Identifier
Identifier
Values
[1] => 0
[1,2] => 1
[2,1] => 0
[1,2,3] => 3
[1,3,2] => 2
[2,1,3] => 1
[2,3,1] => 0
[3,1,2] => 1
[3,2,1] => 0
[1,2,3,4] => 6
[1,2,4,3] => 5
[1,3,2,4] => 4
[1,3,4,2] => 3
[1,4,2,3] => 4
[1,4,3,2] => 3
[2,1,3,4] => 3
[2,1,4,3] => 2
[2,3,1,4] => 1
[2,3,4,1] => 0
[2,4,1,3] => 1
[2,4,3,1] => 0
[3,1,2,4] => 3
[3,1,4,2] => 2
[3,2,1,4] => 1
[3,2,4,1] => 0
[3,4,1,2] => 1
[3,4,2,1] => 0
[4,1,2,3] => 2
[4,1,3,2] => 2
[4,2,1,3] => 1
[4,2,3,1] => 0
[4,3,1,2] => 1
[4,3,2,1] => 0
[1,2,3,4,5] => 10
[1,2,3,5,4] => 9
[1,2,4,3,5] => 8
[1,2,4,5,3] => 7
[1,2,5,3,4] => 8
[1,2,5,4,3] => 7
[1,3,2,4,5] => 7
[1,3,2,5,4] => 6
[1,3,4,2,5] => 5
[1,3,4,5,2] => 4
[1,3,5,2,4] => 5
[1,3,5,4,2] => 4
[1,4,2,3,5] => 7
[1,4,2,5,3] => 6
[1,4,3,2,5] => 5
[1,4,3,5,2] => 4
[1,4,5,2,3] => 5
[1,4,5,3,2] => 4
[1,5,2,3,4] => 6
[1,5,2,4,3] => 6
[1,5,3,2,4] => 5
[1,5,3,4,2] => 4
[1,5,4,2,3] => 5
[1,5,4,3,2] => 4
[2,1,3,4,5] => 6
[2,1,3,5,4] => 5
[2,1,4,3,5] => 4
[2,1,4,5,3] => 3
[2,1,5,3,4] => 4
[2,1,5,4,3] => 3
[2,3,1,4,5] => 3
[2,3,1,5,4] => 2
[2,3,4,1,5] => 1
[2,3,4,5,1] => 0
[2,3,5,1,4] => 1
[2,3,5,4,1] => 0
[2,4,1,3,5] => 3
[2,4,1,5,3] => 2
[2,4,3,1,5] => 1
[2,4,3,5,1] => 0
[2,4,5,1,3] => 1
[2,4,5,3,1] => 0
[2,5,1,3,4] => 2
[2,5,1,4,3] => 2
[2,5,3,1,4] => 1
[2,5,3,4,1] => 0
[2,5,4,1,3] => 1
[2,5,4,3,1] => 0
[3,1,2,4,5] => 6
[3,1,2,5,4] => 5
[3,1,4,2,5] => 4
[3,1,4,5,2] => 3
[3,1,5,2,4] => 4
[3,1,5,4,2] => 3
[3,2,1,4,5] => 3
[3,2,1,5,4] => 2
[3,2,4,1,5] => 1
[3,2,4,5,1] => 0
[3,2,5,1,4] => 1
[3,2,5,4,1] => 0
[3,4,1,2,5] => 3
[3,4,1,5,2] => 2
[3,4,2,1,5] => 1
[3,4,2,5,1] => 0
[3,4,5,1,2] => 1
[3,4,5,2,1] => 0
[3,5,1,2,4] => 2
[3,5,1,4,2] => 2
[3,5,2,1,4] => 1
[3,5,2,4,1] => 0
[3,5,4,1,2] => 1
[3,5,4,2,1] => 0
[4,1,2,3,5] => 4
[4,1,2,5,3] => 3
[4,1,3,2,5] => 4
[4,1,3,5,2] => 3
[4,1,5,2,3] => 3
[4,1,5,3,2] => 3
[4,2,1,3,5] => 3
[4,2,1,5,3] => 2
[4,2,3,1,5] => 1
[4,2,3,5,1] => 0
[4,2,5,1,3] => 1
[4,2,5,3,1] => 0
[4,3,1,2,5] => 3
[4,3,1,5,2] => 2
[4,3,2,1,5] => 1
[4,3,2,5,1] => 0
[4,3,5,1,2] => 1
[4,3,5,2,1] => 0
[4,5,1,2,3] => 2
[4,5,1,3,2] => 2
[4,5,2,1,3] => 1
[4,5,2,3,1] => 0
[4,5,3,1,2] => 1
[4,5,3,2,1] => 0
[5,1,2,3,4] => 4
[5,1,2,4,3] => 3
[5,1,3,2,4] => 4
[5,1,3,4,2] => 3
[5,1,4,2,3] => 3
[5,1,4,3,2] => 3
[5,2,1,3,4] => 2
[5,2,1,4,3] => 2
[5,2,3,1,4] => 1
[5,2,3,4,1] => 0
[5,2,4,1,3] => 1
[5,2,4,3,1] => 0
[5,3,1,2,4] => 2
[5,3,1,4,2] => 2
[5,3,2,1,4] => 1
[5,3,2,4,1] => 0
[5,3,4,1,2] => 1
[5,3,4,2,1] => 0
[5,4,1,2,3] => 2
[5,4,1,3,2] => 2
[5,4,2,1,3] => 1
[5,4,2,3,1] => 0
[5,4,3,1,2] => 1
[5,4,3,2,1] => 0
[1,2,3,4,5,6] => 15
[1,2,3,4,6,5] => 14
[1,2,3,5,4,6] => 13
[1,2,3,5,6,4] => 12
[1,2,3,6,4,5] => 13
[1,2,3,6,5,4] => 12
[1,2,4,3,5,6] => 12
[1,2,4,3,6,5] => 11
[1,2,4,5,3,6] => 10
[1,2,4,5,6,3] => 9
[1,2,4,6,3,5] => 10
[1,2,4,6,5,3] => 9
[1,2,5,3,4,6] => 12
[1,2,5,3,6,4] => 11
[1,2,5,4,3,6] => 10
[1,2,5,4,6,3] => 9
[1,2,5,6,3,4] => 10
[1,2,5,6,4,3] => 9
[1,2,6,3,4,5] => 11
[1,2,6,3,5,4] => 11
[1,2,6,4,3,5] => 10
[1,2,6,4,5,3] => 9
[1,2,6,5,3,4] => 10
[1,2,6,5,4,3] => 9
[1,3,2,4,5,6] => 11
[1,3,2,4,6,5] => 10
[1,3,2,5,4,6] => 9
[1,3,2,5,6,4] => 8
[1,3,2,6,4,5] => 9
[1,3,2,6,5,4] => 8
[1,3,4,2,5,6] => 8
[1,3,4,2,6,5] => 7
[1,3,4,5,2,6] => 6
[1,3,4,5,6,2] => 5
[1,3,4,6,2,5] => 6
[1,3,4,6,5,2] => 5
[1,3,5,2,4,6] => 8
[1,3,5,2,6,4] => 7
[1,3,5,4,2,6] => 6
[1,3,5,4,6,2] => 5
[1,3,5,6,2,4] => 6
[1,3,5,6,4,2] => 5
[1,3,6,2,4,5] => 7
[1,3,6,2,5,4] => 7
[1,3,6,4,2,5] => 6
[1,3,6,4,5,2] => 5
[1,3,6,5,2,4] => 6
[1,3,6,5,4,2] => 5
[1,4,2,3,5,6] => 11
[1,4,2,3,6,5] => 10
[1,4,2,5,3,6] => 9
[1,4,2,5,6,3] => 8
[1,4,2,6,3,5] => 9
[1,4,2,6,5,3] => 8
[1,4,3,2,5,6] => 8
[1,4,3,2,6,5] => 7
[1,4,3,5,2,6] => 6
[1,4,3,5,6,2] => 5
[1,4,3,6,2,5] => 6
[1,4,3,6,5,2] => 5
[1,4,5,2,3,6] => 8
[1,4,5,2,6,3] => 7
[1,4,5,3,2,6] => 6
[1,4,5,3,6,2] => 5
[1,4,5,6,2,3] => 6
[1,4,5,6,3,2] => 5
[1,4,6,2,3,5] => 7
[1,4,6,2,5,3] => 7
[1,4,6,3,2,5] => 6
[1,4,6,3,5,2] => 5
[1,4,6,5,2,3] => 6
[1,4,6,5,3,2] => 5
[1,5,2,3,4,6] => 9
[1,5,2,3,6,4] => 8
[1,5,2,4,3,6] => 9
[1,5,2,4,6,3] => 8
[1,5,2,6,3,4] => 8
[1,5,2,6,4,3] => 8
[1,5,3,2,4,6] => 8
[1,5,3,2,6,4] => 7
[1,5,3,4,2,6] => 6
[1,5,3,4,6,2] => 5
[1,5,3,6,2,4] => 6
[1,5,3,6,4,2] => 5
[1,5,4,2,3,6] => 8
[1,5,4,2,6,3] => 7
[1,5,4,3,2,6] => 6
[1,5,4,3,6,2] => 5
[1,5,4,6,2,3] => 6
[1,5,4,6,3,2] => 5
[1,5,6,2,3,4] => 7
[1,5,6,2,4,3] => 7
[1,5,6,3,2,4] => 6
[1,5,6,3,4,2] => 5
[1,5,6,4,2,3] => 6
[1,5,6,4,3,2] => 5
[1,6,2,3,4,5] => 9
[1,6,2,3,5,4] => 8
[1,6,2,4,3,5] => 9
[1,6,2,4,5,3] => 8
[1,6,2,5,3,4] => 8
[1,6,2,5,4,3] => 8
[1,6,3,2,4,5] => 7
[1,6,3,2,5,4] => 7
[1,6,3,4,2,5] => 6
[1,6,3,4,5,2] => 5
[1,6,3,5,2,4] => 6
[1,6,3,5,4,2] => 5
[1,6,4,2,3,5] => 7
[1,6,4,2,5,3] => 7
[1,6,4,3,2,5] => 6
[1,6,4,3,5,2] => 5
[1,6,4,5,2,3] => 6
[1,6,4,5,3,2] => 5
[1,6,5,2,3,4] => 7
[1,6,5,2,4,3] => 7
[1,6,5,3,2,4] => 6
[1,6,5,3,4,2] => 5
[1,6,5,4,2,3] => 6
[1,6,5,4,3,2] => 5
[2,1,3,4,5,6] => 10
[2,1,3,4,6,5] => 9
[2,1,3,5,4,6] => 8
[2,1,3,5,6,4] => 7
[2,1,3,6,4,5] => 8
[2,1,3,6,5,4] => 7
[2,1,4,3,5,6] => 7
[2,1,4,3,6,5] => 6
[2,1,4,5,3,6] => 5
[2,1,4,5,6,3] => 4
[2,1,4,6,3,5] => 5
[2,1,4,6,5,3] => 4
[2,1,5,3,4,6] => 7
[2,1,5,3,6,4] => 6
[2,1,5,4,3,6] => 5
[2,1,5,4,6,3] => 4
[2,1,5,6,3,4] => 5
[2,1,5,6,4,3] => 4
[2,1,6,3,4,5] => 6
[2,1,6,3,5,4] => 6
[2,1,6,4,3,5] => 5
[2,1,6,4,5,3] => 4
[2,1,6,5,3,4] => 5
[2,1,6,5,4,3] => 4
[2,3,1,4,5,6] => 6
[2,3,1,4,6,5] => 5
[2,3,1,5,4,6] => 4
[2,3,1,5,6,4] => 3
[2,3,1,6,4,5] => 4
[2,3,1,6,5,4] => 3
[2,3,4,1,5,6] => 3
[2,3,4,1,6,5] => 2
[2,3,4,5,1,6] => 1
[2,3,4,5,6,1] => 0
[2,3,4,6,1,5] => 1
[2,3,4,6,5,1] => 0
[2,3,5,1,4,6] => 3
[2,3,5,1,6,4] => 2
[2,3,5,4,1,6] => 1
[2,3,5,4,6,1] => 0
[2,3,5,6,1,4] => 1
[2,3,5,6,4,1] => 0
[2,3,6,1,4,5] => 2
[2,3,6,1,5,4] => 2
[2,3,6,4,1,5] => 1
[2,3,6,4,5,1] => 0
[2,3,6,5,1,4] => 1
[2,3,6,5,4,1] => 0
[2,4,1,3,5,6] => 6
[2,4,1,3,6,5] => 5
[2,4,1,5,3,6] => 4
[2,4,1,5,6,3] => 3
[2,4,1,6,3,5] => 4
[2,4,1,6,5,3] => 3
[2,4,3,1,5,6] => 3
[2,4,3,1,6,5] => 2
[2,4,3,5,1,6] => 1
[2,4,3,5,6,1] => 0
[2,4,3,6,1,5] => 1
[2,4,3,6,5,1] => 0
[2,4,5,1,3,6] => 3
[2,4,5,1,6,3] => 2
[2,4,5,3,1,6] => 1
[2,4,5,3,6,1] => 0
[2,4,5,6,1,3] => 1
[2,4,5,6,3,1] => 0
[2,4,6,1,3,5] => 2
[2,4,6,1,5,3] => 2
[2,4,6,3,1,5] => 1
[2,4,6,3,5,1] => 0
[2,4,6,5,1,3] => 1
[2,4,6,5,3,1] => 0
[2,5,1,3,4,6] => 4
[2,5,1,3,6,4] => 3
[2,5,1,4,3,6] => 4
[2,5,1,4,6,3] => 3
[2,5,1,6,3,4] => 3
[2,5,1,6,4,3] => 3
[2,5,3,1,4,6] => 3
[2,5,3,1,6,4] => 2
[2,5,3,4,1,6] => 1
[2,5,3,4,6,1] => 0
[2,5,3,6,1,4] => 1
[2,5,3,6,4,1] => 0
[2,5,4,1,3,6] => 3
[2,5,4,1,6,3] => 2
[2,5,4,3,1,6] => 1
[2,5,4,3,6,1] => 0
[2,5,4,6,1,3] => 1
[2,5,4,6,3,1] => 0
[2,5,6,1,3,4] => 2
[2,5,6,1,4,3] => 2
[2,5,6,3,1,4] => 1
[2,5,6,3,4,1] => 0
[2,5,6,4,1,3] => 1
[2,5,6,4,3,1] => 0
[2,6,1,3,4,5] => 4
[2,6,1,3,5,4] => 3
[2,6,1,4,3,5] => 4
[2,6,1,4,5,3] => 3
[2,6,1,5,3,4] => 3
[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] => 1
[2,6,3,4,5,1] => 0
[2,6,3,5,1,4] => 1
[2,6,3,5,4,1] => 0
[2,6,4,1,3,5] => 2
[2,6,4,1,5,3] => 2
[2,6,4,3,1,5] => 1
[2,6,4,3,5,1] => 0
[2,6,4,5,1,3] => 1
[2,6,4,5,3,1] => 0
[2,6,5,1,3,4] => 2
[2,6,5,1,4,3] => 2
[2,6,5,3,1,4] => 1
[2,6,5,3,4,1] => 0
[2,6,5,4,1,3] => 1
[2,6,5,4,3,1] => 0
[3,1,2,4,5,6] => 10
[3,1,2,4,6,5] => 9
[3,1,2,5,4,6] => 8
[3,1,2,5,6,4] => 7
[3,1,2,6,4,5] => 8
[3,1,2,6,5,4] => 7
[3,1,4,2,5,6] => 7
[3,1,4,2,6,5] => 6
[3,1,4,5,2,6] => 5
[3,1,4,5,6,2] => 4
[3,1,4,6,2,5] => 5
[3,1,4,6,5,2] => 4
[3,1,5,2,4,6] => 7
[3,1,5,2,6,4] => 6
[3,1,5,4,2,6] => 5
[3,1,5,4,6,2] => 4
[3,1,5,6,2,4] => 5
[3,1,5,6,4,2] => 4
[3,1,6,2,4,5] => 6
[3,1,6,2,5,4] => 6
[3,1,6,4,2,5] => 5
[3,1,6,4,5,2] => 4
[3,1,6,5,2,4] => 5
[3,1,6,5,4,2] => 4
[3,2,1,4,5,6] => 6
[3,2,1,4,6,5] => 5
[3,2,1,5,4,6] => 4
[3,2,1,5,6,4] => 3
[3,2,1,6,4,5] => 4
[3,2,1,6,5,4] => 3
[3,2,4,1,5,6] => 3
[3,2,4,1,6,5] => 2
[3,2,4,5,1,6] => 1
[3,2,4,5,6,1] => 0
[3,2,4,6,1,5] => 1
[3,2,4,6,5,1] => 0
[3,2,5,1,4,6] => 3
[3,2,5,1,6,4] => 2
[3,2,5,4,1,6] => 1
[3,2,5,4,6,1] => 0
[3,2,5,6,1,4] => 1
[3,2,5,6,4,1] => 0
[3,2,6,1,4,5] => 2
[3,2,6,1,5,4] => 2
[3,2,6,4,1,5] => 1
[3,2,6,4,5,1] => 0
[3,2,6,5,1,4] => 1
[3,2,6,5,4,1] => 0
[3,4,1,2,5,6] => 6
[3,4,1,2,6,5] => 5
[3,4,1,5,2,6] => 4
[3,4,1,5,6,2] => 3
[3,4,1,6,2,5] => 4
[3,4,1,6,5,2] => 3
[3,4,2,1,5,6] => 3
[3,4,2,1,6,5] => 2
[3,4,2,5,1,6] => 1
[3,4,2,5,6,1] => 0
[3,4,2,6,1,5] => 1
[3,4,2,6,5,1] => 0
[3,4,5,1,2,6] => 3
[3,4,5,1,6,2] => 2
[3,4,5,2,1,6] => 1
[3,4,5,2,6,1] => 0
[3,4,5,6,1,2] => 1
[3,4,5,6,2,1] => 0
[3,4,6,1,2,5] => 2
[3,4,6,1,5,2] => 2
[3,4,6,2,1,5] => 1
[3,4,6,2,5,1] => 0
[3,4,6,5,1,2] => 1
[3,4,6,5,2,1] => 0
[3,5,1,2,4,6] => 4
[3,5,1,2,6,4] => 3
[3,5,1,4,2,6] => 4
[3,5,1,4,6,2] => 3
[3,5,1,6,2,4] => 3
[3,5,1,6,4,2] => 3
[3,5,2,1,4,6] => 3
[3,5,2,1,6,4] => 2
[3,5,2,4,1,6] => 1
[3,5,2,4,6,1] => 0
[3,5,2,6,1,4] => 1
[3,5,2,6,4,1] => 0
[3,5,4,1,2,6] => 3
[3,5,4,1,6,2] => 2
[3,5,4,2,1,6] => 1
[3,5,4,2,6,1] => 0
[3,5,4,6,1,2] => 1
[3,5,4,6,2,1] => 0
[3,5,6,1,2,4] => 2
[3,5,6,1,4,2] => 2
[3,5,6,2,1,4] => 1
[3,5,6,2,4,1] => 0
[3,5,6,4,1,2] => 1
[3,5,6,4,2,1] => 0
[3,6,1,2,4,5] => 4
[3,6,1,2,5,4] => 3
[3,6,1,4,2,5] => 4
[3,6,1,4,5,2] => 3
[3,6,1,5,2,4] => 3
[3,6,1,5,4,2] => 3
[3,6,2,1,4,5] => 2
[3,6,2,1,5,4] => 2
[3,6,2,4,1,5] => 1
[3,6,2,4,5,1] => 0
[3,6,2,5,1,4] => 1
[3,6,2,5,4,1] => 0
[3,6,4,1,2,5] => 2
[3,6,4,1,5,2] => 2
[3,6,4,2,1,5] => 1
[3,6,4,2,5,1] => 0
[3,6,4,5,1,2] => 1
[3,6,4,5,2,1] => 0
[3,6,5,1,2,4] => 2
[3,6,5,1,4,2] => 2
[3,6,5,2,1,4] => 1
[3,6,5,2,4,1] => 0
[3,6,5,4,1,2] => 1
[3,6,5,4,2,1] => 0
[4,1,2,3,5,6] => 7
[4,1,2,3,6,5] => 6
[4,1,2,5,3,6] => 5
[4,1,2,5,6,3] => 4
[4,1,2,6,3,5] => 5
[4,1,2,6,5,3] => 4
[4,1,3,2,5,6] => 7
[4,1,3,2,6,5] => 6
[4,1,3,5,2,6] => 5
[4,1,3,5,6,2] => 4
[4,1,3,6,2,5] => 5
[4,1,3,6,5,2] => 4
[4,1,5,2,3,6] => 5
[4,1,5,2,6,3] => 4
[4,1,5,3,2,6] => 5
[4,1,5,3,6,2] => 4
[4,1,5,6,2,3] => 4
[4,1,5,6,3,2] => 4
[4,1,6,2,3,5] => 5
[4,1,6,2,5,3] => 4
[4,1,6,3,2,5] => 5
[4,1,6,3,5,2] => 4
[4,1,6,5,2,3] => 4
[4,1,6,5,3,2] => 4
[4,2,1,3,5,6] => 6
[4,2,1,3,6,5] => 5
[4,2,1,5,3,6] => 4
[4,2,1,5,6,3] => 3
[4,2,1,6,3,5] => 4
[4,2,1,6,5,3] => 3
[4,2,3,1,5,6] => 3
[4,2,3,1,6,5] => 2
[4,2,3,5,1,6] => 1
[4,2,3,5,6,1] => 0
[4,2,3,6,1,5] => 1
[4,2,3,6,5,1] => 0
[4,2,5,1,3,6] => 3
[4,2,5,1,6,3] => 2
[4,2,5,3,1,6] => 1
[4,2,5,3,6,1] => 0
[4,2,5,6,1,3] => 1
[4,2,5,6,3,1] => 0
[4,2,6,1,3,5] => 2
[4,2,6,1,5,3] => 2
[4,2,6,3,1,5] => 1
[4,2,6,3,5,1] => 0
[4,2,6,5,1,3] => 1
[4,2,6,5,3,1] => 0
[4,3,1,2,5,6] => 6
[4,3,1,2,6,5] => 5
[4,3,1,5,2,6] => 4
[4,3,1,5,6,2] => 3
[4,3,1,6,2,5] => 4
[4,3,1,6,5,2] => 3
[4,3,2,1,5,6] => 3
[4,3,2,1,6,5] => 2
[4,3,2,5,1,6] => 1
[4,3,2,5,6,1] => 0
[4,3,2,6,1,5] => 1
[4,3,2,6,5,1] => 0
[4,3,5,1,2,6] => 3
[4,3,5,1,6,2] => 2
[4,3,5,2,1,6] => 1
[4,3,5,2,6,1] => 0
[4,3,5,6,1,2] => 1
[4,3,5,6,2,1] => 0
[4,3,6,1,2,5] => 2
[4,3,6,1,5,2] => 2
[4,3,6,2,1,5] => 1
[4,3,6,2,5,1] => 0
[4,3,6,5,1,2] => 1
[4,3,6,5,2,1] => 0
[4,5,1,2,3,6] => 4
[4,5,1,2,6,3] => 3
[4,5,1,3,2,6] => 4
[4,5,1,3,6,2] => 3
[4,5,1,6,2,3] => 3
[4,5,1,6,3,2] => 3
[4,5,2,1,3,6] => 3
[4,5,2,1,6,3] => 2
[4,5,2,3,1,6] => 1
[4,5,2,3,6,1] => 0
[4,5,2,6,1,3] => 1
[4,5,2,6,3,1] => 0
[4,5,3,1,2,6] => 3
[4,5,3,1,6,2] => 2
[4,5,3,2,1,6] => 1
[4,5,3,2,6,1] => 0
[4,5,3,6,1,2] => 1
[4,5,3,6,2,1] => 0
[4,5,6,1,2,3] => 2
[4,5,6,1,3,2] => 2
[4,5,6,2,1,3] => 1
[4,5,6,2,3,1] => 0
[4,5,6,3,1,2] => 1
[4,5,6,3,2,1] => 0
[4,6,1,2,3,5] => 4
[4,6,1,2,5,3] => 3
[4,6,1,3,2,5] => 4
[4,6,1,3,5,2] => 3
[4,6,1,5,2,3] => 3
[4,6,1,5,3,2] => 3
[4,6,2,1,3,5] => 2
[4,6,2,1,5,3] => 2
[4,6,2,3,1,5] => 1
[4,6,2,3,5,1] => 0
[4,6,2,5,1,3] => 1
[4,6,2,5,3,1] => 0
[4,6,3,1,2,5] => 2
[4,6,3,1,5,2] => 2
[4,6,3,2,1,5] => 1
[4,6,3,2,5,1] => 0
[4,6,3,5,1,2] => 1
[4,6,3,5,2,1] => 0
[4,6,5,1,2,3] => 2
[4,6,5,1,3,2] => 2
[4,6,5,2,1,3] => 1
[4,6,5,2,3,1] => 0
[4,6,5,3,1,2] => 1
[4,6,5,3,2,1] => 0
[5,1,2,3,4,6] => 7
[5,1,2,3,6,4] => 6
[5,1,2,4,3,6] => 5
[5,1,2,4,6,3] => 4
[5,1,2,6,3,4] => 5
[5,1,2,6,4,3] => 4
[5,1,3,2,4,6] => 7
[5,1,3,2,6,4] => 6
[5,1,3,4,2,6] => 5
[5,1,3,4,6,2] => 4
[5,1,3,6,2,4] => 5
[5,1,3,6,4,2] => 4
[5,1,4,2,3,6] => 5
[5,1,4,2,6,3] => 4
[5,1,4,3,2,6] => 5
[5,1,4,3,6,2] => 4
[5,1,4,6,2,3] => 4
[5,1,4,6,3,2] => 4
[5,1,6,2,3,4] => 5
[5,1,6,2,4,3] => 4
[5,1,6,3,2,4] => 5
[5,1,6,3,4,2] => 4
[5,1,6,4,2,3] => 4
[5,1,6,4,3,2] => 4
[5,2,1,3,4,6] => 4
[5,2,1,3,6,4] => 3
[5,2,1,4,3,6] => 4
[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] => 2
[5,2,3,4,1,6] => 1
[5,2,3,4,6,1] => 0
[5,2,3,6,1,4] => 1
[5,2,3,6,4,1] => 0
[5,2,4,1,3,6] => 3
[5,2,4,1,6,3] => 2
[5,2,4,3,1,6] => 1
[5,2,4,3,6,1] => 0
[5,2,4,6,1,3] => 1
[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] => 1
[5,2,6,3,4,1] => 0
[5,2,6,4,1,3] => 1
[5,2,6,4,3,1] => 0
[5,3,1,2,4,6] => 4
[5,3,1,2,6,4] => 3
[5,3,1,4,2,6] => 4
[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] => 3
[5,3,2,1,6,4] => 2
[5,3,2,4,1,6] => 1
[5,3,2,4,6,1] => 0
[5,3,2,6,1,4] => 1
[5,3,2,6,4,1] => 0
[5,3,4,1,2,6] => 3
[5,3,4,1,6,2] => 2
[5,3,4,2,1,6] => 1
[5,3,4,2,6,1] => 0
[5,3,4,6,1,2] => 1
[5,3,4,6,2,1] => 0
[5,3,6,1,2,4] => 2
[5,3,6,1,4,2] => 2
[5,3,6,2,1,4] => 1
[5,3,6,2,4,1] => 0
[5,3,6,4,1,2] => 1
[5,3,6,4,2,1] => 0
[5,4,1,2,3,6] => 4
[5,4,1,2,6,3] => 3
[5,4,1,3,2,6] => 4
[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] => 3
[5,4,2,1,6,3] => 2
[5,4,2,3,1,6] => 1
[5,4,2,3,6,1] => 0
[5,4,2,6,1,3] => 1
[5,4,2,6,3,1] => 0
[5,4,3,1,2,6] => 3
[5,4,3,1,6,2] => 2
[5,4,3,2,1,6] => 1
[5,4,3,2,6,1] => 0
[5,4,3,6,1,2] => 1
[5,4,3,6,2,1] => 0
[5,4,6,1,2,3] => 2
[5,4,6,1,3,2] => 2
[5,4,6,2,1,3] => 1
[5,4,6,2,3,1] => 0
[5,4,6,3,1,2] => 1
[5,4,6,3,2,1] => 0
[5,6,1,2,3,4] => 3
[5,6,1,2,4,3] => 3
[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] => 3
[5,6,2,1,3,4] => 2
[5,6,2,1,4,3] => 2
[5,6,2,3,1,4] => 1
[5,6,2,3,4,1] => 0
[5,6,2,4,1,3] => 1
[5,6,2,4,3,1] => 0
[5,6,3,1,2,4] => 2
[5,6,3,1,4,2] => 2
[5,6,3,2,1,4] => 1
[5,6,3,2,4,1] => 0
[5,6,3,4,1,2] => 1
[5,6,3,4,2,1] => 0
[5,6,4,1,2,3] => 2
[5,6,4,1,3,2] => 2
[5,6,4,2,1,3] => 1
[5,6,4,2,3,1] => 0
[5,6,4,3,1,2] => 1
[5,6,4,3,2,1] => 0
[6,1,2,3,4,5] => 6
[6,1,2,3,5,4] => 6
[6,1,2,4,3,5] => 5
[6,1,2,4,5,3] => 4
[6,1,2,5,3,4] => 5
[6,1,2,5,4,3] => 4
[6,1,3,2,4,5] => 6
[6,1,3,2,5,4] => 6
[6,1,3,4,2,5] => 5
[6,1,3,4,5,2] => 4
[6,1,3,5,2,4] => 5
[6,1,3,5,4,2] => 4
[6,1,4,2,3,5] => 5
[6,1,4,2,5,3] => 4
[6,1,4,3,2,5] => 5
[6,1,4,3,5,2] => 4
[6,1,4,5,2,3] => 4
[6,1,4,5,3,2] => 4
[6,1,5,2,3,4] => 5
[6,1,5,2,4,3] => 4
[6,1,5,3,2,4] => 5
[6,1,5,3,4,2] => 4
[6,1,5,4,2,3] => 4
[6,1,5,4,3,2] => 4
[6,2,1,3,4,5] => 4
[6,2,1,3,5,4] => 3
[6,2,1,4,3,5] => 4
[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] => 2
[6,2,3,1,5,4] => 2
[6,2,3,4,1,5] => 1
[6,2,3,4,5,1] => 0
[6,2,3,5,1,4] => 1
[6,2,3,5,4,1] => 0
[6,2,4,1,3,5] => 2
[6,2,4,1,5,3] => 2
[6,2,4,3,1,5] => 1
[6,2,4,3,5,1] => 0
[6,2,4,5,1,3] => 1
[6,2,4,5,3,1] => 0
[6,2,5,1,3,4] => 2
[6,2,5,1,4,3] => 2
[6,2,5,3,1,4] => 1
[6,2,5,3,4,1] => 0
[6,2,5,4,1,3] => 1
[6,2,5,4,3,1] => 0
[6,3,1,2,4,5] => 4
[6,3,1,2,5,4] => 3
[6,3,1,4,2,5] => 4
[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] => 2
[6,3,2,1,5,4] => 2
[6,3,2,4,1,5] => 1
[6,3,2,4,5,1] => 0
[6,3,2,5,1,4] => 1
[6,3,2,5,4,1] => 0
[6,3,4,1,2,5] => 2
[6,3,4,1,5,2] => 2
[6,3,4,2,1,5] => 1
[6,3,4,2,5,1] => 0
[6,3,4,5,1,2] => 1
[6,3,4,5,2,1] => 0
[6,3,5,1,2,4] => 2
[6,3,5,1,4,2] => 2
[6,3,5,2,1,4] => 1
[6,3,5,2,4,1] => 0
[6,3,5,4,1,2] => 1
[6,3,5,4,2,1] => 0
[6,4,1,2,3,5] => 4
[6,4,1,2,5,3] => 3
[6,4,1,3,2,5] => 4
[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] => 2
[6,4,2,1,5,3] => 2
[6,4,2,3,1,5] => 1
[6,4,2,3,5,1] => 0
[6,4,2,5,1,3] => 1
[6,4,2,5,3,1] => 0
[6,4,3,1,2,5] => 2
[6,4,3,1,5,2] => 2
[6,4,3,2,1,5] => 1
[6,4,3,2,5,1] => 0
[6,4,3,5,1,2] => 1
[6,4,3,5,2,1] => 0
[6,4,5,1,2,3] => 2
[6,4,5,1,3,2] => 2
[6,4,5,2,1,3] => 1
[6,4,5,2,3,1] => 0
[6,4,5,3,1,2] => 1
[6,4,5,3,2,1] => 0
[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] => 2
[6,5,2,1,4,3] => 2
[6,5,2,3,1,4] => 1
[6,5,2,3,4,1] => 0
[6,5,2,4,1,3] => 1
[6,5,2,4,3,1] => 0
[6,5,3,1,2,4] => 2
[6,5,3,1,4,2] => 2
[6,5,3,2,1,4] => 1
[6,5,3,2,4,1] => 0
[6,5,3,4,1,2] => 1
[6,5,3,4,2,1] => 0
[6,5,4,1,2,3] => 2
[6,5,4,1,3,2] => 2
[6,5,4,2,1,3] => 1
[6,5,4,2,3,1] => 0
[6,5,4,3,1,2] => 1
[6,5,4,3,2,1] => 0
click to show generating function       
Description
The "bounce" of a permutation.
Code
def statistic(w):
    n = len(w)
    v = w.inverse()
    bounces = [v[0]]
    while bounces[-1] < n:
        bounces.append(max(v[:bounces[-1] + 1]))
    return sum([n - i for i in bounces])
Created
Jun 19, 2013 at 15:40 by Sam Clearman
Updated
Mar 28, 2015 at 22:46 by Martin Rubey