Identifier
Identifier
Values
[1] => 0
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 2
[2,1,3] => 1
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 3
[1,2,3,4] => 0
[1,2,4,3] => 3
[1,3,2,4] => 2
[1,3,4,2] => 2
[1,4,2,3] => 2
[1,4,3,2] => 5
[2,1,3,4] => 1
[2,1,4,3] => 4
[2,3,1,4] => 1
[2,3,4,1] => 1
[2,4,1,3] => 1
[2,4,3,1] => 4
[3,1,2,4] => 1
[3,1,4,2] => 3
[3,2,1,4] => 3
[3,2,4,1] => 3
[3,4,1,2] => 1
[3,4,2,1] => 3
[4,1,2,3] => 1
[4,1,3,2] => 3
[4,2,1,3] => 3
[4,2,3,1] => 3
[4,3,1,2] => 4
[4,3,2,1] => 6
[1,2,3,4,5] => 0
[1,2,3,5,4] => 4
[1,2,4,3,5] => 3
[1,2,4,5,3] => 3
[1,2,5,3,4] => 3
[1,2,5,4,3] => 7
[1,3,2,4,5] => 2
[1,3,2,5,4] => 6
[1,3,4,2,5] => 2
[1,3,4,5,2] => 2
[1,3,5,2,4] => 2
[1,3,5,4,2] => 6
[1,4,2,3,5] => 2
[1,4,2,5,3] => 5
[1,4,3,2,5] => 5
[1,4,3,5,2] => 5
[1,4,5,2,3] => 2
[1,4,5,3,2] => 5
[1,5,2,3,4] => 2
[1,5,2,4,3] => 5
[1,5,3,2,4] => 5
[1,5,3,4,2] => 5
[1,5,4,2,3] => 6
[1,5,4,3,2] => 9
[2,1,3,4,5] => 1
[2,1,3,5,4] => 5
[2,1,4,3,5] => 4
[2,1,4,5,3] => 4
[2,1,5,3,4] => 4
[2,1,5,4,3] => 8
[2,3,1,4,5] => 1
[2,3,1,5,4] => 5
[2,3,4,1,5] => 1
[2,3,4,5,1] => 1
[2,3,5,1,4] => 1
[2,3,5,4,1] => 5
[2,4,1,3,5] => 1
[2,4,1,5,3] => 4
[2,4,3,1,5] => 4
[2,4,3,5,1] => 4
[2,4,5,1,3] => 1
[2,4,5,3,1] => 4
[2,5,1,3,4] => 1
[2,5,1,4,3] => 4
[2,5,3,1,4] => 4
[2,5,3,4,1] => 4
[2,5,4,1,3] => 5
[2,5,4,3,1] => 8
[3,1,2,4,5] => 1
[3,1,2,5,4] => 5
[3,1,4,2,5] => 3
[3,1,4,5,2] => 3
[3,1,5,2,4] => 3
[3,1,5,4,2] => 7
[3,2,1,4,5] => 3
[3,2,1,5,4] => 7
[3,2,4,1,5] => 3
[3,2,4,5,1] => 3
[3,2,5,1,4] => 3
[3,2,5,4,1] => 7
[3,4,1,2,5] => 1
[3,4,1,5,2] => 3
[3,4,2,1,5] => 3
[3,4,2,5,1] => 3
[3,4,5,1,2] => 1
[3,4,5,2,1] => 3
[3,5,1,2,4] => 1
[3,5,1,4,2] => 3
[3,5,2,1,4] => 3
[3,5,2,4,1] => 3
[3,5,4,1,2] => 5
[3,5,4,2,1] => 7
[4,1,2,3,5] => 1
[4,1,2,5,3] => 4
[4,1,3,2,5] => 3
[4,1,3,5,2] => 3
[4,1,5,2,3] => 3
[4,1,5,3,2] => 6
[4,2,1,3,5] => 3
[4,2,1,5,3] => 6
[4,2,3,1,5] => 3
[4,2,3,5,1] => 3
[4,2,5,1,3] => 3
[4,2,5,3,1] => 6
[4,3,1,2,5] => 4
[4,3,1,5,2] => 6
[4,3,2,1,5] => 6
[4,3,2,5,1] => 6
[4,3,5,1,2] => 4
[4,3,5,2,1] => 6
[4,5,1,2,3] => 1
[4,5,1,3,2] => 3
[4,5,2,1,3] => 3
[4,5,2,3,1] => 3
[4,5,3,1,2] => 4
[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] => 3
[5,1,4,3,2] => 6
[5,2,1,3,4] => 3
[5,2,1,4,3] => 6
[5,2,3,1,4] => 3
[5,2,3,4,1] => 3
[5,2,4,1,3] => 3
[5,2,4,3,1] => 6
[5,3,1,2,4] => 4
[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] => 6
[5,4,1,2,3] => 5
[5,4,1,3,2] => 7
[5,4,2,1,3] => 7
[5,4,2,3,1] => 7
[5,4,3,1,2] => 8
[5,4,3,2,1] => 10
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 5
[1,2,3,5,4,6] => 4
[1,2,3,5,6,4] => 4
[1,2,3,6,4,5] => 4
[1,2,3,6,5,4] => 9
[1,2,4,3,5,6] => 3
[1,2,4,3,6,5] => 8
[1,2,4,5,3,6] => 3
[1,2,4,5,6,3] => 3
[1,2,4,6,3,5] => 3
[1,2,4,6,5,3] => 8
[1,2,5,3,4,6] => 3
[1,2,5,3,6,4] => 7
[1,2,5,4,3,6] => 7
[1,2,5,4,6,3] => 7
[1,2,5,6,3,4] => 3
[1,2,5,6,4,3] => 7
[1,2,6,3,4,5] => 3
[1,2,6,3,5,4] => 7
[1,2,6,4,3,5] => 7
[1,2,6,4,5,3] => 7
[1,2,6,5,3,4] => 8
[1,2,6,5,4,3] => 12
[1,3,2,4,5,6] => 2
[1,3,2,4,6,5] => 7
[1,3,2,5,4,6] => 6
[1,3,2,5,6,4] => 6
[1,3,2,6,4,5] => 6
[1,3,2,6,5,4] => 11
[1,3,4,2,5,6] => 2
[1,3,4,2,6,5] => 7
[1,3,4,5,2,6] => 2
[1,3,4,5,6,2] => 2
[1,3,4,6,2,5] => 2
[1,3,4,6,5,2] => 7
[1,3,5,2,4,6] => 2
[1,3,5,2,6,4] => 6
[1,3,5,4,2,6] => 6
[1,3,5,4,6,2] => 6
[1,3,5,6,2,4] => 2
[1,3,5,6,4,2] => 6
[1,3,6,2,4,5] => 2
[1,3,6,2,5,4] => 6
[1,3,6,4,2,5] => 6
[1,3,6,4,5,2] => 6
[1,3,6,5,2,4] => 7
[1,3,6,5,4,2] => 11
[1,4,2,3,5,6] => 2
[1,4,2,3,6,5] => 7
[1,4,2,5,3,6] => 5
[1,4,2,5,6,3] => 5
[1,4,2,6,3,5] => 5
[1,4,2,6,5,3] => 10
[1,4,3,2,5,6] => 5
[1,4,3,2,6,5] => 10
[1,4,3,5,2,6] => 5
[1,4,3,5,6,2] => 5
[1,4,3,6,2,5] => 5
[1,4,3,6,5,2] => 10
[1,4,5,2,3,6] => 2
[1,4,5,2,6,3] => 5
[1,4,5,3,2,6] => 5
[1,4,5,3,6,2] => 5
[1,4,5,6,2,3] => 2
[1,4,5,6,3,2] => 5
[1,4,6,2,3,5] => 2
[1,4,6,2,5,3] => 5
[1,4,6,3,2,5] => 5
[1,4,6,3,5,2] => 5
[1,4,6,5,2,3] => 7
[1,4,6,5,3,2] => 10
[1,5,2,3,4,6] => 2
[1,5,2,3,6,4] => 6
[1,5,2,4,3,6] => 5
[1,5,2,4,6,3] => 5
[1,5,2,6,3,4] => 5
[1,5,2,6,4,3] => 9
[1,5,3,2,4,6] => 5
[1,5,3,2,6,4] => 9
[1,5,3,4,2,6] => 5
[1,5,3,4,6,2] => 5
[1,5,3,6,2,4] => 5
[1,5,3,6,4,2] => 9
[1,5,4,2,3,6] => 6
[1,5,4,2,6,3] => 9
[1,5,4,3,2,6] => 9
[1,5,4,3,6,2] => 9
[1,5,4,6,2,3] => 6
[1,5,4,6,3,2] => 9
[1,5,6,2,3,4] => 2
[1,5,6,2,4,3] => 5
[1,5,6,3,2,4] => 5
[1,5,6,3,4,2] => 5
[1,5,6,4,2,3] => 6
[1,5,6,4,3,2] => 9
[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] => 5
[1,6,2,5,4,3] => 9
[1,6,3,2,4,5] => 5
[1,6,3,2,5,4] => 9
[1,6,3,4,2,5] => 5
[1,6,3,4,5,2] => 5
[1,6,3,5,2,4] => 5
[1,6,3,5,4,2] => 9
[1,6,4,2,3,5] => 6
[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] => 9
[1,6,5,2,3,4] => 7
[1,6,5,2,4,3] => 10
[1,6,5,3,2,4] => 10
[1,6,5,3,4,2] => 10
[1,6,5,4,2,3] => 11
[1,6,5,4,3,2] => 14
[2,1,3,4,5,6] => 1
[2,1,3,4,6,5] => 6
[2,1,3,5,4,6] => 5
[2,1,3,5,6,4] => 5
[2,1,3,6,4,5] => 5
[2,1,3,6,5,4] => 10
[2,1,4,3,5,6] => 4
[2,1,4,3,6,5] => 9
[2,1,4,5,3,6] => 4
[2,1,4,5,6,3] => 4
[2,1,4,6,3,5] => 4
[2,1,4,6,5,3] => 9
[2,1,5,3,4,6] => 4
[2,1,5,3,6,4] => 8
[2,1,5,4,3,6] => 8
[2,1,5,4,6,3] => 8
[2,1,5,6,3,4] => 4
[2,1,5,6,4,3] => 8
[2,1,6,3,4,5] => 4
[2,1,6,3,5,4] => 8
[2,1,6,4,3,5] => 8
[2,1,6,4,5,3] => 8
[2,1,6,5,3,4] => 9
[2,1,6,5,4,3] => 13
[2,3,1,4,5,6] => 1
[2,3,1,4,6,5] => 6
[2,3,1,5,4,6] => 5
[2,3,1,5,6,4] => 5
[2,3,1,6,4,5] => 5
[2,3,1,6,5,4] => 10
[2,3,4,1,5,6] => 1
[2,3,4,1,6,5] => 6
[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] => 6
[2,3,5,1,4,6] => 1
[2,3,5,1,6,4] => 5
[2,3,5,4,1,6] => 5
[2,3,5,4,6,1] => 5
[2,3,5,6,1,4] => 1
[2,3,5,6,4,1] => 5
[2,3,6,1,4,5] => 1
[2,3,6,1,5,4] => 5
[2,3,6,4,1,5] => 5
[2,3,6,4,5,1] => 5
[2,3,6,5,1,4] => 6
[2,3,6,5,4,1] => 10
[2,4,1,3,5,6] => 1
[2,4,1,3,6,5] => 6
[2,4,1,5,3,6] => 4
[2,4,1,5,6,3] => 4
[2,4,1,6,3,5] => 4
[2,4,1,6,5,3] => 9
[2,4,3,1,5,6] => 4
[2,4,3,1,6,5] => 9
[2,4,3,5,1,6] => 4
[2,4,3,5,6,1] => 4
[2,4,3,6,1,5] => 4
[2,4,3,6,5,1] => 9
[2,4,5,1,3,6] => 1
[2,4,5,1,6,3] => 4
[2,4,5,3,1,6] => 4
[2,4,5,3,6,1] => 4
[2,4,5,6,1,3] => 1
[2,4,5,6,3,1] => 4
[2,4,6,1,3,5] => 1
[2,4,6,1,5,3] => 4
[2,4,6,3,1,5] => 4
[2,4,6,3,5,1] => 4
[2,4,6,5,1,3] => 6
[2,4,6,5,3,1] => 9
[2,5,1,3,4,6] => 1
[2,5,1,3,6,4] => 5
[2,5,1,4,3,6] => 4
[2,5,1,4,6,3] => 4
[2,5,1,6,3,4] => 4
[2,5,1,6,4,3] => 8
[2,5,3,1,4,6] => 4
[2,5,3,1,6,4] => 8
[2,5,3,4,1,6] => 4
[2,5,3,4,6,1] => 4
[2,5,3,6,1,4] => 4
[2,5,3,6,4,1] => 8
[2,5,4,1,3,6] => 5
[2,5,4,1,6,3] => 8
[2,5,4,3,1,6] => 8
[2,5,4,3,6,1] => 8
[2,5,4,6,1,3] => 5
[2,5,4,6,3,1] => 8
[2,5,6,1,3,4] => 1
[2,5,6,1,4,3] => 4
[2,5,6,3,1,4] => 4
[2,5,6,3,4,1] => 4
[2,5,6,4,1,3] => 5
[2,5,6,4,3,1] => 8
[2,6,1,3,4,5] => 1
[2,6,1,3,5,4] => 5
[2,6,1,4,3,5] => 4
[2,6,1,4,5,3] => 4
[2,6,1,5,3,4] => 4
[2,6,1,5,4,3] => 8
[2,6,3,1,4,5] => 4
[2,6,3,1,5,4] => 8
[2,6,3,4,1,5] => 4
[2,6,3,4,5,1] => 4
[2,6,3,5,1,4] => 4
[2,6,3,5,4,1] => 8
[2,6,4,1,3,5] => 5
[2,6,4,1,5,3] => 8
[2,6,4,3,1,5] => 8
[2,6,4,3,5,1] => 8
[2,6,4,5,1,3] => 5
[2,6,4,5,3,1] => 8
[2,6,5,1,3,4] => 6
[2,6,5,1,4,3] => 9
[2,6,5,3,1,4] => 9
[2,6,5,3,4,1] => 9
[2,6,5,4,1,3] => 10
[2,6,5,4,3,1] => 13
[3,1,2,4,5,6] => 1
[3,1,2,4,6,5] => 6
[3,1,2,5,4,6] => 5
[3,1,2,5,6,4] => 5
[3,1,2,6,4,5] => 5
[3,1,2,6,5,4] => 10
[3,1,4,2,5,6] => 3
[3,1,4,2,6,5] => 8
[3,1,4,5,2,6] => 3
[3,1,4,5,6,2] => 3
[3,1,4,6,2,5] => 3
[3,1,4,6,5,2] => 8
[3,1,5,2,4,6] => 3
[3,1,5,2,6,4] => 7
[3,1,5,4,2,6] => 7
[3,1,5,4,6,2] => 7
[3,1,5,6,2,4] => 3
[3,1,5,6,4,2] => 7
[3,1,6,2,4,5] => 3
[3,1,6,2,5,4] => 7
[3,1,6,4,2,5] => 7
[3,1,6,4,5,2] => 7
[3,1,6,5,2,4] => 8
[3,1,6,5,4,2] => 12
[3,2,1,4,5,6] => 3
[3,2,1,4,6,5] => 8
[3,2,1,5,4,6] => 7
[3,2,1,5,6,4] => 7
[3,2,1,6,4,5] => 7
[3,2,1,6,5,4] => 12
[3,2,4,1,5,6] => 3
[3,2,4,1,6,5] => 8
[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] => 8
[3,2,5,1,4,6] => 3
[3,2,5,1,6,4] => 7
[3,2,5,4,1,6] => 7
[3,2,5,4,6,1] => 7
[3,2,5,6,1,4] => 3
[3,2,5,6,4,1] => 7
[3,2,6,1,4,5] => 3
[3,2,6,1,5,4] => 7
[3,2,6,4,1,5] => 7
[3,2,6,4,5,1] => 7
[3,2,6,5,1,4] => 8
[3,2,6,5,4,1] => 12
[3,4,1,2,5,6] => 1
[3,4,1,2,6,5] => 6
[3,4,1,5,2,6] => 3
[3,4,1,5,6,2] => 3
[3,4,1,6,2,5] => 3
[3,4,1,6,5,2] => 8
[3,4,2,1,5,6] => 3
[3,4,2,1,6,5] => 8
[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] => 8
[3,4,5,1,2,6] => 1
[3,4,5,1,6,2] => 3
[3,4,5,2,1,6] => 3
[3,4,5,2,6,1] => 3
[3,4,5,6,1,2] => 1
[3,4,5,6,2,1] => 3
[3,4,6,1,2,5] => 1
[3,4,6,1,5,2] => 3
[3,4,6,2,1,5] => 3
[3,4,6,2,5,1] => 3
[3,4,6,5,1,2] => 6
[3,4,6,5,2,1] => 8
[3,5,1,2,4,6] => 1
[3,5,1,2,6,4] => 5
[3,5,1,4,2,6] => 3
[3,5,1,4,6,2] => 3
[3,5,1,6,2,4] => 3
[3,5,1,6,4,2] => 7
[3,5,2,1,4,6] => 3
[3,5,2,1,6,4] => 7
[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] => 7
[3,5,4,1,2,6] => 5
[3,5,4,1,6,2] => 7
[3,5,4,2,1,6] => 7
[3,5,4,2,6,1] => 7
[3,5,4,6,1,2] => 5
[3,5,4,6,2,1] => 7
[3,5,6,1,2,4] => 1
[3,5,6,1,4,2] => 3
[3,5,6,2,1,4] => 3
[3,5,6,2,4,1] => 3
[3,5,6,4,1,2] => 5
[3,5,6,4,2,1] => 7
[3,6,1,2,4,5] => 1
[3,6,1,2,5,4] => 5
[3,6,1,4,2,5] => 3
[3,6,1,4,5,2] => 3
[3,6,1,5,2,4] => 3
[3,6,1,5,4,2] => 7
[3,6,2,1,4,5] => 3
[3,6,2,1,5,4] => 7
[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] => 7
[3,6,4,1,2,5] => 5
[3,6,4,1,5,2] => 7
[3,6,4,2,1,5] => 7
[3,6,4,2,5,1] => 7
[3,6,4,5,1,2] => 5
[3,6,4,5,2,1] => 7
[3,6,5,1,2,4] => 6
[3,6,5,1,4,2] => 8
[3,6,5,2,1,4] => 8
[3,6,5,2,4,1] => 8
[3,6,5,4,1,2] => 10
[3,6,5,4,2,1] => 12
[4,1,2,3,5,6] => 1
[4,1,2,3,6,5] => 6
[4,1,2,5,3,6] => 4
[4,1,2,5,6,3] => 4
[4,1,2,6,3,5] => 4
[4,1,2,6,5,3] => 9
[4,1,3,2,5,6] => 3
[4,1,3,2,6,5] => 8
[4,1,3,5,2,6] => 3
[4,1,3,5,6,2] => 3
[4,1,3,6,2,5] => 3
[4,1,3,6,5,2] => 8
[4,1,5,2,3,6] => 3
[4,1,5,2,6,3] => 6
[4,1,5,3,2,6] => 6
[4,1,5,3,6,2] => 6
[4,1,5,6,2,3] => 3
[4,1,5,6,3,2] => 6
[4,1,6,2,3,5] => 3
[4,1,6,2,5,3] => 6
[4,1,6,3,2,5] => 6
[4,1,6,3,5,2] => 6
[4,1,6,5,2,3] => 8
[4,1,6,5,3,2] => 11
[4,2,1,3,5,6] => 3
[4,2,1,3,6,5] => 8
[4,2,1,5,3,6] => 6
[4,2,1,5,6,3] => 6
[4,2,1,6,3,5] => 6
[4,2,1,6,5,3] => 11
[4,2,3,1,5,6] => 3
[4,2,3,1,6,5] => 8
[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] => 8
[4,2,5,1,3,6] => 3
[4,2,5,1,6,3] => 6
[4,2,5,3,1,6] => 6
[4,2,5,3,6,1] => 6
[4,2,5,6,1,3] => 3
[4,2,5,6,3,1] => 6
[4,2,6,1,3,5] => 3
[4,2,6,1,5,3] => 6
[4,2,6,3,1,5] => 6
[4,2,6,3,5,1] => 6
[4,2,6,5,1,3] => 8
[4,2,6,5,3,1] => 11
[4,3,1,2,5,6] => 4
[4,3,1,2,6,5] => 9
[4,3,1,5,2,6] => 6
[4,3,1,5,6,2] => 6
[4,3,1,6,2,5] => 6
[4,3,1,6,5,2] => 11
[4,3,2,1,5,6] => 6
[4,3,2,1,6,5] => 11
[4,3,2,5,1,6] => 6
[4,3,2,5,6,1] => 6
[4,3,2,6,1,5] => 6
[4,3,2,6,5,1] => 11
[4,3,5,1,2,6] => 4
[4,3,5,1,6,2] => 6
[4,3,5,2,1,6] => 6
[4,3,5,2,6,1] => 6
[4,3,5,6,1,2] => 4
[4,3,5,6,2,1] => 6
[4,3,6,1,2,5] => 4
[4,3,6,1,5,2] => 6
[4,3,6,2,1,5] => 6
[4,3,6,2,5,1] => 6
[4,3,6,5,1,2] => 9
[4,3,6,5,2,1] => 11
[4,5,1,2,3,6] => 1
[4,5,1,2,6,3] => 4
[4,5,1,3,2,6] => 3
[4,5,1,3,6,2] => 3
[4,5,1,6,2,3] => 3
[4,5,1,6,3,2] => 6
[4,5,2,1,3,6] => 3
[4,5,2,1,6,3] => 6
[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] => 6
[4,5,3,1,2,6] => 4
[4,5,3,1,6,2] => 6
[4,5,3,2,1,6] => 6
[4,5,3,2,6,1] => 6
[4,5,3,6,1,2] => 4
[4,5,3,6,2,1] => 6
[4,5,6,1,2,3] => 1
[4,5,6,1,3,2] => 3
[4,5,6,2,1,3] => 3
[4,5,6,2,3,1] => 3
[4,5,6,3,1,2] => 4
[4,5,6,3,2,1] => 6
[4,6,1,2,3,5] => 1
[4,6,1,2,5,3] => 4
[4,6,1,3,2,5] => 3
[4,6,1,3,5,2] => 3
[4,6,1,5,2,3] => 3
[4,6,1,5,3,2] => 6
[4,6,2,1,3,5] => 3
[4,6,2,1,5,3] => 6
[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] => 6
[4,6,3,1,2,5] => 4
[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] => 4
[4,6,3,5,2,1] => 6
[4,6,5,1,2,3] => 6
[4,6,5,1,3,2] => 8
[4,6,5,2,1,3] => 8
[4,6,5,2,3,1] => 8
[4,6,5,3,1,2] => 9
[4,6,5,3,2,1] => 11
[5,1,2,3,4,6] => 1
[5,1,2,3,6,4] => 5
[5,1,2,4,3,6] => 4
[5,1,2,4,6,3] => 4
[5,1,2,6,3,4] => 4
[5,1,2,6,4,3] => 8
[5,1,3,2,4,6] => 3
[5,1,3,2,6,4] => 7
[5,1,3,4,2,6] => 3
[5,1,3,4,6,2] => 3
[5,1,3,6,2,4] => 3
[5,1,3,6,4,2] => 7
[5,1,4,2,3,6] => 3
[5,1,4,2,6,3] => 6
[5,1,4,3,2,6] => 6
[5,1,4,3,6,2] => 6
[5,1,4,6,2,3] => 3
[5,1,4,6,3,2] => 6
[5,1,6,2,3,4] => 3
[5,1,6,2,4,3] => 6
[5,1,6,3,2,4] => 6
[5,1,6,3,4,2] => 6
[5,1,6,4,2,3] => 7
[5,1,6,4,3,2] => 10
[5,2,1,3,4,6] => 3
[5,2,1,3,6,4] => 7
[5,2,1,4,3,6] => 6
[5,2,1,4,6,3] => 6
[5,2,1,6,3,4] => 6
[5,2,1,6,4,3] => 10
[5,2,3,1,4,6] => 3
[5,2,3,1,6,4] => 7
[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] => 7
[5,2,4,1,3,6] => 3
[5,2,4,1,6,3] => 6
[5,2,4,3,1,6] => 6
[5,2,4,3,6,1] => 6
[5,2,4,6,1,3] => 3
[5,2,4,6,3,1] => 6
[5,2,6,1,3,4] => 3
[5,2,6,1,4,3] => 6
[5,2,6,3,1,4] => 6
[5,2,6,3,4,1] => 6
[5,2,6,4,1,3] => 7
[5,2,6,4,3,1] => 10
[5,3,1,2,4,6] => 4
[5,3,1,2,6,4] => 8
[5,3,1,4,2,6] => 6
[5,3,1,4,6,2] => 6
[5,3,1,6,2,4] => 6
[5,3,1,6,4,2] => 10
[5,3,2,1,4,6] => 6
[5,3,2,1,6,4] => 10
[5,3,2,4,1,6] => 6
[5,3,2,4,6,1] => 6
[5,3,2,6,1,4] => 6
[5,3,2,6,4,1] => 10
[5,3,4,1,2,6] => 4
[5,3,4,1,6,2] => 6
[5,3,4,2,1,6] => 6
[5,3,4,2,6,1] => 6
[5,3,4,6,1,2] => 4
[5,3,4,6,2,1] => 6
[5,3,6,1,2,4] => 4
[5,3,6,1,4,2] => 6
[5,3,6,2,1,4] => 6
[5,3,6,2,4,1] => 6
[5,3,6,4,1,2] => 8
[5,3,6,4,2,1] => 10
[5,4,1,2,3,6] => 5
[5,4,1,2,6,3] => 8
[5,4,1,3,2,6] => 7
[5,4,1,3,6,2] => 7
[5,4,1,6,2,3] => 7
[5,4,1,6,3,2] => 10
[5,4,2,1,3,6] => 7
[5,4,2,1,6,3] => 10
[5,4,2,3,1,6] => 7
[5,4,2,3,6,1] => 7
[5,4,2,6,1,3] => 7
[5,4,2,6,3,1] => 10
[5,4,3,1,2,6] => 8
[5,4,3,1,6,2] => 10
[5,4,3,2,1,6] => 10
[5,4,3,2,6,1] => 10
[5,4,3,6,1,2] => 8
[5,4,3,6,2,1] => 10
[5,4,6,1,2,3] => 5
[5,4,6,1,3,2] => 7
[5,4,6,2,1,3] => 7
[5,4,6,2,3,1] => 7
[5,4,6,3,1,2] => 8
[5,4,6,3,2,1] => 10
[5,6,1,2,3,4] => 1
[5,6,1,2,4,3] => 4
[5,6,1,3,2,4] => 3
[5,6,1,3,4,2] => 3
[5,6,1,4,2,3] => 3
[5,6,1,4,3,2] => 6
[5,6,2,1,3,4] => 3
[5,6,2,1,4,3] => 6
[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] => 6
[5,6,3,1,2,4] => 4
[5,6,3,1,4,2] => 6
[5,6,3,2,1,4] => 6
[5,6,3,2,4,1] => 6
[5,6,3,4,1,2] => 4
[5,6,3,4,2,1] => 6
[5,6,4,1,2,3] => 5
[5,6,4,1,3,2] => 7
[5,6,4,2,1,3] => 7
[5,6,4,2,3,1] => 7
[5,6,4,3,1,2] => 8
[5,6,4,3,2,1] => 10
[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] => 4
[6,1,2,5,4,3] => 8
[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] => 3
[6,1,3,5,4,2] => 7
[6,1,4,2,3,5] => 3
[6,1,4,2,5,3] => 6
[6,1,4,3,2,5] => 6
[6,1,4,3,5,2] => 6
[6,1,4,5,2,3] => 3
[6,1,4,5,3,2] => 6
[6,1,5,2,3,4] => 3
[6,1,5,2,4,3] => 6
[6,1,5,3,2,4] => 6
[6,1,5,3,4,2] => 6
[6,1,5,4,2,3] => 7
[6,1,5,4,3,2] => 10
[6,2,1,3,4,5] => 3
[6,2,1,3,5,4] => 7
[6,2,1,4,3,5] => 6
[6,2,1,4,5,3] => 6
[6,2,1,5,3,4] => 6
[6,2,1,5,4,3] => 10
[6,2,3,1,4,5] => 3
[6,2,3,1,5,4] => 7
[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] => 7
[6,2,4,1,3,5] => 3
[6,2,4,1,5,3] => 6
[6,2,4,3,1,5] => 6
[6,2,4,3,5,1] => 6
[6,2,4,5,1,3] => 3
[6,2,4,5,3,1] => 6
[6,2,5,1,3,4] => 3
[6,2,5,1,4,3] => 6
[6,2,5,3,1,4] => 6
[6,2,5,3,4,1] => 6
[6,2,5,4,1,3] => 7
[6,2,5,4,3,1] => 10
[6,3,1,2,4,5] => 4
[6,3,1,2,5,4] => 8
[6,3,1,4,2,5] => 6
[6,3,1,4,5,2] => 6
[6,3,1,5,2,4] => 6
[6,3,1,5,4,2] => 10
[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] => 6
[6,3,2,5,4,1] => 10
[6,3,4,1,2,5] => 4
[6,3,4,1,5,2] => 6
[6,3,4,2,1,5] => 6
[6,3,4,2,5,1] => 6
[6,3,4,5,1,2] => 4
[6,3,4,5,2,1] => 6
[6,3,5,1,2,4] => 4
[6,3,5,1,4,2] => 6
[6,3,5,2,1,4] => 6
[6,3,5,2,4,1] => 6
[6,3,5,4,1,2] => 8
[6,3,5,4,2,1] => 10
[6,4,1,2,3,5] => 5
[6,4,1,2,5,3] => 8
[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] => 10
[6,4,2,1,3,5] => 7
[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] => 10
[6,4,3,1,2,5] => 8
[6,4,3,1,5,2] => 10
[6,4,3,2,1,5] => 10
[6,4,3,2,5,1] => 10
[6,4,3,5,1,2] => 8
[6,4,3,5,2,1] => 10
[6,4,5,1,2,3] => 5
[6,4,5,1,3,2] => 7
[6,4,5,2,1,3] => 7
[6,4,5,2,3,1] => 7
[6,4,5,3,1,2] => 8
[6,4,5,3,2,1] => 10
[6,5,1,2,3,4] => 6
[6,5,1,2,4,3] => 9
[6,5,1,3,2,4] => 8
[6,5,1,3,4,2] => 8
[6,5,1,4,2,3] => 8
[6,5,1,4,3,2] => 11
[6,5,2,1,3,4] => 8
[6,5,2,1,4,3] => 11
[6,5,2,3,1,4] => 8
[6,5,2,3,4,1] => 8
[6,5,2,4,1,3] => 8
[6,5,2,4,3,1] => 11
[6,5,3,1,2,4] => 9
[6,5,3,1,4,2] => 11
[6,5,3,2,1,4] => 11
[6,5,3,2,4,1] => 11
[6,5,3,4,1,2] => 9
[6,5,3,4,2,1] => 11
[6,5,4,1,2,3] => 10
[6,5,4,1,3,2] => 12
[6,5,4,2,1,3] => 12
[6,5,4,2,3,1] => 12
[6,5,4,3,1,2] => 13
[6,5,4,3,2,1] => 15
click to show generating function       
Description
The sum of the descent bottoms of a permutation.
This statistic is given by
$$\pi \mapsto \sum_{i\in\operatorname{Des}(\pi)} \pi_{i+1}.$$
For the descent tops, see St000111The sum of the descent tops (or Genocchi descents) of a permutation..
References
[1] Babson, E., Steingr'─▒msson, E. Generalized permutation patterns and a classification of the Mahonian statistics MathSciNet:1758852
Code
def statistic(pi):
    return sum( pi[i+1] for i in range(pi.size()-1) if pi[i] > pi[i+1] )
Created
Jul 19, 2013 at 20:21 by Christian Stump
Updated
Jun 09, 2016 at 16:19 by Martin Rubey