,1,5,6,2,3] => 4
[4,1,5,6,3,2] => 4
[4,1,6,2,3,5] => 2
[4,1,6,2,5,3] => 0
[4,1,6,3,2,5] => 2
[4,1,6,3,5,2] => 0
[4,1,6,5,2,3] => 4
[4,1,6,5,3,2] => 4
[4,2,1,3,5,6] => 4
[4,2,1,3,6,5] => 4
[4,2,1,5,3,6] => 2
[4,2,1,5,6,3] => 4
[4,2,1,6,3,5] => 2
[4,2,1,6,5,3] => 4
[4,2,3,1,5,6] => 4
[4,2,3,1,6,5] => 4
[4,2,3,5,1,6] => 2
[4,2,3,5,6,1] => 4
[4,2,3,6,1,5] => 2
[4,2,3,6,5,1] => 4
[4,2,5,1,3,6] => 0
[4,2,5,1,6,3] => 0
[4,2,5,3,1,6] => 0
[4,2,5,3,6,1] => 0
[4,2,5,6,1,3] => 2
[4,2,5,6,3,1] => 2
[4,2,6,1,3,5] => 0
[4,2,6,1,5,3] => 0
[4,2,6,3,1,5] => 0
[4,2,6,3,5,1] => 0
[4,2,6,5,1,3] => 2
[4,2,6,5,3,1] => 2
[4,3,1,2,5,6] => 6
[4,3,1,2,6,5] => 6
[4,3,1,5,2,6] => 2
[4,3,1,5,6,2] => 4
[4,3,1,6,2,5] => 2
[4,3,1,6,5,2] => 4
[4,3,2,1,5,6] => 6
[4,3,2,1,6,5] => 6
[4,3,2,5,1,6] => 3
[4,3,2,5,6,1] => 5
[4,3,2,6,1,5] => 3
[4,3,2,6,5,1] => 5
[4,3,5,1,2,6] => 4
[4,3,5,1,6,2] => 2
[4,3,5,2,1,6] => 4
[4,3,5,2,6,1] => 2
[4,3,5,6,1,2] => 6
[4,3,5,6,2,1] => 6
[4,3,6,1,2,5] => 4
[4,3,6,1,5,2] => 2
[4,3,6,2,1,5] => 4
[4,3,6,2,5,1] => 2
[4,3,6,5,1,2] => 6
[4,3,6,5,2,1] => 6
[4,5,1,2,3,6] => 5
[4,5,1,2,6,3] => 4
[4,5,1,3,2,6] => 4
[4,5,1,3,6,2] => 2
[4,5,1,6,2,3] => 4
[4,5,1,6,3,2] => 4
[4,5,2,1,3,6] => 4
[4,5,2,1,6,3] => 4
[4,5,2,3,1,6] => 4
[4,5,2,3,6,1] => 4
[4,5,2,6,1,3] => 2
[4,5,2,6,3,1] => 2
[4,5,3,1,2,6] => 4
[4,5,3,1,6,2] => 2
[4,5,3,2,1,6] => 5
[4,5,3,2,6,1] => 4
[4,5,3,6,1,2] => 4
[4,5,3,6,2,1] => 4
[4,5,6,1,2,3] => 6
[4,5,6,1,3,2] => 5
[4,5,6,2,1,3] => 5
[4,5,6,2,3,1] => 5
[4,5,6,3,1,2] => 5
[4,5,6,3,2,1] => 6
[4,6,1,2,3,5] => 3
[4,6,1,2,5,3] => 2
[4,6,1,3,2,5] => 2
[4,6,1,3,5,2] => 0
[4,6,1,5,2,3] => 2
[4,6,1,5,3,2] => 2
[4,6,2,1,3,5] => 2
[4,6,2,1,5,3] => 2
[4,6,2,3,1,5] => 2
[4,6,2,3,5,1] => 2
[4,6,2,5,1,3] => 0
[4,6,2,5,3,1] => 0
[4,6,3,1,2,5] => 2
[4,6,3,1,5,2] => 0
[4,6,3,2,1,5] => 3
[4,6,3,2,5,1] => 2
[4,6,3,5,1,2] => 2
[4,6,3,5,2,1] => 2
[4,6,5,1,2,3] => 5
[4,6,5,1,3,2] => 4
[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] => 4
[5,1,2,3,6,4] => 3
[5,1,2,4,3,6] => 4
[5,1,2,4,6,3] => 2
[5,1,2,6,3,4] => 4
[5,1,2,6,4,3] => 4
[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] => 0
[5,1,3,6,4,2] => 0
[5,1,4,2,3,6] => 2
[5,1,4,2,6,3] => 0
[5,1,4,3,2,6] => 3
[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] => 3
[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] => 3
[5,2,1,3,4,6] => 4
[5,2,1,3,6,4] => 2
[5,2,1,4,3,6] => 4
[5,2,1,4,6,3] => 2
[5,2,1,6,3,4] => 4
[5,2,1,6,4,3] => 4
[5,2,3,1,4,6] => 2
[5,2,3,1,6,4] => 2
[5,2,3,4,1,6] => 3
[5,2,3,4,6,1] => 3
[5,2,3,6,1,4] => 2
[5,2,3,6,4,1] => 2
[5,2,4,1,3,6] => 0
[5,2,4,1,6,3] => 0
[5,2,4,3,1,6] => 2
[5,2,4,3,6,1] => 2
[5,2,4,6,1,3] => 0
[5,2,4,6,3,1] => 0
[5,2,6,1,3,4] => 2
[5,2,6,1,4,3] => 2
[5,2,6,3,1,4] => 0
[5,2,6,3,4,1] => 2
[5,2,6,4,1,3] => 0
[5,2,6,4,3,1] => 2
[5,3,1,2,4,6] => 2
[5,3,1,2,6,4] => 2
[5,3,1,4,2,6] => 0
[5,3,1,4,6,2] => 0
[5,3,1,6,2,4] => 0
[5,3,1,6,4,2] => 0
[5,3,2,1,4,6] => 3
[5,3,2,1,6,4] => 3
[5,3,2,4,1,6] => 2
[5,3,2,4,6,1] => 2
[5,3,2,6,1,4] => 2
[5,3,2,6,4,1] => 2
[5,3,4,1,2,6] => 4
[5,3,4,1,6,2] => 2
[5,3,4,2,1,6] => 4
[5,3,4,2,6,1] => 2
[5,3,4,6,1,2] => 4
[5,3,4,6,2,1] => 4
[5,3,6,1,2,4] => 2
[5,3,6,1,4,2] => 0
[5,3,6,2,1,4] => 2
[5,3,6,2,4,1] => 0
[5,3,6,4,1,2] => 2
[5,3,6,4,2,1] => 2
[5,4,1,2,3,6] => 5
[5,4,1,2,6,3] => 4
[5,4,1,3,2,6] => 4
[5,4,1,3,6,2] => 2
[5,4,1,6,2,3] => 4
[5,4,1,6,3,2] => 4
[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] => 2
[5,4,2,6,3,1] => 2
[5,4,3,1,2,6] => 5
[5,4,3,1,6,2] => 3
[5,4,3,2,1,6] => 5
[5,4,3,2,6,1] => 4
[5,4,3,6,1,2] => 5
[5,4,3,6,2,1] => 5
[5,4,6,1,2,3] => 5
[5,4,6,1,3,2] => 4
[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] => 6
[5,6,1,2,4,3] => 6
[5,6,1,3,2,4] => 4
[5,6,1,3,4,2] => 4
[5,6,1,4,2,3] => 4
[5,6,1,4,3,2] => 5
[5,6,2,1,3,4] => 6
[5,6,2,1,4,3] => 6
[5,6,2,3,1,4] => 4
[5,6,2,3,4,1] => 5
[5,6,2,4,1,3] => 2
[5,6,2,4,3,1] => 4
[5,6,3,1,2,4] => 4
[5,6,3,1,4,2] => 2
[5,6,3,2,1,4] => 5
[5,6,3,2,4,1] => 4
[5,6,3,4,1,2] => 6
[5,6,3,4,2,1] => 6
[5,6,4,1,2,3] => 5
[5,6,4,1,3,2] => 4
[5,6,4,2,1,3] => 4
[5,6,4,2,3,1] => 4
[5,6,4,3,1,2] => 6
[5,6,4,3,2,1] => 6
[6,1,2,3,4,5] => 5
[6,1,2,3,5,4] => 5
[6,1,2,4,3,5] => 4
[6,1,2,4,5,3] => 4
[6,1,2,5,3,4] => 4
[6,1,2,5,4,3] => 5
[6,1,3,2,4,5] => 4
[6,1,3,2,5,4] => 4
[6,1,3,4,2,5] => 2
[6,1,3,4,5,2] => 3
[6,1,3,5,2,4] => 0
[6,1,3,5,4,2] => 2
[6,1,4,2,3,5] => 2
[6,1,4,2,5,3] => 0
[6,1,4,3,2,5] => 3
[6,1,4,3,5,2] => 2
[6,1,4,5,2,3] => 4
[6,1,4,5,3,2] => 4
[6,1,5,2,3,4] => 3
[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] => 4
[6,1,5,4,3,2] => 4
[6,2,1,3,4,5] => 5
[6,2,1,3,5,4] => 4
[6,2,1,4,3,5] => 4
[6,2,1,4,5,3] => 4
[6,2,1,5,3,4] => 4
[6,2,1,5,4,3] => 5
[6,2,3,1,4,5] => 4
[6,2,3,1,5,4] => 4
[6,2,3,4,1,5] => 3
[6,2,3,4,5,1] => 4
[6,2,3,5,1,4] => 2
[6,2,3,5,4,1] => 4
[6,2,4,1,3,5] => 0
[6,2,4,1,5,3] => 0
[6,2,4,3,1,5] => 2
[6,2,4,3,5,1] => 2
[6,2,4,5,1,3] => 2
[6,2,4,5,3,1] => 2
[6,2,5,1,3,4] => 2
[6,2,5,1,4,3] => 2
[6,2,5,3,1,4] => 0
[6,2,5,3,4,1] => 2
[6,2,5,4,1,3] => 2
[6,2,5,4,3,1] => 3
[6,3,1,2,4,5] => 4
[6,3,1,2,5,4] => 4
[6,3,1,4,2,5] => 0
[6,3,1,4,5,2] => 2
[6,3,1,5,2,4] => 0
[6,3,1,5,4,2] => 2
[6,3,2,1,4,5] => 5
[6,3,2,1,5,4] => 5
[6,3,2,4,1,5] => 2
[6,3,2,4,5,1] => 4
[6,3,2,5,1,4] => 2
[6,3,2,5,4,1] => 4
[6,3,4,1,2,5] => 4
[6,3,4,1,5,2] => 2
[6,3,4,2,1,5] => 4
[6,3,4,2,5,1] => 2
[6,3,4,5,1,2] => 5
[6,3,4,5,2,1] => 5
[6,3,5,1,2,4] => 2
[6,3,5,1,4,2] => 0
[6,3,5,2,1,4] => 2
[6,3,5,2,4,1] => 0
[6,3,5,4,1,2] => 4
[6,3,5,4,2,1] => 4
[6,4,1,2,3,5] => 3
[6,4,1,2,5,3] => 2
[6,4,1,3,2,5] => 2
[6,4,1,3,5,2] => 0
[6,4,1,5,2,3] => 2
[6,4,1,5,3,2] => 2
[6,4,2,1,3,5] => 2
[6,4,2,1,5,3] => 2
[6,4,2,3,1,5] => 2
[6,4,2,3,5,1] => 2
[6,4,2,5,1,3] => 0
[6,4,2,5,3,1] => 0
[6,4,3,1,2,5] => 4
[6,4,3,1,5,2] => 2
[6,4,3,2,1,5] => 4
[6,4,3,2,5,1] => 3
[6,4,3,5,1,2] => 4
[6,4,3,5,2,1] => 4
[6,4,5,1,2,3] => 5
[6,4,5,1,3,2] => 4
[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] => 6
[6,5,1,2,4,3] => 6
[6,5,1,3,2,4] => 4
[6,5,1,3,4,2] => 4
[6,5,1,4,2,3] => 4
[6,5,1,4,3,2] => 5
[6,5,2,1,3,4] => 6
[6,5,2,1,4,3] => 6
[6,5,2,3,1,4] => 4
[6,5,2,3,4,1] => 5
[6,5,2,4,1,3] => 2
[6,5,2,4,3,1] => 4
[6,5,3,1,2,4] => 4
[6,5,3,1,4,2] => 2
[6,5,3,2,1,4] => 5
[6,5,3,2,4,1] => 4
[6,5,3,4,1,2] => 6
[6,5,3,4,2,1] => 6
[6,5,4,1,2,3] => 6
[6,5,4,1,3,2] => 5
[6,5,4,2,1,3] => 5
[6,5,4,2,3,1] => 5
[6,5,4,3,1,2] => 6
[6,5,4,3,2,1] => 6
click to show generating function       
Description
The number of one-box pattern of a permutation.
This is the number of $i$ for which there is a $j$ such that $(i,\sigma_i)$ and $(j,\sigma_j)$ have distance 2 in the taxi metric on the $\mathbb{Z}^2$ grid.
References
[1] Kitaev, S., Remmel, J. The 1-box pattern on pattern avoiding permutations arXiv:1305.6970 MathSciNet:3168685
Code
def statistic( pi ):
    counter = 0
    for i in range(len(pi)):
        if i > 0 and abs(pi[i]-pi[i-1]) == 1:
            counter += 1
        elif i < len(pi)-1 and abs(pi[i]-pi[i+1]) == 1:
            counter += 1
    return counter

Created
Jun 04, 2013 at 09:21 by Christian Stump
Updated
May 29, 2015 at 16:35 by Martin Rubey