Identifier
Identifier
Values
[1] => 0
[1,2] => 0
[2,1] => 2
[1,2,3] => 0
[1,3,2] => 3
[2,1,3] => 2
[2,3,1] => 3
[3,1,2] => 3
[3,2,1] => 5
[1,2,3,4] => 0
[1,2,4,3] => 4
[1,3,2,4] => 3
[1,3,4,2] => 4
[1,4,2,3] => 4
[1,4,3,2] => 7
[2,1,3,4] => 2
[2,1,4,3] => 6
[2,3,1,4] => 3
[2,3,4,1] => 4
[2,4,1,3] => 4
[2,4,3,1] => 7
[3,1,2,4] => 3
[3,1,4,2] => 7
[3,2,1,4] => 5
[3,2,4,1] => 7
[3,4,1,2] => 4
[3,4,2,1] => 6
[4,1,2,3] => 4
[4,1,3,2] => 7
[4,2,1,3] => 6
[4,2,3,1] => 7
[4,3,1,2] => 7
[4,3,2,1] => 9
[1,2,3,4,5] => 0
[1,2,3,5,4] => 5
[1,2,4,3,5] => 4
[1,2,4,5,3] => 5
[1,2,5,3,4] => 5
[1,2,5,4,3] => 9
[1,3,2,4,5] => 3
[1,3,2,5,4] => 8
[1,3,4,2,5] => 4
[1,3,4,5,2] => 5
[1,3,5,2,4] => 5
[1,3,5,4,2] => 9
[1,4,2,3,5] => 4
[1,4,2,5,3] => 9
[1,4,3,2,5] => 7
[1,4,3,5,2] => 9
[1,4,5,2,3] => 5
[1,4,5,3,2] => 8
[1,5,2,3,4] => 5
[1,5,2,4,3] => 9
[1,5,3,2,4] => 8
[1,5,3,4,2] => 9
[1,5,4,2,3] => 9
[1,5,4,3,2] => 12
[2,1,3,4,5] => 2
[2,1,3,5,4] => 7
[2,1,4,3,5] => 6
[2,1,4,5,3] => 7
[2,1,5,3,4] => 7
[2,1,5,4,3] => 11
[2,3,1,4,5] => 3
[2,3,1,5,4] => 8
[2,3,4,1,5] => 4
[2,3,4,5,1] => 5
[2,3,5,1,4] => 5
[2,3,5,4,1] => 9
[2,4,1,3,5] => 4
[2,4,1,5,3] => 9
[2,4,3,1,5] => 7
[2,4,3,5,1] => 9
[2,4,5,1,3] => 5
[2,4,5,3,1] => 8
[2,5,1,3,4] => 5
[2,5,1,4,3] => 9
[2,5,3,1,4] => 8
[2,5,3,4,1] => 9
[2,5,4,1,3] => 9
[2,5,4,3,1] => 12
[3,1,2,4,5] => 3
[3,1,2,5,4] => 8
[3,1,4,2,5] => 7
[3,1,4,5,2] => 8
[3,1,5,2,4] => 8
[3,1,5,4,2] => 12
[3,2,1,4,5] => 5
[3,2,1,5,4] => 10
[3,2,4,1,5] => 7
[3,2,4,5,1] => 8
[3,2,5,1,4] => 8
[3,2,5,4,1] => 12
[3,4,1,2,5] => 4
[3,4,1,5,2] => 9
[3,4,2,1,5] => 6
[3,4,2,5,1] => 9
[3,4,5,1,2] => 5
[3,4,5,2,1] => 7
[3,5,1,2,4] => 5
[3,5,1,4,2] => 9
[3,5,2,1,4] => 7
[3,5,2,4,1] => 9
[3,5,4,1,2] => 9
[3,5,4,2,1] => 11
[4,1,2,3,5] => 4
[4,1,2,5,3] => 9
[4,1,3,2,5] => 7
[4,1,3,5,2] => 9
[4,1,5,2,3] => 9
[4,1,5,3,2] => 12
[4,2,1,3,5] => 6
[4,2,1,5,3] => 11
[4,2,3,1,5] => 7
[4,2,3,5,1] => 9
[4,2,5,1,3] => 9
[4,2,5,3,1] => 12
[4,3,1,2,5] => 7
[4,3,1,5,2] => 12
[4,3,2,1,5] => 9
[4,3,2,5,1] => 12
[4,3,5,1,2] => 9
[4,3,5,2,1] => 11
[4,5,1,2,3] => 5
[4,5,1,3,2] => 8
[4,5,2,1,3] => 7
[4,5,2,3,1] => 8
[4,5,3,1,2] => 8
[4,5,3,2,1] => 10
[5,1,2,3,4] => 5
[5,1,2,4,3] => 9
[5,1,3,2,4] => 8
[5,1,3,4,2] => 9
[5,1,4,2,3] => 9
[5,1,4,3,2] => 12
[5,2,1,3,4] => 7
[5,2,1,4,3] => 11
[5,2,3,1,4] => 8
[5,2,3,4,1] => 9
[5,2,4,1,3] => 9
[5,2,4,3,1] => 12
[5,3,1,2,4] => 8
[5,3,1,4,2] => 12
[5,3,2,1,4] => 10
[5,3,2,4,1] => 12
[5,3,4,1,2] => 9
[5,3,4,2,1] => 11
[5,4,1,2,3] => 9
[5,4,1,3,2] => 12
[5,4,2,1,3] => 11
[5,4,2,3,1] => 12
[5,4,3,1,2] => 12
[5,4,3,2,1] => 14
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 6
[1,2,3,5,4,6] => 5
[1,2,3,5,6,4] => 6
[1,2,3,6,4,5] => 6
[1,2,3,6,5,4] => 11
[1,2,4,3,5,6] => 4
[1,2,4,3,6,5] => 10
[1,2,4,5,3,6] => 5
[1,2,4,5,6,3] => 6
[1,2,4,6,3,5] => 6
[1,2,4,6,5,3] => 11
[1,2,5,3,4,6] => 5
[1,2,5,3,6,4] => 11
[1,2,5,4,3,6] => 9
[1,2,5,4,6,3] => 11
[1,2,5,6,3,4] => 6
[1,2,5,6,4,3] => 10
[1,2,6,3,4,5] => 6
[1,2,6,3,5,4] => 11
[1,2,6,4,3,5] => 10
[1,2,6,4,5,3] => 11
[1,2,6,5,3,4] => 11
[1,2,6,5,4,3] => 15
[1,3,2,4,5,6] => 3
[1,3,2,4,6,5] => 9
[1,3,2,5,4,6] => 8
[1,3,2,5,6,4] => 9
[1,3,2,6,4,5] => 9
[1,3,2,6,5,4] => 14
[1,3,4,2,5,6] => 4
[1,3,4,2,6,5] => 10
[1,3,4,5,2,6] => 5
[1,3,4,5,6,2] => 6
[1,3,4,6,2,5] => 6
[1,3,4,6,5,2] => 11
[1,3,5,2,4,6] => 5
[1,3,5,2,6,4] => 11
[1,3,5,4,2,6] => 9
[1,3,5,4,6,2] => 11
[1,3,5,6,2,4] => 6
[1,3,5,6,4,2] => 10
[1,3,6,2,4,5] => 6
[1,3,6,2,5,4] => 11
[1,3,6,4,2,5] => 10
[1,3,6,4,5,2] => 11
[1,3,6,5,2,4] => 11
[1,3,6,5,4,2] => 15
[1,4,2,3,5,6] => 4
[1,4,2,3,6,5] => 10
[1,4,2,5,3,6] => 9
[1,4,2,5,6,3] => 10
[1,4,2,6,3,5] => 10
[1,4,2,6,5,3] => 15
[1,4,3,2,5,6] => 7
[1,4,3,2,6,5] => 13
[1,4,3,5,2,6] => 9
[1,4,3,5,6,2] => 10
[1,4,3,6,2,5] => 10
[1,4,3,6,5,2] => 15
[1,4,5,2,3,6] => 5
[1,4,5,2,6,3] => 11
[1,4,5,3,2,6] => 8
[1,4,5,3,6,2] => 11
[1,4,5,6,2,3] => 6
[1,4,5,6,3,2] => 9
[1,4,6,2,3,5] => 6
[1,4,6,2,5,3] => 11
[1,4,6,3,2,5] => 9
[1,4,6,3,5,2] => 11
[1,4,6,5,2,3] => 11
[1,4,6,5,3,2] => 14
[1,5,2,3,4,6] => 5
[1,5,2,3,6,4] => 11
[1,5,2,4,3,6] => 9
[1,5,2,4,6,3] => 11
[1,5,2,6,3,4] => 11
[1,5,2,6,4,3] => 15
[1,5,3,2,4,6] => 8
[1,5,3,2,6,4] => 14
[1,5,3,4,2,6] => 9
[1,5,3,4,6,2] => 11
[1,5,3,6,2,4] => 11
[1,5,3,6,4,2] => 15
[1,5,4,2,3,6] => 9
[1,5,4,2,6,3] => 15
[1,5,4,3,2,6] => 12
[1,5,4,3,6,2] => 15
[1,5,4,6,2,3] => 11
[1,5,4,6,3,2] => 14
[1,5,6,2,3,4] => 6
[1,5,6,2,4,3] => 10
[1,5,6,3,2,4] => 9
[1,5,6,3,4,2] => 10
[1,5,6,4,2,3] => 10
[1,5,6,4,3,2] => 13
[1,6,2,3,4,5] => 6
[1,6,2,3,5,4] => 11
[1,6,2,4,3,5] => 10
[1,6,2,4,5,3] => 11
[1,6,2,5,3,4] => 11
[1,6,2,5,4,3] => 15
[1,6,3,2,4,5] => 9
[1,6,3,2,5,4] => 14
[1,6,3,4,2,5] => 10
[1,6,3,4,5,2] => 11
[1,6,3,5,2,4] => 11
[1,6,3,5,4,2] => 15
[1,6,4,2,3,5] => 10
[1,6,4,2,5,3] => 15
[1,6,4,3,2,5] => 13
[1,6,4,3,5,2] => 15
[1,6,4,5,2,3] => 11
[1,6,4,5,3,2] => 14
[1,6,5,2,3,4] => 11
[1,6,5,2,4,3] => 15
[1,6,5,3,2,4] => 14
[1,6,5,3,4,2] => 15
[1,6,5,4,2,3] => 15
[1,6,5,4,3,2] => 18
[2,1,3,4,5,6] => 2
[2,1,3,4,6,5] => 8
[2,1,3,5,4,6] => 7
[2,1,3,5,6,4] => 8
[2,1,3,6,4,5] => 8
[2,1,3,6,5,4] => 13
[2,1,4,3,5,6] => 6
[2,1,4,3,6,5] => 12
[2,1,4,5,3,6] => 7
[2,1,4,5,6,3] => 8
[2,1,4,6,3,5] => 8
[2,1,4,6,5,3] => 13
[2,1,5,3,4,6] => 7
[2,1,5,3,6,4] => 13
[2,1,5,4,3,6] => 11
[2,1,5,4,6,3] => 13
[2,1,5,6,3,4] => 8
[2,1,5,6,4,3] => 12
[2,1,6,3,4,5] => 8
[2,1,6,3,5,4] => 13
[2,1,6,4,3,5] => 12
[2,1,6,4,5,3] => 13
[2,1,6,5,3,4] => 13
[2,1,6,5,4,3] => 17
[2,3,1,4,5,6] => 3
[2,3,1,4,6,5] => 9
[2,3,1,5,4,6] => 8
[2,3,1,5,6,4] => 9
[2,3,1,6,4,5] => 9
[2,3,1,6,5,4] => 14
[2,3,4,1,5,6] => 4
[2,3,4,1,6,5] => 10
[2,3,4,5,1,6] => 5
[2,3,4,5,6,1] => 6
[2,3,4,6,1,5] => 6
[2,3,4,6,5,1] => 11
[2,3,5,1,4,6] => 5
[2,3,5,1,6,4] => 11
[2,3,5,4,1,6] => 9
[2,3,5,4,6,1] => 11
[2,3,5,6,1,4] => 6
[2,3,5,6,4,1] => 10
[2,3,6,1,4,5] => 6
[2,3,6,1,5,4] => 11
[2,3,6,4,1,5] => 10
[2,3,6,4,5,1] => 11
[2,3,6,5,1,4] => 11
[2,3,6,5,4,1] => 15
[2,4,1,3,5,6] => 4
[2,4,1,3,6,5] => 10
[2,4,1,5,3,6] => 9
[2,4,1,5,6,3] => 10
[2,4,1,6,3,5] => 10
[2,4,1,6,5,3] => 15
[2,4,3,1,5,6] => 7
[2,4,3,1,6,5] => 13
[2,4,3,5,1,6] => 9
[2,4,3,5,6,1] => 10
[2,4,3,6,1,5] => 10
[2,4,3,6,5,1] => 15
[2,4,5,1,3,6] => 5
[2,4,5,1,6,3] => 11
[2,4,5,3,1,6] => 8
[2,4,5,3,6,1] => 11
[2,4,5,6,1,3] => 6
[2,4,5,6,3,1] => 9
[2,4,6,1,3,5] => 6
[2,4,6,1,5,3] => 11
[2,4,6,3,1,5] => 9
[2,4,6,3,5,1] => 11
[2,4,6,5,1,3] => 11
[2,4,6,5,3,1] => 14
[2,5,1,3,4,6] => 5
[2,5,1,3,6,4] => 11
[2,5,1,4,3,6] => 9
[2,5,1,4,6,3] => 11
[2,5,1,6,3,4] => 11
[2,5,1,6,4,3] => 15
[2,5,3,1,4,6] => 8
[2,5,3,1,6,4] => 14
[2,5,3,4,1,6] => 9
[2,5,3,4,6,1] => 11
[2,5,3,6,1,4] => 11
[2,5,3,6,4,1] => 15
[2,5,4,1,3,6] => 9
[2,5,4,1,6,3] => 15
[2,5,4,3,1,6] => 12
[2,5,4,3,6,1] => 15
[2,5,4,6,1,3] => 11
[2,5,4,6,3,1] => 14
[2,5,6,1,3,4] => 6
[2,5,6,1,4,3] => 10
[2,5,6,3,1,4] => 9
[2,5,6,3,4,1] => 10
[2,5,6,4,1,3] => 10
[2,5,6,4,3,1] => 13
[2,6,1,3,4,5] => 6
[2,6,1,3,5,4] => 11
[2,6,1,4,3,5] => 10
[2,6,1,4,5,3] => 11
[2,6,1,5,3,4] => 11
[2,6,1,5,4,3] => 15
[2,6,3,1,4,5] => 9
[2,6,3,1,5,4] => 14
[2,6,3,4,1,5] => 10
[2,6,3,4,5,1] => 11
[2,6,3,5,1,4] => 11
[2,6,3,5,4,1] => 15
[2,6,4,1,3,5] => 10
[2,6,4,1,5,3] => 15
[2,6,4,3,1,5] => 13
[2,6,4,3,5,1] => 15
[2,6,4,5,1,3] => 11
[2,6,4,5,3,1] => 14
[2,6,5,1,3,4] => 11
[2,6,5,1,4,3] => 15
[2,6,5,3,1,4] => 14
[2,6,5,3,4,1] => 15
[2,6,5,4,1,3] => 15
[2,6,5,4,3,1] => 18
[3,1,2,4,5,6] => 3
[3,1,2,4,6,5] => 9
[3,1,2,5,4,6] => 8
[3,1,2,5,6,4] => 9
[3,1,2,6,4,5] => 9
[3,1,2,6,5,4] => 14
[3,1,4,2,5,6] => 7
[3,1,4,2,6,5] => 13
[3,1,4,5,2,6] => 8
[3,1,4,5,6,2] => 9
[3,1,4,6,2,5] => 9
[3,1,4,6,5,2] => 14
[3,1,5,2,4,6] => 8
[3,1,5,2,6,4] => 14
[3,1,5,4,2,6] => 12
[3,1,5,4,6,2] => 14
[3,1,5,6,2,4] => 9
[3,1,5,6,4,2] => 13
[3,1,6,2,4,5] => 9
[3,1,6,2,5,4] => 14
[3,1,6,4,2,5] => 13
[3,1,6,4,5,2] => 14
[3,1,6,5,2,4] => 14
[3,1,6,5,4,2] => 18
[3,2,1,4,5,6] => 5
[3,2,1,4,6,5] => 11
[3,2,1,5,4,6] => 10
[3,2,1,5,6,4] => 11
[3,2,1,6,4,5] => 11
[3,2,1,6,5,4] => 16
[3,2,4,1,5,6] => 7
[3,2,4,1,6,5] => 13
[3,2,4,5,1,6] => 8
[3,2,4,5,6,1] => 9
[3,2,4,6,1,5] => 9
[3,2,4,6,5,1] => 14
[3,2,5,1,4,6] => 8
[3,2,5,1,6,4] => 14
[3,2,5,4,1,6] => 12
[3,2,5,4,6,1] => 14
[3,2,5,6,1,4] => 9
[3,2,5,6,4,1] => 13
[3,2,6,1,4,5] => 9
[3,2,6,1,5,4] => 14
[3,2,6,4,1,5] => 13
[3,2,6,4,5,1] => 14
[3,2,6,5,1,4] => 14
[3,2,6,5,4,1] => 18
[3,4,1,2,5,6] => 4
[3,4,1,2,6,5] => 10
[3,4,1,5,2,6] => 9
[3,4,1,5,6,2] => 10
[3,4,1,6,2,5] => 10
[3,4,1,6,5,2] => 15
[3,4,2,1,5,6] => 6
[3,4,2,1,6,5] => 12
[3,4,2,5,1,6] => 9
[3,4,2,5,6,1] => 10
[3,4,2,6,1,5] => 10
[3,4,2,6,5,1] => 15
[3,4,5,1,2,6] => 5
[3,4,5,1,6,2] => 11
[3,4,5,2,1,6] => 7
[3,4,5,2,6,1] => 11
[3,4,5,6,1,2] => 6
[3,4,5,6,2,1] => 8
[3,4,6,1,2,5] => 6
[3,4,6,1,5,2] => 11
[3,4,6,2,1,5] => 8
[3,4,6,2,5,1] => 11
[3,4,6,5,1,2] => 11
[3,4,6,5,2,1] => 13
[3,5,1,2,4,6] => 5
[3,5,1,2,6,4] => 11
[3,5,1,4,2,6] => 9
[3,5,1,4,6,2] => 11
[3,5,1,6,2,4] => 11
[3,5,1,6,4,2] => 15
[3,5,2,1,4,6] => 7
[3,5,2,1,6,4] => 13
[3,5,2,4,1,6] => 9
[3,5,2,4,6,1] => 11
[3,5,2,6,1,4] => 11
[3,5,2,6,4,1] => 15
[3,5,4,1,2,6] => 9
[3,5,4,1,6,2] => 15
[3,5,4,2,1,6] => 11
[3,5,4,2,6,1] => 15
[3,5,4,6,1,2] => 11
[3,5,4,6,2,1] => 13
[3,5,6,1,2,4] => 6
[3,5,6,1,4,2] => 10
[3,5,6,2,1,4] => 8
[3,5,6,2,4,1] => 10
[3,5,6,4,1,2] => 10
[3,5,6,4,2,1] => 12
[3,6,1,2,4,5] => 6
[3,6,1,2,5,4] => 11
[3,6,1,4,2,5] => 10
[3,6,1,4,5,2] => 11
[3,6,1,5,2,4] => 11
[3,6,1,5,4,2] => 15
[3,6,2,1,4,5] => 8
[3,6,2,1,5,4] => 13
[3,6,2,4,1,5] => 10
[3,6,2,4,5,1] => 11
[3,6,2,5,1,4] => 11
[3,6,2,5,4,1] => 15
[3,6,4,1,2,5] => 10
[3,6,4,1,5,2] => 15
[3,6,4,2,1,5] => 12
[3,6,4,2,5,1] => 15
[3,6,4,5,1,2] => 11
[3,6,4,5,2,1] => 13
[3,6,5,1,2,4] => 11
[3,6,5,1,4,2] => 15
[3,6,5,2,1,4] => 13
[3,6,5,2,4,1] => 15
[3,6,5,4,1,2] => 15
[3,6,5,4,2,1] => 17
[4,1,2,3,5,6] => 4
[4,1,2,3,6,5] => 10
[4,1,2,5,3,6] => 9
[4,1,2,5,6,3] => 10
[4,1,2,6,3,5] => 10
[4,1,2,6,5,3] => 15
[4,1,3,2,5,6] => 7
[4,1,3,2,6,5] => 13
[4,1,3,5,2,6] => 9
[4,1,3,5,6,2] => 10
[4,1,3,6,2,5] => 10
[4,1,3,6,5,2] => 15
[4,1,5,2,3,6] => 9
[4,1,5,2,6,3] => 15
[4,1,5,3,2,6] => 12
[4,1,5,3,6,2] => 15
[4,1,5,6,2,3] => 10
[4,1,5,6,3,2] => 13
[4,1,6,2,3,5] => 10
[4,1,6,2,5,3] => 15
[4,1,6,3,2,5] => 13
[4,1,6,3,5,2] => 15
[4,1,6,5,2,3] => 15
[4,1,6,5,3,2] => 18
[4,2,1,3,5,6] => 6
[4,2,1,3,6,5] => 12
[4,2,1,5,3,6] => 11
[4,2,1,5,6,3] => 12
[4,2,1,6,3,5] => 12
[4,2,1,6,5,3] => 17
[4,2,3,1,5,6] => 7
[4,2,3,1,6,5] => 13
[4,2,3,5,1,6] => 9
[4,2,3,5,6,1] => 10
[4,2,3,6,1,5] => 10
[4,2,3,6,5,1] => 15
[4,2,5,1,3,6] => 9
[4,2,5,1,6,3] => 15
[4,2,5,3,1,6] => 12
[4,2,5,3,6,1] => 15
[4,2,5,6,1,3] => 10
[4,2,5,6,3,1] => 13
[4,2,6,1,3,5] => 10
[4,2,6,1,5,3] => 15
[4,2,6,3,1,5] => 13
[4,2,6,3,5,1] => 15
[4,2,6,5,1,3] => 15
[4,2,6,5,3,1] => 18
[4,3,1,2,5,6] => 7
[4,3,1,2,6,5] => 13
[4,3,1,5,2,6] => 12
[4,3,1,5,6,2] => 13
[4,3,1,6,2,5] => 13
[4,3,1,6,5,2] => 18
[4,3,2,1,5,6] => 9
[4,3,2,1,6,5] => 15
[4,3,2,5,1,6] => 12
[4,3,2,5,6,1] => 13
[4,3,2,6,1,5] => 13
[4,3,2,6,5,1] => 18
[4,3,5,1,2,6] => 9
[4,3,5,1,6,2] => 15
[4,3,5,2,1,6] => 11
[4,3,5,2,6,1] => 15
[4,3,5,6,1,2] => 10
[4,3,5,6,2,1] => 12
[4,3,6,1,2,5] => 10
[4,3,6,1,5,2] => 15
[4,3,6,2,1,5] => 12
[4,3,6,2,5,1] => 15
[4,3,6,5,1,2] => 15
[4,3,6,5,2,1] => 17
[4,5,1,2,3,6] => 5
[4,5,1,2,6,3] => 11
[4,5,1,3,2,6] => 8
[4,5,1,3,6,2] => 11
[4,5,1,6,2,3] => 11
[4,5,1,6,3,2] => 14
[4,5,2,1,3,6] => 7
[4,5,2,1,6,3] => 13
[4,5,2,3,1,6] => 8
[4,5,2,3,6,1] => 11
[4,5,2,6,1,3] => 11
[4,5,2,6,3,1] => 14
[4,5,3,1,2,6] => 8
[4,5,3,1,6,2] => 14
[4,5,3,2,1,6] => 10
[4,5,3,2,6,1] => 14
[4,5,3,6,1,2] => 11
[4,5,3,6,2,1] => 13
[4,5,6,1,2,3] => 6
[4,5,6,1,3,2] => 9
[4,5,6,2,1,3] => 8
[4,5,6,2,3,1] => 9
[4,5,6,3,1,2] => 9
[4,5,6,3,2,1] => 11
[4,6,1,2,3,5] => 6
[4,6,1,2,5,3] => 11
[4,6,1,3,2,5] => 9
[4,6,1,3,5,2] => 11
[4,6,1,5,2,3] => 11
[4,6,1,5,3,2] => 14
[4,6,2,1,3,5] => 8
[4,6,2,1,5,3] => 13
[4,6,2,3,1,5] => 9
[4,6,2,3,5,1] => 11
[4,6,2,5,1,3] => 11
[4,6,2,5,3,1] => 14
[4,6,3,1,2,5] => 9
[4,6,3,1,5,2] => 14
[4,6,3,2,1,5] => 11
[4,6,3,2,5,1] => 14
[4,6,3,5,1,2] => 11
[4,6,3,5,2,1] => 13
[4,6,5,1,2,3] => 11
[4,6,5,1,3,2] => 14
[4,6,5,2,1,3] => 13
[4,6,5,2,3,1] => 14
[4,6,5,3,1,2] => 14
[4,6,5,3,2,1] => 16
[5,1,2,3,4,6] => 5
[5,1,2,3,6,4] => 11
[5,1,2,4,3,6] => 9
[5,1,2,4,6,3] => 11
[5,1,2,6,3,4] => 11
[5,1,2,6,4,3] => 15
[5,1,3,2,4,6] => 8
[5,1,3,2,6,4] => 14
[5,1,3,4,2,6] => 9
[5,1,3,4,6,2] => 11
[5,1,3,6,2,4] => 11
[5,1,3,6,4,2] => 15
[5,1,4,2,3,6] => 9
[5,1,4,2,6,3] => 15
[5,1,4,3,2,6] => 12
[5,1,4,3,6,2] => 15
[5,1,4,6,2,3] => 11
[5,1,4,6,3,2] => 14
[5,1,6,2,3,4] => 11
[5,1,6,2,4,3] => 15
[5,1,6,3,2,4] => 14
[5,1,6,3,4,2] => 15
[5,1,6,4,2,3] => 15
[5,1,6,4,3,2] => 18
[5,2,1,3,4,6] => 7
[5,2,1,3,6,4] => 13
[5,2,1,4,3,6] => 11
[5,2,1,4,6,3] => 13
[5,2,1,6,3,4] => 13
[5,2,1,6,4,3] => 17
[5,2,3,1,4,6] => 8
[5,2,3,1,6,4] => 14
[5,2,3,4,1,6] => 9
[5,2,3,4,6,1] => 11
[5,2,3,6,1,4] => 11
[5,2,3,6,4,1] => 15
[5,2,4,1,3,6] => 9
[5,2,4,1,6,3] => 15
[5,2,4,3,1,6] => 12
[5,2,4,3,6,1] => 15
[5,2,4,6,1,3] => 11
[5,2,4,6,3,1] => 14
[5,2,6,1,3,4] => 11
[5,2,6,1,4,3] => 15
[5,2,6,3,1,4] => 14
[5,2,6,3,4,1] => 15
[5,2,6,4,1,3] => 15
[5,2,6,4,3,1] => 18
[5,3,1,2,4,6] => 8
[5,3,1,2,6,4] => 14
[5,3,1,4,2,6] => 12
[5,3,1,4,6,2] => 14
[5,3,1,6,2,4] => 14
[5,3,1,6,4,2] => 18
[5,3,2,1,4,6] => 10
[5,3,2,1,6,4] => 16
[5,3,2,4,1,6] => 12
[5,3,2,4,6,1] => 14
[5,3,2,6,1,4] => 14
[5,3,2,6,4,1] => 18
[5,3,4,1,2,6] => 9
[5,3,4,1,6,2] => 15
[5,3,4,2,1,6] => 11
[5,3,4,2,6,1] => 15
[5,3,4,6,1,2] => 11
[5,3,4,6,2,1] => 13
[5,3,6,1,2,4] => 11
[5,3,6,1,4,2] => 15
[5,3,6,2,1,4] => 13
[5,3,6,2,4,1] => 15
[5,3,6,4,1,2] => 15
[5,3,6,4,2,1] => 17
[5,4,1,2,3,6] => 9
[5,4,1,2,6,3] => 15
[5,4,1,3,2,6] => 12
[5,4,1,3,6,2] => 15
[5,4,1,6,2,3] => 15
[5,4,1,6,3,2] => 18
[5,4,2,1,3,6] => 11
[5,4,2,1,6,3] => 17
[5,4,2,3,1,6] => 12
[5,4,2,3,6,1] => 15
[5,4,2,6,1,3] => 15
[5,4,2,6,3,1] => 18
[5,4,3,1,2,6] => 12
[5,4,3,1,6,2] => 18
[5,4,3,2,1,6] => 14
[5,4,3,2,6,1] => 18
[5,4,3,6,1,2] => 15
[5,4,3,6,2,1] => 17
[5,4,6,1,2,3] => 11
[5,4,6,1,3,2] => 14
[5,4,6,2,1,3] => 13
[5,4,6,2,3,1] => 14
[5,4,6,3,1,2] => 14
[5,4,6,3,2,1] => 16
[5,6,1,2,3,4] => 6
[5,6,1,2,4,3] => 10
[5,6,1,3,2,4] => 9
[5,6,1,3,4,2] => 10
[5,6,1,4,2,3] => 10
[5,6,1,4,3,2] => 13
[5,6,2,1,3,4] => 8
[5,6,2,1,4,3] => 12
[5,6,2,3,1,4] => 9
[5,6,2,3,4,1] => 10
[5,6,2,4,1,3] => 10
[5,6,2,4,3,1] => 13
[5,6,3,1,2,4] => 9
[5,6,3,1,4,2] => 13
[5,6,3,2,1,4] => 11
[5,6,3,2,4,1] => 13
[5,6,3,4,1,2] => 10
[5,6,3,4,2,1] => 12
[5,6,4,1,2,3] => 10
[5,6,4,1,3,2] => 13
[5,6,4,2,1,3] => 12
[5,6,4,2,3,1] => 13
[5,6,4,3,1,2] => 13
[5,6,4,3,2,1] => 15
[6,1,2,3,4,5] => 6
[6,1,2,3,5,4] => 11
[6,1,2,4,3,5] => 10
[6,1,2,4,5,3] => 11
[6,1,2,5,3,4] => 11
[6,1,2,5,4,3] => 15
[6,1,3,2,4,5] => 9
[6,1,3,2,5,4] => 14
[6,1,3,4,2,5] => 10
[6,1,3,4,5,2] => 11
[6,1,3,5,2,4] => 11
[6,1,3,5,4,2] => 15
[6,1,4,2,3,5] => 10
[6,1,4,2,5,3] => 15
[6,1,4,3,2,5] => 13
[6,1,4,3,5,2] => 15
[6,1,4,5,2,3] => 11
[6,1,4,5,3,2] => 14
[6,1,5,2,3,4] => 11
[6,1,5,2,4,3] => 15
[6,1,5,3,2,4] => 14
[6,1,5,3,4,2] => 15
[6,1,5,4,2,3] => 15
[6,1,5,4,3,2] => 18
[6,2,1,3,4,5] => 8
[6,2,1,3,5,4] => 13
[6,2,1,4,3,5] => 12
[6,2,1,4,5,3] => 13
[6,2,1,5,3,4] => 13
[6,2,1,5,4,3] => 17
[6,2,3,1,4,5] => 9
[6,2,3,1,5,4] => 14
[6,2,3,4,1,5] => 10
[6,2,3,4,5,1] => 11
[6,2,3,5,1,4] => 11
[6,2,3,5,4,1] => 15
[6,2,4,1,3,5] => 10
[6,2,4,1,5,3] => 15
[6,2,4,3,1,5] => 13
[6,2,4,3,5,1] => 15
[6,2,4,5,1,3] => 11
[6,2,4,5,3,1] => 14
[6,2,5,1,3,4] => 11
[6,2,5,1,4,3] => 15
[6,2,5,3,1,4] => 14
[6,2,5,3,4,1] => 15
[6,2,5,4,1,3] => 15
[6,2,5,4,3,1] => 18
[6,3,1,2,4,5] => 9
[6,3,1,2,5,4] => 14
[6,3,1,4,2,5] => 13
[6,3,1,4,5,2] => 14
[6,3,1,5,2,4] => 14
[6,3,1,5,4,2] => 18
[6,3,2,1,4,5] => 11
[6,3,2,1,5,4] => 16
[6,3,2,4,1,5] => 13
[6,3,2,4,5,1] => 14
[6,3,2,5,1,4] => 14
[6,3,2,5,4,1] => 18
[6,3,4,1,2,5] => 10
[6,3,4,1,5,2] => 15
[6,3,4,2,1,5] => 12
[6,3,4,2,5,1] => 15
[6,3,4,5,1,2] => 11
[6,3,4,5,2,1] => 13
[6,3,5,1,2,4] => 11
[6,3,5,1,4,2] => 15
[6,3,5,2,1,4] => 13
[6,3,5,2,4,1] => 15
[6,3,5,4,1,2] => 15
[6,3,5,4,2,1] => 17
[6,4,1,2,3,5] => 10
[6,4,1,2,5,3] => 15
[6,4,1,3,2,5] => 13
[6,4,1,3,5,2] => 15
[6,4,1,5,2,3] => 15
[6,4,1,5,3,2] => 18
[6,4,2,1,3,5] => 12
[6,4,2,1,5,3] => 17
[6,4,2,3,1,5] => 13
[6,4,2,3,5,1] => 15
[6,4,2,5,1,3] => 15
[6,4,2,5,3,1] => 18
[6,4,3,1,2,5] => 13
[6,4,3,1,5,2] => 18
[6,4,3,2,1,5] => 15
[6,4,3,2,5,1] => 18
[6,4,3,5,1,2] => 15
[6,4,3,5,2,1] => 17
[6,4,5,1,2,3] => 11
[6,4,5,1,3,2] => 14
[6,4,5,2,1,3] => 13
[6,4,5,2,3,1] => 14
[6,4,5,3,1,2] => 14
[6,4,5,3,2,1] => 16
[6,5,1,2,3,4] => 11
[6,5,1,2,4,3] => 15
[6,5,1,3,2,4] => 14
[6,5,1,3,4,2] => 15
[6,5,1,4,2,3] => 15
[6,5,1,4,3,2] => 18
[6,5,2,1,3,4] => 13
[6,5,2,1,4,3] => 17
[6,5,2,3,1,4] => 14
[6,5,2,3,4,1] => 15
[6,5,2,4,1,3] => 15
[6,5,2,4,3,1] => 18
[6,5,3,1,2,4] => 14
[6,5,3,1,4,2] => 18
[6,5,3,2,1,4] => 16
[6,5,3,2,4,1] => 18
[6,5,3,4,1,2] => 15
[6,5,3,4,2,1] => 17
[6,5,4,1,2,3] => 15
[6,5,4,1,3,2] => 18
[6,5,4,2,1,3] => 17
[6,5,4,2,3,1] => 18
[6,5,4,3,1,2] => 18
[6,5,4,3,2,1] => 20
click to show generating function       
Description
The sum of the descent tops (or Genocchi descents) of a permutation.
This statistic is given by
$$\pi \mapsto \sum_{i\in\operatorname{Des}(\pi)} \pi_i.$$
References
[1] Babson, E., Steingr'─▒msson, E. Generalized permutation patterns and a classification of the Mahonian statistics MathSciNet:1758852
[2] Nunge, A. An equivalence of multistatistics on permutations arXiv:1601.02928
[3] Clarke, R. J., Steingr'─▒msson, E., Zeng, J. New Euler-Mahonian statistics on permutations and words MathSciNet:1436481
Code
def statistic(pi):
    return sum( pi[i] for i in range(pi.size()-1) if pi[i] > pi[i+1] )
Created
Jun 15, 2013 at 13:31 by Chris Berg
Updated
Apr 06, 2016 at 06:56 by Martin Rubey