Identifier
Identifier
Values
[1] => 0
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 2
[2,1,3] => 3
[2,3,1] => 2
[3,1,2] => 1
[3,2,1] => 1
[1,2,3,4] => 0
[1,2,4,3] => 3
[1,3,2,4] => 5
[1,3,4,2] => 3
[1,4,2,3] => 2
[1,4,3,2] => 2
[2,1,3,4] => 3
[2,1,4,3] => 4
[2,3,1,4] => 5
[2,3,4,1] => 3
[2,4,1,3] => 2
[2,4,3,1] => 2
[3,1,2,4] => 4
[3,1,4,2] => 4
[3,2,1,4] => 4
[3,2,4,1] => 4
[3,4,1,2] => 2
[3,4,2,1] => 5
[4,1,2,3] => 1
[4,1,3,2] => 3
[4,2,1,3] => 1
[4,2,3,1] => 1
[4,3,1,2] => 3
[4,3,2,1] => 6
[1,2,3,4,5] => 0
[1,2,3,5,4] => 4
[1,2,4,3,5] => 7
[1,2,4,5,3] => 4
[1,2,5,3,4] => 3
[1,2,5,4,3] => 3
[1,3,2,4,5] => 5
[1,3,2,5,4] => 6
[1,3,4,2,5] => 7
[1,3,4,5,2] => 4
[1,3,5,2,4] => 3
[1,3,5,4,2] => 3
[1,4,2,3,5] => 6
[1,4,2,5,3] => 6
[1,4,3,2,5] => 6
[1,4,3,5,2] => 6
[1,4,5,2,3] => 3
[1,4,5,3,2] => 7
[1,5,2,3,4] => 2
[1,5,2,4,3] => 5
[1,5,3,2,4] => 2
[1,5,3,4,2] => 2
[1,5,4,2,3] => 5
[1,5,4,3,2] => 9
[2,1,3,4,5] => 3
[2,1,3,5,4] => 7
[2,1,4,3,5] => 8
[2,1,4,5,3] => 5
[2,1,5,3,4] => 4
[2,1,5,4,3] => 4
[2,3,1,4,5] => 5
[2,3,1,5,4] => 6
[2,3,4,1,5] => 7
[2,3,4,5,1] => 4
[2,3,5,1,4] => 3
[2,3,5,4,1] => 3
[2,4,1,3,5] => 6
[2,4,1,5,3] => 6
[2,4,3,1,5] => 6
[2,4,3,5,1] => 6
[2,4,5,1,3] => 3
[2,4,5,3,1] => 7
[2,5,1,3,4] => 2
[2,5,1,4,3] => 5
[2,5,3,1,4] => 2
[2,5,3,4,1] => 2
[2,5,4,1,3] => 5
[2,5,4,3,1] => 9
[3,1,2,4,5] => 4
[3,1,2,5,4] => 5
[3,1,4,2,5] => 8
[3,1,4,5,2] => 5
[3,1,5,2,4] => 4
[3,1,5,4,2] => 4
[3,2,1,4,5] => 4
[3,2,1,5,4] => 5
[3,2,4,1,5] => 8
[3,2,4,5,1] => 5
[3,2,5,1,4] => 4
[3,2,5,4,1] => 4
[3,4,1,2,5] => 6
[3,4,1,5,2] => 6
[3,4,2,1,5] => 9
[3,4,2,5,1] => 6
[3,4,5,1,2] => 3
[3,4,5,2,1] => 7
[3,5,1,2,4] => 2
[3,5,1,4,2] => 5
[3,5,2,1,4] => 5
[3,5,2,4,1] => 5
[3,5,4,1,2] => 5
[3,5,4,2,1] => 9
[4,1,2,3,5] => 5
[4,1,2,5,3] => 5
[4,1,3,2,5] => 7
[4,1,3,5,2] => 7
[4,1,5,2,3] => 4
[4,1,5,3,2] => 8
[4,2,1,3,5] => 5
[4,2,1,5,3] => 5
[4,2,3,1,5] => 5
[4,2,3,5,1] => 5
[4,2,5,1,3] => 4
[4,2,5,3,1] => 8
[4,3,1,2,5] => 7
[4,3,1,5,2] => 7
[4,3,2,1,5] => 10
[4,3,2,5,1] => 7
[4,3,5,1,2] => 4
[4,3,5,2,1] => 8
[4,5,1,2,3] => 2
[4,5,1,3,2] => 6
[4,5,2,1,3] => 5
[4,5,2,3,1] => 6
[4,5,3,1,2] => 2
[4,5,3,2,1] => 6
[5,1,2,3,4] => 1
[5,1,2,4,3] => 4
[5,1,3,2,4] => 3
[5,1,3,4,2] => 3
[5,1,4,2,3] => 4
[5,1,4,3,2] => 8
[5,2,1,3,4] => 1
[5,2,1,4,3] => 4
[5,2,3,1,4] => 1
[5,2,3,4,1] => 1
[5,2,4,1,3] => 4
[5,2,4,3,1] => 8
[5,3,1,2,4] => 3
[5,3,1,4,2] => 6
[5,3,2,1,4] => 6
[5,3,2,4,1] => 6
[5,3,4,1,2] => 4
[5,3,4,2,1] => 8
[5,4,1,2,3] => 3
[5,4,1,3,2] => 7
[5,4,2,1,3] => 6
[5,4,2,3,1] => 7
[5,4,3,1,2] => 3
[5,4,3,2,1] => 7
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 5
[1,2,3,5,4,6] => 9
[1,2,3,5,6,4] => 5
[1,2,3,6,4,5] => 4
[1,2,3,6,5,4] => 4
[1,2,4,3,5,6] => 7
[1,2,4,3,6,5] => 8
[1,2,4,5,3,6] => 9
[1,2,4,5,6,3] => 5
[1,2,4,6,3,5] => 4
[1,2,4,6,5,3] => 4
[1,2,5,3,4,6] => 8
[1,2,5,3,6,4] => 8
[1,2,5,4,3,6] => 8
[1,2,5,4,6,3] => 8
[1,2,5,6,3,4] => 4
[1,2,5,6,4,3] => 9
[1,2,6,3,4,5] => 3
[1,2,6,3,5,4] => 7
[1,2,6,4,3,5] => 3
[1,2,6,4,5,3] => 3
[1,2,6,5,3,4] => 7
[1,2,6,5,4,3] => 12
[1,3,2,4,5,6] => 5
[1,3,2,4,6,5] => 10
[1,3,2,5,4,6] => 11
[1,3,2,5,6,4] => 7
[1,3,2,6,4,5] => 6
[1,3,2,6,5,4] => 6
[1,3,4,2,5,6] => 7
[1,3,4,2,6,5] => 8
[1,3,4,5,2,6] => 9
[1,3,4,5,6,2] => 5
[1,3,4,6,2,5] => 4
[1,3,4,6,5,2] => 4
[1,3,5,2,4,6] => 8
[1,3,5,2,6,4] => 8
[1,3,5,4,2,6] => 8
[1,3,5,4,6,2] => 8
[1,3,5,6,2,4] => 4
[1,3,5,6,4,2] => 9
[1,3,6,2,4,5] => 3
[1,3,6,2,5,4] => 7
[1,3,6,4,2,5] => 3
[1,3,6,4,5,2] => 3
[1,3,6,5,2,4] => 7
[1,3,6,5,4,2] => 12
[1,4,2,3,5,6] => 6
[1,4,2,3,6,5] => 7
[1,4,2,5,3,6] => 11
[1,4,2,5,6,3] => 7
[1,4,2,6,3,5] => 6
[1,4,2,6,5,3] => 6
[1,4,3,2,5,6] => 6
[1,4,3,2,6,5] => 7
[1,4,3,5,2,6] => 11
[1,4,3,5,6,2] => 7
[1,4,3,6,2,5] => 6
[1,4,3,6,5,2] => 6
[1,4,5,2,3,6] => 8
[1,4,5,2,6,3] => 8
[1,4,5,3,2,6] => 12
[1,4,5,3,6,2] => 8
[1,4,5,6,2,3] => 4
[1,4,5,6,3,2] => 9
[1,4,6,2,3,5] => 3
[1,4,6,2,5,3] => 7
[1,4,6,3,2,5] => 7
[1,4,6,3,5,2] => 7
[1,4,6,5,2,3] => 7
[1,4,6,5,3,2] => 12
[1,5,2,3,4,6] => 7
[1,5,2,3,6,4] => 7
[1,5,2,4,3,6] => 10
[1,5,2,4,6,3] => 10
[1,5,2,6,3,4] => 6
[1,5,2,6,4,3] => 11
[1,5,3,2,4,6] => 7
[1,5,3,2,6,4] => 7
[1,5,3,4,2,6] => 7
[1,5,3,4,6,2] => 7
[1,5,3,6,2,4] => 6
[1,5,3,6,4,2] => 11
[1,5,4,2,3,6] => 10
[1,5,4,2,6,3] => 10
[1,5,4,3,2,6] => 14
[1,5,4,3,6,2] => 10
[1,5,4,6,2,3] => 6
[1,5,4,6,3,2] => 11
[1,5,6,2,3,4] => 3
[1,5,6,2,4,3] => 8
[1,5,6,3,2,4] => 7
[1,5,6,3,4,2] => 8
[1,5,6,4,2,3] => 3
[1,5,6,4,3,2] => 8
[1,6,2,3,4,5] => 2
[1,6,2,3,5,4] => 6
[1,6,2,4,3,5] => 5
[1,6,2,4,5,3] => 5
[1,6,2,5,3,4] => 6
[1,6,2,5,4,3] => 11
[1,6,3,2,4,5] => 2
[1,6,3,2,5,4] => 6
[1,6,3,4,2,5] => 2
[1,6,3,4,5,2] => 2
[1,6,3,5,2,4] => 6
[1,6,3,5,4,2] => 11
[1,6,4,2,3,5] => 5
[1,6,4,2,5,3] => 9
[1,6,4,3,2,5] => 9
[1,6,4,3,5,2] => 9
[1,6,4,5,2,3] => 6
[1,6,4,5,3,2] => 11
[1,6,5,2,3,4] => 5
[1,6,5,2,4,3] => 10
[1,6,5,3,2,4] => 9
[1,6,5,3,4,2] => 10
[1,6,5,4,2,3] => 5
[1,6,5,4,3,2] => 10
[2,1,3,4,5,6] => 3
[2,1,3,4,6,5] => 8
[2,1,3,5,4,6] => 12
[2,1,3,5,6,4] => 8
[2,1,3,6,4,5] => 7
[2,1,3,6,5,4] => 7
[2,1,4,3,5,6] => 8
[2,1,4,3,6,5] => 9
[2,1,4,5,3,6] => 10
[2,1,4,5,6,3] => 6
[2,1,4,6,3,5] => 5
[2,1,4,6,5,3] => 5
[2,1,5,3,4,6] => 9
[2,1,5,3,6,4] => 9
[2,1,5,4,3,6] => 9
[2,1,5,4,6,3] => 9
[2,1,5,6,3,4] => 5
[2,1,5,6,4,3] => 10
[2,1,6,3,4,5] => 4
[2,1,6,3,5,4] => 8
[2,1,6,4,3,5] => 4
[2,1,6,4,5,3] => 4
[2,1,6,5,3,4] => 8
[2,1,6,5,4,3] => 13
[2,3,1,4,5,6] => 5
[2,3,1,4,6,5] => 10
[2,3,1,5,4,6] => 11
[2,3,1,5,6,4] => 7
[2,3,1,6,4,5] => 6
[2,3,1,6,5,4] => 6
[2,3,4,1,5,6] => 7
[2,3,4,1,6,5] => 8
[2,3,4,5,1,6] => 9
[2,3,4,5,6,1] => 5
[2,3,4,6,1,5] => 4
[2,3,4,6,5,1] => 4
[2,3,5,1,4,6] => 8
[2,3,5,1,6,4] => 8
[2,3,5,4,1,6] => 8
[2,3,5,4,6,1] => 8
[2,3,5,6,1,4] => 4
[2,3,5,6,4,1] => 9
[2,3,6,1,4,5] => 3
[2,3,6,1,5,4] => 7
[2,3,6,4,1,5] => 3
[2,3,6,4,5,1] => 3
[2,3,6,5,1,4] => 7
[2,3,6,5,4,1] => 12
[2,4,1,3,5,6] => 6
[2,4,1,3,6,5] => 7
[2,4,1,5,3,6] => 11
[2,4,1,5,6,3] => 7
[2,4,1,6,3,5] => 6
[2,4,1,6,5,3] => 6
[2,4,3,1,5,6] => 6
[2,4,3,1,6,5] => 7
[2,4,3,5,1,6] => 11
[2,4,3,5,6,1] => 7
[2,4,3,6,1,5] => 6
[2,4,3,6,5,1] => 6
[2,4,5,1,3,6] => 8
[2,4,5,1,6,3] => 8
[2,4,5,3,1,6] => 12
[2,4,5,3,6,1] => 8
[2,4,5,6,1,3] => 4
[2,4,5,6,3,1] => 9
[2,4,6,1,3,5] => 3
[2,4,6,1,5,3] => 7
[2,4,6,3,1,5] => 7
[2,4,6,3,5,1] => 7
[2,4,6,5,1,3] => 7
[2,4,6,5,3,1] => 12
[2,5,1,3,4,6] => 7
[2,5,1,3,6,4] => 7
[2,5,1,4,3,6] => 10
[2,5,1,4,6,3] => 10
[2,5,1,6,3,4] => 6
[2,5,1,6,4,3] => 11
[2,5,3,1,4,6] => 7
[2,5,3,1,6,4] => 7
[2,5,3,4,1,6] => 7
[2,5,3,4,6,1] => 7
[2,5,3,6,1,4] => 6
[2,5,3,6,4,1] => 11
[2,5,4,1,3,6] => 10
[2,5,4,1,6,3] => 10
[2,5,4,3,1,6] => 14
[2,5,4,3,6,1] => 10
[2,5,4,6,1,3] => 6
[2,5,4,6,3,1] => 11
[2,5,6,1,3,4] => 3
[2,5,6,1,4,3] => 8
[2,5,6,3,1,4] => 7
[2,5,6,3,4,1] => 8
[2,5,6,4,1,3] => 3
[2,5,6,4,3,1] => 8
[2,6,1,3,4,5] => 2
[2,6,1,3,5,4] => 6
[2,6,1,4,3,5] => 5
[2,6,1,4,5,3] => 5
[2,6,1,5,3,4] => 6
[2,6,1,5,4,3] => 11
[2,6,3,1,4,5] => 2
[2,6,3,1,5,4] => 6
[2,6,3,4,1,5] => 2
[2,6,3,4,5,1] => 2
[2,6,3,5,1,4] => 6
[2,6,3,5,4,1] => 11
[2,6,4,1,3,5] => 5
[2,6,4,1,5,3] => 9
[2,6,4,3,1,5] => 9
[2,6,4,3,5,1] => 9
[2,6,4,5,1,3] => 6
[2,6,4,5,3,1] => 11
[2,6,5,1,3,4] => 5
[2,6,5,1,4,3] => 10
[2,6,5,3,1,4] => 9
[2,6,5,3,4,1] => 10
[2,6,5,4,1,3] => 5
[2,6,5,4,3,1] => 10
[3,1,2,4,5,6] => 4
[3,1,2,4,6,5] => 9
[3,1,2,5,4,6] => 10
[3,1,2,5,6,4] => 6
[3,1,2,6,4,5] => 5
[3,1,2,6,5,4] => 5
[3,1,4,2,5,6] => 8
[3,1,4,2,6,5] => 9
[3,1,4,5,2,6] => 10
[3,1,4,5,6,2] => 6
[3,1,4,6,2,5] => 5
[3,1,4,6,5,2] => 5
[3,1,5,2,4,6] => 9
[3,1,5,2,6,4] => 9
[3,1,5,4,2,6] => 9
[3,1,5,4,6,2] => 9
[3,1,5,6,2,4] => 5
[3,1,5,6,4,2] => 10
[3,1,6,2,4,5] => 4
[3,1,6,2,5,4] => 8
[3,1,6,4,2,5] => 4
[3,1,6,4,5,2] => 4
[3,1,6,5,2,4] => 8
[3,1,6,5,4,2] => 13
[3,2,1,4,5,6] => 4
[3,2,1,4,6,5] => 9
[3,2,1,5,4,6] => 10
[3,2,1,5,6,4] => 6
[3,2,1,6,4,5] => 5
[3,2,1,6,5,4] => 5
[3,2,4,1,5,6] => 8
[3,2,4,1,6,5] => 9
[3,2,4,5,1,6] => 10
[3,2,4,5,6,1] => 6
[3,2,4,6,1,5] => 5
[3,2,4,6,5,1] => 5
[3,2,5,1,4,6] => 9
[3,2,5,1,6,4] => 9
[3,2,5,4,1,6] => 9
[3,2,5,4,6,1] => 9
[3,2,5,6,1,4] => 5
[3,2,5,6,4,1] => 10
[3,2,6,1,4,5] => 4
[3,2,6,1,5,4] => 8
[3,2,6,4,1,5] => 4
[3,2,6,4,5,1] => 4
[3,2,6,5,1,4] => 8
[3,2,6,5,4,1] => 13
[3,4,1,2,5,6] => 6
[3,4,1,2,6,5] => 7
[3,4,1,5,2,6] => 11
[3,4,1,5,6,2] => 7
[3,4,1,6,2,5] => 6
[3,4,1,6,5,2] => 6
[3,4,2,1,5,6] => 9
[3,4,2,1,6,5] => 10
[3,4,2,5,1,6] => 11
[3,4,2,5,6,1] => 7
[3,4,2,6,1,5] => 6
[3,4,2,6,5,1] => 6
[3,4,5,1,2,6] => 8
[3,4,5,1,6,2] => 8
[3,4,5,2,1,6] => 12
[3,4,5,2,6,1] => 8
[3,4,5,6,1,2] => 4
[3,4,5,6,2,1] => 9
[3,4,6,1,2,5] => 3
[3,4,6,1,5,2] => 7
[3,4,6,2,1,5] => 7
[3,4,6,2,5,1] => 7
[3,4,6,5,1,2] => 7
[3,4,6,5,2,1] => 12
[3,5,1,2,4,6] => 7
[3,5,1,2,6,4] => 7
[3,5,1,4,2,6] => 10
[3,5,1,4,6,2] => 10
[3,5,1,6,2,4] => 6
[3,5,1,6,4,2] => 11
[3,5,2,1,4,6] => 10
[3,5,2,1,6,4] => 10
[3,5,2,4,1,6] => 10
[3,5,2,4,6,1] => 10
[3,5,2,6,1,4] => 6
[3,5,2,6,4,1] => 11
[3,5,4,1,2,6] => 10
[3,5,4,1,6,2] => 10
[3,5,4,2,1,6] => 14
[3,5,4,2,6,1] => 10
[3,5,4,6,1,2] => 6
[3,5,4,6,2,1] => 11
[3,5,6,1,2,4] => 3
[3,5,6,1,4,2] => 8
[3,5,6,2,1,4] => 7
[3,5,6,2,4,1] => 8
[3,5,6,4,1,2] => 3
[3,5,6,4,2,1] => 8
[3,6,1,2,4,5] => 2
[3,6,1,2,5,4] => 6
[3,6,1,4,2,5] => 5
[3,6,1,4,5,2] => 5
[3,6,1,5,2,4] => 6
[3,6,1,5,4,2] => 11
[3,6,2,1,4,5] => 5
[3,6,2,1,5,4] => 9
[3,6,2,4,1,5] => 5
[3,6,2,4,5,1] => 5
[3,6,2,5,1,4] => 6
[3,6,2,5,4,1] => 11
[3,6,4,1,2,5] => 5
[3,6,4,1,5,2] => 9
[3,6,4,2,1,5] => 9
[3,6,4,2,5,1] => 9
[3,6,4,5,1,2] => 6
[3,6,4,5,2,1] => 11
[3,6,5,1,2,4] => 5
[3,6,5,1,4,2] => 10
[3,6,5,2,1,4] => 9
[3,6,5,2,4,1] => 10
[3,6,5,4,1,2] => 5
[3,6,5,4,2,1] => 10
[4,1,2,3,5,6] => 5
[4,1,2,3,6,5] => 6
[4,1,2,5,3,6] => 10
[4,1,2,5,6,3] => 6
[4,1,2,6,3,5] => 5
[4,1,2,6,5,3] => 5
[4,1,3,2,5,6] => 7
[4,1,3,2,6,5] => 8
[4,1,3,5,2,6] => 12
[4,1,3,5,6,2] => 8
[4,1,3,6,2,5] => 7
[4,1,3,6,5,2] => 7
[4,1,5,2,3,6] => 9
[4,1,5,2,6,3] => 9
[4,1,5,3,2,6] => 13
[4,1,5,3,6,2] => 9
[4,1,5,6,2,3] => 5
[4,1,5,6,3,2] => 10
[4,1,6,2,3,5] => 4
[4,1,6,2,5,3] => 8
[4,1,6,3,2,5] => 8
[4,1,6,3,5,2] => 8
[4,1,6,5,2,3] => 8
[4,1,6,5,3,2] => 13
[4,2,1,3,5,6] => 5
[4,2,1,3,6,5] => 6
[4,2,1,5,3,6] => 10
[4,2,1,5,6,3] => 6
[4,2,1,6,3,5] => 5
[4,2,1,6,5,3] => 5
[4,2,3,1,5,6] => 5
[4,2,3,1,6,5] => 6
[4,2,3,5,1,6] => 10
[4,2,3,5,6,1] => 6
[4,2,3,6,1,5] => 5
[4,2,3,6,5,1] => 5
[4,2,5,1,3,6] => 9
[4,2,5,1,6,3] => 9
[4,2,5,3,1,6] => 13
[4,2,5,3,6,1] => 9
[4,2,5,6,1,3] => 5
[4,2,5,6,3,1] => 10
[4,2,6,1,3,5] => 4
[4,2,6,1,5,3] => 8
[4,2,6,3,1,5] => 8
[4,2,6,3,5,1] => 8
[4,2,6,5,1,3] => 8
[4,2,6,5,3,1] => 13
[4,3,1,2,5,6] => 7
[4,3,1,2,6,5] => 8
[4,3,1,5,2,6] => 12
[4,3,1,5,6,2] => 8
[4,3,1,6,2,5] => 7
[4,3,1,6,5,2] => 7
[4,3,2,1,5,6] => 10
[4,3,2,1,6,5] => 11
[4,3,2,5,1,6] => 12
[4,3,2,5,6,1] => 8
[4,3,2,6,1,5] => 7
[4,3,2,6,5,1] => 7
[4,3,5,1,2,6] => 9
[4,3,5,1,6,2] => 9
[4,3,5,2,1,6] => 13
[4,3,5,2,6,1] => 9
[4,3,5,6,1,2] => 5
[4,3,5,6,2,1] => 10
[4,3,6,1,2,5] => 4
[4,3,6,1,5,2] => 8
[4,3,6,2,1,5] => 8
[4,3,6,2,5,1] => 8
[4,3,6,5,1,2] => 8
[4,3,6,5,2,1] => 13
[4,5,1,2,3,6] => 7
[4,5,1,2,6,3] => 7
[4,5,1,3,2,6] => 11
[4,5,1,3,6,2] => 7
[4,5,1,6,2,3] => 6
[4,5,1,6,3,2] => 11
[4,5,2,1,3,6] => 10
[4,5,2,1,6,3] => 10
[4,5,2,3,1,6] => 11
[4,5,2,3,6,1] => 7
[4,5,2,6,1,3] => 6
[4,5,2,6,3,1] => 11
[4,5,3,1,2,6] => 7
[4,5,3,1,6,2] => 7
[4,5,3,2,1,6] => 11
[4,5,3,2,6,1] => 7
[4,5,3,6,1,2] => 6
[4,5,3,6,2,1] => 11
[4,5,6,1,2,3] => 3
[4,5,6,1,3,2] => 8
[4,5,6,2,1,3] => 7
[4,5,6,2,3,1] => 8
[4,5,6,3,1,2] => 7
[4,5,6,3,2,1] => 12
[4,6,1,2,3,5] => 2
[4,6,1,2,5,3] => 6
[4,6,1,3,2,5] => 6
[4,6,1,3,5,2] => 6
[4,6,1,5,2,3] => 6
[4,6,1,5,3,2] => 11
[4,6,2,1,3,5] => 5
[4,6,2,1,5,3] => 9
[4,6,2,3,1,5] => 6
[4,6,2,3,5,1] => 6
[4,6,2,5,1,3] => 6
[4,6,2,5,3,1] => 11
[4,6,3,1,2,5] => 2
[4,6,3,1,5,2] => 6
[4,6,3,2,1,5] => 6
[4,6,3,2,5,1] => 6
[4,6,3,5,1,2] => 6
[4,6,3,5,2,1] => 11
[4,6,5,1,2,3] => 5
[4,6,5,1,3,2] => 10
[4,6,5,2,1,3] => 9
[4,6,5,2,3,1] => 10
[4,6,5,3,1,2] => 9
[4,6,5,3,2,1] => 14
[5,1,2,3,4,6] => 6
[5,1,2,3,6,4] => 6
[5,1,2,4,3,6] => 9
[5,1,2,4,6,3] => 9
[5,1,2,6,3,4] => 5
[5,1,2,6,4,3] => 10
[5,1,3,2,4,6] => 8
[5,1,3,2,6,4] => 8
[5,1,3,4,2,6] => 8
[5,1,3,4,6,2] => 8
[5,1,3,6,2,4] => 7
[5,1,3,6,4,2] => 12
[5,1,4,2,3,6] => 9
[5,1,4,2,6,3] => 9
[5,1,4,3,2,6] => 13
[5,1,4,3,6,2] => 9
[5,1,4,6,2,3] => 5
[5,1,4,6,3,2] => 10
[5,1,6,2,3,4] => 4
[5,1,6,2,4,3] => 9
[5,1,6,3,2,4] => 8
[5,1,6,3,4,2] => 9
[5,1,6,4,2,3] => 4
[5,1,6,4,3,2] => 9
[5,2,1,3,4,6] => 6
[5,2,1,3,6,4] => 6
[5,2,1,4,3,6] => 9
[5,2,1,4,6,3] => 9
[5,2,1,6,3,4] => 5
[5,2,1,6,4,3] => 10
[5,2,3,1,4,6] => 6
[5,2,3,1,6,4] => 6
[5,2,3,4,1,6] => 6
[5,2,3,4,6,1] => 6
[5,2,3,6,1,4] => 5
[5,2,3,6,4,1] => 10
[5,2,4,1,3,6] => 9
[5,2,4,1,6,3] => 9
[5,2,4,3,1,6] => 13
[5,2,4,3,6,1] => 9
[5,2,4,6,1,3] => 5
[5,2,4,6,3,1] => 10
[5,2,6,1,3,4] => 4
[5,2,6,1,4,3] => 9
[5,2,6,3,1,4] => 8
[5,2,6,3,4,1] => 9
[5,2,6,4,1,3] => 4
[5,2,6,4,3,1] => 9
[5,3,1,2,4,6] => 8
[5,3,1,2,6,4] => 8
[5,3,1,4,2,6] => 11
[5,3,1,4,6,2] => 11
[5,3,1,6,2,4] => 7
[5,3,1,6,4,2] => 12
[5,3,2,1,4,6] => 11
[5,3,2,1,6,4] => 11
[5,3,2,4,1,6] => 11
[5,3,2,4,6,1] => 11
[5,3,2,6,1,4] => 7
[5,3,2,6,4,1] => 12
[5,3,4,1,2,6] => 9
[5,3,4,1,6,2] => 9
[5,3,4,2,1,6] => 13
[5,3,4,2,6,1] => 9
[5,3,4,6,1,2] => 5
[5,3,4,6,2,1] => 10
[5,3,6,1,2,4] => 4
[5,3,6,1,4,2] => 9
[5,3,6,2,1,4] => 8
[5,3,6,2,4,1] => 9
[5,3,6,4,1,2] => 4
[5,3,6,4,2,1] => 9
[5,4,1,2,3,6] => 8
[5,4,1,2,6,3] => 8
[5,4,1,3,2,6] => 12
[5,4,1,3,6,2] => 8
[5,4,1,6,2,3] => 7
[5,4,1,6,3,2] => 12
[5,4,2,1,3,6] => 11
[5,4,2,1,6,3] => 11
[5,4,2,3,1,6] => 12
[5,4,2,3,6,1] => 8
[5,4,2,6,1,3] => 7
[5,4,2,6,3,1] => 12
[5,4,3,1,2,6] => 8
[5,4,3,1,6,2] => 8
[5,4,3,2,1,6] => 12
[5,4,3,2,6,1] => 8
[5,4,3,6,1,2] => 7
[5,4,3,6,2,1] => 12
[5,4,6,1,2,3] => 4
[5,4,6,1,3,2] => 9
[5,4,6,2,1,3] => 8
[5,4,6,2,3,1] => 9
[5,4,6,3,1,2] => 8
[5,4,6,3,2,1] => 13
[5,6,1,2,3,4] => 2
[5,6,1,2,4,3] => 7
[5,6,1,3,2,4] => 6
[5,6,1,3,4,2] => 7
[5,6,1,4,2,3] => 5
[5,6,1,4,3,2] => 10
[5,6,2,1,3,4] => 5
[5,6,2,1,4,3] => 10
[5,6,2,3,1,4] => 6
[5,6,2,3,4,1] => 7
[5,6,2,4,1,3] => 5
[5,6,2,4,3,1] => 10
[5,6,3,1,2,4] => 2
[5,6,3,1,4,2] => 7
[5,6,3,2,1,4] => 6
[5,6,3,2,4,1] => 7
[5,6,3,4,1,2] => 2
[5,6,3,4,2,1] => 7
[5,6,4,1,2,3] => 5
[5,6,4,1,3,2] => 10
[5,6,4,2,1,3] => 9
[5,6,4,2,3,1] => 10
[5,6,4,3,1,2] => 9
[5,6,4,3,2,1] => 14
[6,1,2,3,4,5] => 1
[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] => 5
[6,1,2,5,4,3] => 10
[6,1,3,2,4,5] => 3
[6,1,3,2,5,4] => 7
[6,1,3,4,2,5] => 3
[6,1,3,4,5,2] => 3
[6,1,3,5,2,4] => 7
[6,1,3,5,4,2] => 12
[6,1,4,2,3,5] => 4
[6,1,4,2,5,3] => 8
[6,1,4,3,2,5] => 8
[6,1,4,3,5,2] => 8
[6,1,4,5,2,3] => 5
[6,1,4,5,3,2] => 10
[6,1,5,2,3,4] => 4
[6,1,5,2,4,3] => 9
[6,1,5,3,2,4] => 8
[6,1,5,3,4,2] => 9
[6,1,5,4,2,3] => 4
[6,1,5,4,3,2] => 9
[6,2,1,3,4,5] => 1
[6,2,1,3,5,4] => 5
[6,2,1,4,3,5] => 4
[6,2,1,4,5,3] => 4
[6,2,1,5,3,4] => 5
[6,2,1,5,4,3] => 10
[6,2,3,1,4,5] => 1
[6,2,3,1,5,4] => 5
[6,2,3,4,1,5] => 1
[6,2,3,4,5,1] => 1
[6,2,3,5,1,4] => 5
[6,2,3,5,4,1] => 10
[6,2,4,1,3,5] => 4
[6,2,4,1,5,3] => 8
[6,2,4,3,1,5] => 8
[6,2,4,3,5,1] => 8
[6,2,4,5,1,3] => 5
[6,2,4,5,3,1] => 10
[6,2,5,1,3,4] => 4
[6,2,5,1,4,3] => 9
[6,2,5,3,1,4] => 8
[6,2,5,3,4,1] => 9
[6,2,5,4,1,3] => 4
[6,2,5,4,3,1] => 9
[6,3,1,2,4,5] => 3
[6,3,1,2,5,4] => 7
[6,3,1,4,2,5] => 6
[6,3,1,4,5,2] => 6
[6,3,1,5,2,4] => 7
[6,3,1,5,4,2] => 12
[6,3,2,1,4,5] => 6
[6,3,2,1,5,4] => 10
[6,3,2,4,1,5] => 6
[6,3,2,4,5,1] => 6
[6,3,2,5,1,4] => 7
[6,3,2,5,4,1] => 12
[6,3,4,1,2,5] => 4
[6,3,4,1,5,2] => 8
[6,3,4,2,1,5] => 8
[6,3,4,2,5,1] => 8
[6,3,4,5,1,2] => 5
[6,3,4,5,2,1] => 10
[6,3,5,1,2,4] => 4
[6,3,5,1,4,2] => 9
[6,3,5,2,1,4] => 8
[6,3,5,2,4,1] => 9
[6,3,5,4,1,2] => 4
[6,3,5,4,2,1] => 9
[6,4,1,2,3,5] => 3
[6,4,1,2,5,3] => 7
[6,4,1,3,2,5] => 7
[6,4,1,3,5,2] => 7
[6,4,1,5,2,3] => 7
[6,4,1,5,3,2] => 12
[6,4,2,1,3,5] => 6
[6,4,2,1,5,3] => 10
[6,4,2,3,1,5] => 7
[6,4,2,3,5,1] => 7
[6,4,2,5,1,3] => 7
[6,4,2,5,3,1] => 12
[6,4,3,1,2,5] => 3
[6,4,3,1,5,2] => 7
[6,4,3,2,1,5] => 7
[6,4,3,2,5,1] => 7
[6,4,3,5,1,2] => 7
[6,4,3,5,2,1] => 12
[6,4,5,1,2,3] => 4
[6,4,5,1,3,2] => 9
[6,4,5,2,1,3] => 8
[6,4,5,2,3,1] => 9
[6,4,5,3,1,2] => 8
[6,4,5,3,2,1] => 13
[6,5,1,2,3,4] => 3
[6,5,1,2,4,3] => 8
[6,5,1,3,2,4] => 7
[6,5,1,3,4,2] => 8
[6,5,1,4,2,3] => 6
[6,5,1,4,3,2] => 11
[6,5,2,1,3,4] => 6
[6,5,2,1,4,3] => 11
[6,5,2,3,1,4] => 7
[6,5,2,3,4,1] => 8
[6,5,2,4,1,3] => 6
[6,5,2,4,3,1] => 11
[6,5,3,1,2,4] => 3
[6,5,3,1,4,2] => 8
[6,5,3,2,1,4] => 7
[6,5,3,2,4,1] => 8
[6,5,3,4,1,2] => 3
[6,5,3,4,2,1] => 8
[6,5,4,1,2,3] => 6
[6,5,4,1,3,2] => 11
[6,5,4,2,1,3] => 10
[6,5,4,2,3,1] => 11
[6,5,4,3,1,2] => 10
[6,5,4,3,2,1] => 15
click to show generating function       
Description
The maz index, the major index of a permutation after replacing fixed points by zeros.
The descent set is denoted by $\operatorname{ZDer}(\sigma)$ in [1].
References
[1] Foata, D., Han, G.-N. Fix-Mahonian Calculus, II: further statistics arXiv:math/0703101
[2] Han, G.-N., Xin, G. Permutations with Extremal number of Fixed Points arXiv:0706.1738
Code
def statistic(x):
    return Word(sz(x)).major_index()

#Returns the word (as a list) where fixed points of x are changed to zero (see [2])
def sz(x):
    l = list(x)
    for i in x.fixed_points():
            l[i-1] = 0
    return l
Created
Dec 18, 2015 at 13:44 by Joseph Bernstein
Updated
Apr 07, 2016 at 07:57 by Martin Rubey