Identifier
- St000472: Permutations ⟶ ℤ
Values
[1,2] => 1
[2,1] => 0
[1,2,3] => 3
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 2
[3,1,2] => 1
[3,2,1] => 0
[1,2,3,4] => 6
[1,2,4,3] => 3
[1,3,2,4] => 3
[1,3,4,2] => 4
[1,4,2,3] => 3
[1,4,3,2] => 1
[2,1,3,4] => 4
[2,1,4,3] => 1
[2,3,1,4] => 3
[2,3,4,1] => 5
[2,4,1,3] => 3
[2,4,3,1] => 2
[3,1,2,4] => 3
[3,1,4,2] => 1
[3,2,1,4] => 1
[3,2,4,1] => 2
[3,4,1,2] => 4
[3,4,2,1] => 3
[4,1,2,3] => 3
[4,1,3,2] => 1
[4,2,1,3] => 1
[4,2,3,1] => 2
[4,3,1,2] => 1
[4,3,2,1] => 0
[1,2,3,4,5] => 10
[1,2,3,5,4] => 6
[1,2,4,3,5] => 6
[1,2,4,5,3] => 7
[1,2,5,3,4] => 6
[1,2,5,4,3] => 3
[1,3,2,4,5] => 7
[1,3,2,5,4] => 3
[1,3,4,2,5] => 6
[1,3,4,5,2] => 8
[1,3,5,2,4] => 6
[1,3,5,4,2] => 4
[1,4,2,3,5] => 6
[1,4,2,5,3] => 3
[1,4,3,2,5] => 3
[1,4,3,5,2] => 4
[1,4,5,2,3] => 7
[1,4,5,3,2] => 5
[1,5,2,3,4] => 6
[1,5,2,4,3] => 3
[1,5,3,2,4] => 3
[1,5,3,4,2] => 4
[1,5,4,2,3] => 3
[1,5,4,3,2] => 1
[2,1,3,4,5] => 8
[2,1,3,5,4] => 4
[2,1,4,3,5] => 4
[2,1,4,5,3] => 5
[2,1,5,3,4] => 4
[2,1,5,4,3] => 1
[2,3,1,4,5] => 7
[2,3,1,5,4] => 3
[2,3,4,1,5] => 6
[2,3,4,5,1] => 9
[2,3,5,1,4] => 6
[2,3,5,4,1] => 5
[2,4,1,3,5] => 6
[2,4,1,5,3] => 3
[2,4,3,1,5] => 3
[2,4,3,5,1] => 5
[2,4,5,1,3] => 7
[2,4,5,3,1] => 6
[2,5,1,3,4] => 6
[2,5,1,4,3] => 3
[2,5,3,1,4] => 3
[2,5,3,4,1] => 5
[2,5,4,1,3] => 3
[2,5,4,3,1] => 2
[3,1,2,4,5] => 7
[3,1,2,5,4] => 3
[3,1,4,2,5] => 3
[3,1,4,5,2] => 5
[3,1,5,2,4] => 3
[3,1,5,4,2] => 1
[3,2,1,4,5] => 5
[3,2,1,5,4] => 1
[3,2,4,1,5] => 3
[3,2,4,5,1] => 6
[3,2,5,1,4] => 3
[3,2,5,4,1] => 2
[3,4,1,2,5] => 6
[3,4,1,5,2] => 4
[3,4,2,1,5] => 4
[3,4,2,5,1] => 5
[3,4,5,1,2] => 8
[3,4,5,2,1] => 7
[3,5,1,2,4] => 6
[3,5,1,4,2] => 4
[3,5,2,1,4] => 4
>>> Load all 1200 entries. <<<[3,5,2,4,1] => 5
[3,5,4,1,2] => 4
[3,5,4,2,1] => 3
[4,1,2,3,5] => 6
[4,1,2,5,3] => 3
[4,1,3,2,5] => 3
[4,1,3,5,2] => 4
[4,1,5,2,3] => 3
[4,1,5,3,2] => 1
[4,2,1,3,5] => 4
[4,2,1,5,3] => 1
[4,2,3,1,5] => 3
[4,2,3,5,1] => 5
[4,2,5,1,3] => 3
[4,2,5,3,1] => 2
[4,3,1,2,5] => 3
[4,3,1,5,2] => 1
[4,3,2,1,5] => 1
[4,3,2,5,1] => 2
[4,3,5,1,2] => 4
[4,3,5,2,1] => 3
[4,5,1,2,3] => 7
[4,5,1,3,2] => 5
[4,5,2,1,3] => 5
[4,5,2,3,1] => 6
[4,5,3,1,2] => 5
[4,5,3,2,1] => 4
[5,1,2,3,4] => 6
[5,1,2,4,3] => 3
[5,1,3,2,4] => 3
[5,1,3,4,2] => 4
[5,1,4,2,3] => 3
[5,1,4,3,2] => 1
[5,2,1,3,4] => 4
[5,2,1,4,3] => 1
[5,2,3,1,4] => 3
[5,2,3,4,1] => 5
[5,2,4,1,3] => 3
[5,2,4,3,1] => 2
[5,3,1,2,4] => 3
[5,3,1,4,2] => 1
[5,3,2,1,4] => 1
[5,3,2,4,1] => 2
[5,3,4,1,2] => 4
[5,3,4,2,1] => 3
[5,4,1,2,3] => 3
[5,4,1,3,2] => 1
[5,4,2,1,3] => 1
[5,4,2,3,1] => 2
[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] => 10
[1,2,3,5,4,6] => 10
[1,2,3,5,6,4] => 11
[1,2,3,6,4,5] => 10
[1,2,3,6,5,4] => 6
[1,2,4,3,5,6] => 11
[1,2,4,3,6,5] => 6
[1,2,4,5,3,6] => 10
[1,2,4,5,6,3] => 12
[1,2,4,6,3,5] => 10
[1,2,4,6,5,3] => 7
[1,2,5,3,4,6] => 10
[1,2,5,3,6,4] => 6
[1,2,5,4,3,6] => 6
[1,2,5,4,6,3] => 7
[1,2,5,6,3,4] => 11
[1,2,5,6,4,3] => 8
[1,2,6,3,4,5] => 10
[1,2,6,3,5,4] => 6
[1,2,6,4,3,5] => 6
[1,2,6,4,5,3] => 7
[1,2,6,5,3,4] => 6
[1,2,6,5,4,3] => 3
[1,3,2,4,5,6] => 12
[1,3,2,4,6,5] => 7
[1,3,2,5,4,6] => 7
[1,3,2,5,6,4] => 8
[1,3,2,6,4,5] => 7
[1,3,2,6,5,4] => 3
[1,3,4,2,5,6] => 11
[1,3,4,2,6,5] => 6
[1,3,4,5,2,6] => 10
[1,3,4,5,6,2] => 13
[1,3,4,6,2,5] => 10
[1,3,4,6,5,2] => 8
[1,3,5,2,4,6] => 10
[1,3,5,2,6,4] => 6
[1,3,5,4,2,6] => 6
[1,3,5,4,6,2] => 8
[1,3,5,6,2,4] => 11
[1,3,5,6,4,2] => 9
[1,3,6,2,4,5] => 10
[1,3,6,2,5,4] => 6
[1,3,6,4,2,5] => 6
[1,3,6,4,5,2] => 8
[1,3,6,5,2,4] => 6
[1,3,6,5,4,2] => 4
[1,4,2,3,5,6] => 11
[1,4,2,3,6,5] => 6
[1,4,2,5,3,6] => 6
[1,4,2,5,6,3] => 8
[1,4,2,6,3,5] => 6
[1,4,2,6,5,3] => 3
[1,4,3,2,5,6] => 8
[1,4,3,2,6,5] => 3
[1,4,3,5,2,6] => 6
[1,4,3,5,6,2] => 9
[1,4,3,6,2,5] => 6
[1,4,3,6,5,2] => 4
[1,4,5,2,3,6] => 10
[1,4,5,2,6,3] => 7
[1,4,5,3,2,6] => 7
[1,4,5,3,6,2] => 8
[1,4,5,6,2,3] => 12
[1,4,5,6,3,2] => 10
[1,4,6,2,3,5] => 10
[1,4,6,2,5,3] => 7
[1,4,6,3,2,5] => 7
[1,4,6,3,5,2] => 8
[1,4,6,5,2,3] => 7
[1,4,6,5,3,2] => 5
[1,5,2,3,4,6] => 10
[1,5,2,3,6,4] => 6
[1,5,2,4,3,6] => 6
[1,5,2,4,6,3] => 7
[1,5,2,6,3,4] => 6
[1,5,2,6,4,3] => 3
[1,5,3,2,4,6] => 7
[1,5,3,2,6,4] => 3
[1,5,3,4,2,6] => 6
[1,5,3,4,6,2] => 8
[1,5,3,6,2,4] => 6
[1,5,3,6,4,2] => 4
[1,5,4,2,3,6] => 6
[1,5,4,2,6,3] => 3
[1,5,4,3,2,6] => 3
[1,5,4,3,6,2] => 4
[1,5,4,6,2,3] => 7
[1,5,4,6,3,2] => 5
[1,5,6,2,3,4] => 11
[1,5,6,2,4,3] => 8
[1,5,6,3,2,4] => 8
[1,5,6,3,4,2] => 9
[1,5,6,4,2,3] => 8
[1,5,6,4,3,2] => 6
[1,6,2,3,4,5] => 10
[1,6,2,3,5,4] => 6
[1,6,2,4,3,5] => 6
[1,6,2,4,5,3] => 7
[1,6,2,5,3,4] => 6
[1,6,2,5,4,3] => 3
[1,6,3,2,4,5] => 7
[1,6,3,2,5,4] => 3
[1,6,3,4,2,5] => 6
[1,6,3,4,5,2] => 8
[1,6,3,5,2,4] => 6
[1,6,3,5,4,2] => 4
[1,6,4,2,3,5] => 6
[1,6,4,2,5,3] => 3
[1,6,4,3,2,5] => 3
[1,6,4,3,5,2] => 4
[1,6,4,5,2,3] => 7
[1,6,4,5,3,2] => 5
[1,6,5,2,3,4] => 6
[1,6,5,2,4,3] => 3
[1,6,5,3,2,4] => 3
[1,6,5,3,4,2] => 4
[1,6,5,4,2,3] => 3
[1,6,5,4,3,2] => 1
[2,1,3,4,5,6] => 13
[2,1,3,4,6,5] => 8
[2,1,3,5,4,6] => 8
[2,1,3,5,6,4] => 9
[2,1,3,6,4,5] => 8
[2,1,3,6,5,4] => 4
[2,1,4,3,5,6] => 9
[2,1,4,3,6,5] => 4
[2,1,4,5,3,6] => 8
[2,1,4,5,6,3] => 10
[2,1,4,6,3,5] => 8
[2,1,4,6,5,3] => 5
[2,1,5,3,4,6] => 8
[2,1,5,3,6,4] => 4
[2,1,5,4,3,6] => 4
[2,1,5,4,6,3] => 5
[2,1,5,6,3,4] => 9
[2,1,5,6,4,3] => 6
[2,1,6,3,4,5] => 8
[2,1,6,3,5,4] => 4
[2,1,6,4,3,5] => 4
[2,1,6,4,5,3] => 5
[2,1,6,5,3,4] => 4
[2,1,6,5,4,3] => 1
[2,3,1,4,5,6] => 12
[2,3,1,4,6,5] => 7
[2,3,1,5,4,6] => 7
[2,3,1,5,6,4] => 8
[2,3,1,6,4,5] => 7
[2,3,1,6,5,4] => 3
[2,3,4,1,5,6] => 11
[2,3,4,1,6,5] => 6
[2,3,4,5,1,6] => 10
[2,3,4,5,6,1] => 14
[2,3,4,6,1,5] => 10
[2,3,4,6,5,1] => 9
[2,3,5,1,4,6] => 10
[2,3,5,1,6,4] => 6
[2,3,5,4,1,6] => 6
[2,3,5,4,6,1] => 9
[2,3,5,6,1,4] => 11
[2,3,5,6,4,1] => 10
[2,3,6,1,4,5] => 10
[2,3,6,1,5,4] => 6
[2,3,6,4,1,5] => 6
[2,3,6,4,5,1] => 9
[2,3,6,5,1,4] => 6
[2,3,6,5,4,1] => 5
[2,4,1,3,5,6] => 11
[2,4,1,3,6,5] => 6
[2,4,1,5,3,6] => 6
[2,4,1,5,6,3] => 8
[2,4,1,6,3,5] => 6
[2,4,1,6,5,3] => 3
[2,4,3,1,5,6] => 8
[2,4,3,1,6,5] => 3
[2,4,3,5,1,6] => 6
[2,4,3,5,6,1] => 10
[2,4,3,6,1,5] => 6
[2,4,3,6,5,1] => 5
[2,4,5,1,3,6] => 10
[2,4,5,1,6,3] => 7
[2,4,5,3,1,6] => 7
[2,4,5,3,6,1] => 9
[2,4,5,6,1,3] => 12
[2,4,5,6,3,1] => 11
[2,4,6,1,3,5] => 10
[2,4,6,1,5,3] => 7
[2,4,6,3,1,5] => 7
[2,4,6,3,5,1] => 9
[2,4,6,5,1,3] => 7
[2,4,6,5,3,1] => 6
[2,5,1,3,4,6] => 10
[2,5,1,3,6,4] => 6
[2,5,1,4,3,6] => 6
[2,5,1,4,6,3] => 7
[2,5,1,6,3,4] => 6
[2,5,1,6,4,3] => 3
[2,5,3,1,4,6] => 7
[2,5,3,1,6,4] => 3
[2,5,3,4,1,6] => 6
[2,5,3,4,6,1] => 9
[2,5,3,6,1,4] => 6
[2,5,3,6,4,1] => 5
[2,5,4,1,3,6] => 6
[2,5,4,1,6,3] => 3
[2,5,4,3,1,6] => 3
[2,5,4,3,6,1] => 5
[2,5,4,6,1,3] => 7
[2,5,4,6,3,1] => 6
[2,5,6,1,3,4] => 11
[2,5,6,1,4,3] => 8
[2,5,6,3,1,4] => 8
[2,5,6,3,4,1] => 10
[2,5,6,4,1,3] => 8
[2,5,6,4,3,1] => 7
[2,6,1,3,4,5] => 10
[2,6,1,3,5,4] => 6
[2,6,1,4,3,5] => 6
[2,6,1,4,5,3] => 7
[2,6,1,5,3,4] => 6
[2,6,1,5,4,3] => 3
[2,6,3,1,4,5] => 7
[2,6,3,1,5,4] => 3
[2,6,3,4,1,5] => 6
[2,6,3,4,5,1] => 9
[2,6,3,5,1,4] => 6
[2,6,3,5,4,1] => 5
[2,6,4,1,3,5] => 6
[2,6,4,1,5,3] => 3
[2,6,4,3,1,5] => 3
[2,6,4,3,5,1] => 5
[2,6,4,5,1,3] => 7
[2,6,4,5,3,1] => 6
[2,6,5,1,3,4] => 6
[2,6,5,1,4,3] => 3
[2,6,5,3,1,4] => 3
[2,6,5,3,4,1] => 5
[2,6,5,4,1,3] => 3
[2,6,5,4,3,1] => 2
[3,1,2,4,5,6] => 12
[3,1,2,4,6,5] => 7
[3,1,2,5,4,6] => 7
[3,1,2,5,6,4] => 8
[3,1,2,6,4,5] => 7
[3,1,2,6,5,4] => 3
[3,1,4,2,5,6] => 8
[3,1,4,2,6,5] => 3
[3,1,4,5,2,6] => 7
[3,1,4,5,6,2] => 10
[3,1,4,6,2,5] => 7
[3,1,4,6,5,2] => 5
[3,1,5,2,4,6] => 7
[3,1,5,2,6,4] => 3
[3,1,5,4,2,6] => 3
[3,1,5,4,6,2] => 5
[3,1,5,6,2,4] => 8
[3,1,5,6,4,2] => 6
[3,1,6,2,4,5] => 7
[3,1,6,2,5,4] => 3
[3,1,6,4,2,5] => 3
[3,1,6,4,5,2] => 5
[3,1,6,5,2,4] => 3
[3,1,6,5,4,2] => 1
[3,2,1,4,5,6] => 10
[3,2,1,4,6,5] => 5
[3,2,1,5,4,6] => 5
[3,2,1,5,6,4] => 6
[3,2,1,6,4,5] => 5
[3,2,1,6,5,4] => 1
[3,2,4,1,5,6] => 8
[3,2,4,1,6,5] => 3
[3,2,4,5,1,6] => 7
[3,2,4,5,6,1] => 11
[3,2,4,6,1,5] => 7
[3,2,4,6,5,1] => 6
[3,2,5,1,4,6] => 7
[3,2,5,1,6,4] => 3
[3,2,5,4,1,6] => 3
[3,2,5,4,6,1] => 6
[3,2,5,6,1,4] => 8
[3,2,5,6,4,1] => 7
[3,2,6,1,4,5] => 7
[3,2,6,1,5,4] => 3
[3,2,6,4,1,5] => 3
[3,2,6,4,5,1] => 6
[3,2,6,5,1,4] => 3
[3,2,6,5,4,1] => 2
[3,4,1,2,5,6] => 11
[3,4,1,2,6,5] => 6
[3,4,1,5,2,6] => 6
[3,4,1,5,6,2] => 9
[3,4,1,6,2,5] => 6
[3,4,1,6,5,2] => 4
[3,4,2,1,5,6] => 9
[3,4,2,1,6,5] => 4
[3,4,2,5,1,6] => 6
[3,4,2,5,6,1] => 10
[3,4,2,6,1,5] => 6
[3,4,2,6,5,1] => 5
[3,4,5,1,2,6] => 10
[3,4,5,1,6,2] => 8
[3,4,5,2,1,6] => 8
[3,4,5,2,6,1] => 9
[3,4,5,6,1,2] => 13
[3,4,5,6,2,1] => 12
[3,4,6,1,2,5] => 10
[3,4,6,1,5,2] => 8
[3,4,6,2,1,5] => 8
[3,4,6,2,5,1] => 9
[3,4,6,5,1,2] => 8
[3,4,6,5,2,1] => 7
[3,5,1,2,4,6] => 10
[3,5,1,2,6,4] => 6
[3,5,1,4,2,6] => 6
[3,5,1,4,6,2] => 8
[3,5,1,6,2,4] => 6
[3,5,1,6,4,2] => 4
[3,5,2,1,4,6] => 8
[3,5,2,1,6,4] => 4
[3,5,2,4,1,6] => 6
[3,5,2,4,6,1] => 9
[3,5,2,6,1,4] => 6
[3,5,2,6,4,1] => 5
[3,5,4,1,2,6] => 6
[3,5,4,1,6,2] => 4
[3,5,4,2,1,6] => 4
[3,5,4,2,6,1] => 5
[3,5,4,6,1,2] => 8
[3,5,4,6,2,1] => 7
[3,5,6,1,2,4] => 11
[3,5,6,1,4,2] => 9
[3,5,6,2,1,4] => 9
[3,5,6,2,4,1] => 10
[3,5,6,4,1,2] => 9
[3,5,6,4,2,1] => 8
[3,6,1,2,4,5] => 10
[3,6,1,2,5,4] => 6
[3,6,1,4,2,5] => 6
[3,6,1,4,5,2] => 8
[3,6,1,5,2,4] => 6
[3,6,1,5,4,2] => 4
[3,6,2,1,4,5] => 8
[3,6,2,1,5,4] => 4
[3,6,2,4,1,5] => 6
[3,6,2,4,5,1] => 9
[3,6,2,5,1,4] => 6
[3,6,2,5,4,1] => 5
[3,6,4,1,2,5] => 6
[3,6,4,1,5,2] => 4
[3,6,4,2,1,5] => 4
[3,6,4,2,5,1] => 5
[3,6,4,5,1,2] => 8
[3,6,4,5,2,1] => 7
[3,6,5,1,2,4] => 6
[3,6,5,1,4,2] => 4
[3,6,5,2,1,4] => 4
[3,6,5,2,4,1] => 5
[3,6,5,4,1,2] => 4
[3,6,5,4,2,1] => 3
[4,1,2,3,5,6] => 11
[4,1,2,3,6,5] => 6
[4,1,2,5,3,6] => 6
[4,1,2,5,6,3] => 8
[4,1,2,6,3,5] => 6
[4,1,2,6,5,3] => 3
[4,1,3,2,5,6] => 8
[4,1,3,2,6,5] => 3
[4,1,3,5,2,6] => 6
[4,1,3,5,6,2] => 9
[4,1,3,6,2,5] => 6
[4,1,3,6,5,2] => 4
[4,1,5,2,3,6] => 6
[4,1,5,2,6,3] => 3
[4,1,5,3,2,6] => 3
[4,1,5,3,6,2] => 4
[4,1,5,6,2,3] => 8
[4,1,5,6,3,2] => 6
[4,1,6,2,3,5] => 6
[4,1,6,2,5,3] => 3
[4,1,6,3,2,5] => 3
[4,1,6,3,5,2] => 4
[4,1,6,5,2,3] => 3
[4,1,6,5,3,2] => 1
[4,2,1,3,5,6] => 9
[4,2,1,3,6,5] => 4
[4,2,1,5,3,6] => 4
[4,2,1,5,6,3] => 6
[4,2,1,6,3,5] => 4
[4,2,1,6,5,3] => 1
[4,2,3,1,5,6] => 8
[4,2,3,1,6,5] => 3
[4,2,3,5,1,6] => 6
[4,2,3,5,6,1] => 10
[4,2,3,6,1,5] => 6
[4,2,3,6,5,1] => 5
[4,2,5,1,3,6] => 6
[4,2,5,1,6,3] => 3
[4,2,5,3,1,6] => 3
[4,2,5,3,6,1] => 5
[4,2,5,6,1,3] => 8
[4,2,5,6,3,1] => 7
[4,2,6,1,3,5] => 6
[4,2,6,1,5,3] => 3
[4,2,6,3,1,5] => 3
[4,2,6,3,5,1] => 5
[4,2,6,5,1,3] => 3
[4,2,6,5,3,1] => 2
[4,3,1,2,5,6] => 8
[4,3,1,2,6,5] => 3
[4,3,1,5,2,6] => 3
[4,3,1,5,6,2] => 6
[4,3,1,6,2,5] => 3
[4,3,1,6,5,2] => 1
[4,3,2,1,5,6] => 6
[4,3,2,1,6,5] => 1
[4,3,2,5,1,6] => 3
[4,3,2,5,6,1] => 7
[4,3,2,6,1,5] => 3
[4,3,2,6,5,1] => 2
[4,3,5,1,2,6] => 6
[4,3,5,1,6,2] => 4
[4,3,5,2,1,6] => 4
[4,3,5,2,6,1] => 5
[4,3,5,6,1,2] => 9
[4,3,5,6,2,1] => 8
[4,3,6,1,2,5] => 6
[4,3,6,1,5,2] => 4
[4,3,6,2,1,5] => 4
[4,3,6,2,5,1] => 5
[4,3,6,5,1,2] => 4
[4,3,6,5,2,1] => 3
[4,5,1,2,3,6] => 10
[4,5,1,2,6,3] => 7
[4,5,1,3,2,6] => 7
[4,5,1,3,6,2] => 8
[4,5,1,6,2,3] => 7
[4,5,1,6,3,2] => 5
[4,5,2,1,3,6] => 8
[4,5,2,1,6,3] => 5
[4,5,2,3,1,6] => 7
[4,5,2,3,6,1] => 9
[4,5,2,6,1,3] => 7
[4,5,2,6,3,1] => 6
[4,5,3,1,2,6] => 7
[4,5,3,1,6,2] => 5
[4,5,3,2,1,6] => 5
[4,5,3,2,6,1] => 6
[4,5,3,6,1,2] => 8
[4,5,3,6,2,1] => 7
[4,5,6,1,2,3] => 12
[4,5,6,1,3,2] => 10
[4,5,6,2,1,3] => 10
[4,5,6,2,3,1] => 11
[4,5,6,3,1,2] => 10
[4,5,6,3,2,1] => 9
[4,6,1,2,3,5] => 10
[4,6,1,2,5,3] => 7
[4,6,1,3,2,5] => 7
[4,6,1,3,5,2] => 8
[4,6,1,5,2,3] => 7
[4,6,1,5,3,2] => 5
[4,6,2,1,3,5] => 8
[4,6,2,1,5,3] => 5
[4,6,2,3,1,5] => 7
[4,6,2,3,5,1] => 9
[4,6,2,5,1,3] => 7
[4,6,2,5,3,1] => 6
[4,6,3,1,2,5] => 7
[4,6,3,1,5,2] => 5
[4,6,3,2,1,5] => 5
[4,6,3,2,5,1] => 6
[4,6,3,5,1,2] => 8
[4,6,3,5,2,1] => 7
[4,6,5,1,2,3] => 7
[4,6,5,1,3,2] => 5
[4,6,5,2,1,3] => 5
[4,6,5,2,3,1] => 6
[4,6,5,3,1,2] => 5
[4,6,5,3,2,1] => 4
[5,1,2,3,4,6] => 10
[5,1,2,3,6,4] => 6
[5,1,2,4,3,6] => 6
[5,1,2,4,6,3] => 7
[5,1,2,6,3,4] => 6
[5,1,2,6,4,3] => 3
[5,1,3,2,4,6] => 7
[5,1,3,2,6,4] => 3
[5,1,3,4,2,6] => 6
[5,1,3,4,6,2] => 8
[5,1,3,6,2,4] => 6
[5,1,3,6,4,2] => 4
[5,1,4,2,3,6] => 6
[5,1,4,2,6,3] => 3
[5,1,4,3,2,6] => 3
[5,1,4,3,6,2] => 4
[5,1,4,6,2,3] => 7
[5,1,4,6,3,2] => 5
[5,1,6,2,3,4] => 6
[5,1,6,2,4,3] => 3
[5,1,6,3,2,4] => 3
[5,1,6,3,4,2] => 4
[5,1,6,4,2,3] => 3
[5,1,6,4,3,2] => 1
[5,2,1,3,4,6] => 8
[5,2,1,3,6,4] => 4
[5,2,1,4,3,6] => 4
[5,2,1,4,6,3] => 5
[5,2,1,6,3,4] => 4
[5,2,1,6,4,3] => 1
[5,2,3,1,4,6] => 7
[5,2,3,1,6,4] => 3
[5,2,3,4,1,6] => 6
[5,2,3,4,6,1] => 9
[5,2,3,6,1,4] => 6
[5,2,3,6,4,1] => 5
[5,2,4,1,3,6] => 6
[5,2,4,1,6,3] => 3
[5,2,4,3,1,6] => 3
[5,2,4,3,6,1] => 5
[5,2,4,6,1,3] => 7
[5,2,4,6,3,1] => 6
[5,2,6,1,3,4] => 6
[5,2,6,1,4,3] => 3
[5,2,6,3,1,4] => 3
[5,2,6,3,4,1] => 5
[5,2,6,4,1,3] => 3
[5,2,6,4,3,1] => 2
[5,3,1,2,4,6] => 7
[5,3,1,2,6,4] => 3
[5,3,1,4,2,6] => 3
[5,3,1,4,6,2] => 5
[5,3,1,6,2,4] => 3
[5,3,1,6,4,2] => 1
[5,3,2,1,4,6] => 5
[5,3,2,1,6,4] => 1
[5,3,2,4,1,6] => 3
[5,3,2,4,6,1] => 6
[5,3,2,6,1,4] => 3
[5,3,2,6,4,1] => 2
[5,3,4,1,2,6] => 6
[5,3,4,1,6,2] => 4
[5,3,4,2,1,6] => 4
[5,3,4,2,6,1] => 5
[5,3,4,6,1,2] => 8
[5,3,4,6,2,1] => 7
[5,3,6,1,2,4] => 6
[5,3,6,1,4,2] => 4
[5,3,6,2,1,4] => 4
[5,3,6,2,4,1] => 5
[5,3,6,4,1,2] => 4
[5,3,6,4,2,1] => 3
[5,4,1,2,3,6] => 6
[5,4,1,2,6,3] => 3
[5,4,1,3,2,6] => 3
[5,4,1,3,6,2] => 4
[5,4,1,6,2,3] => 3
[5,4,1,6,3,2] => 1
[5,4,2,1,3,6] => 4
[5,4,2,1,6,3] => 1
[5,4,2,3,1,6] => 3
[5,4,2,3,6,1] => 5
[5,4,2,6,1,3] => 3
[5,4,2,6,3,1] => 2
[5,4,3,1,2,6] => 3
[5,4,3,1,6,2] => 1
[5,4,3,2,1,6] => 1
[5,4,3,2,6,1] => 2
[5,4,3,6,1,2] => 4
[5,4,3,6,2,1] => 3
[5,4,6,1,2,3] => 7
[5,4,6,1,3,2] => 5
[5,4,6,2,1,3] => 5
[5,4,6,2,3,1] => 6
[5,4,6,3,1,2] => 5
[5,4,6,3,2,1] => 4
[5,6,1,2,3,4] => 11
[5,6,1,2,4,3] => 8
[5,6,1,3,2,4] => 8
[5,6,1,3,4,2] => 9
[5,6,1,4,2,3] => 8
[5,6,1,4,3,2] => 6
[5,6,2,1,3,4] => 9
[5,6,2,1,4,3] => 6
[5,6,2,3,1,4] => 8
[5,6,2,3,4,1] => 10
[5,6,2,4,1,3] => 8
[5,6,2,4,3,1] => 7
[5,6,3,1,2,4] => 8
[5,6,3,1,4,2] => 6
[5,6,3,2,1,4] => 6
[5,6,3,2,4,1] => 7
[5,6,3,4,1,2] => 9
[5,6,3,4,2,1] => 8
[5,6,4,1,2,3] => 8
[5,6,4,1,3,2] => 6
[5,6,4,2,1,3] => 6
[5,6,4,2,3,1] => 7
[5,6,4,3,1,2] => 6
[5,6,4,3,2,1] => 5
[6,1,2,3,4,5] => 10
[6,1,2,3,5,4] => 6
[6,1,2,4,3,5] => 6
[6,1,2,4,5,3] => 7
[6,1,2,5,3,4] => 6
[6,1,2,5,4,3] => 3
[6,1,3,2,4,5] => 7
[6,1,3,2,5,4] => 3
[6,1,3,4,2,5] => 6
[6,1,3,4,5,2] => 8
[6,1,3,5,2,4] => 6
[6,1,3,5,4,2] => 4
[6,1,4,2,3,5] => 6
[6,1,4,2,5,3] => 3
[6,1,4,3,2,5] => 3
[6,1,4,3,5,2] => 4
[6,1,4,5,2,3] => 7
[6,1,4,5,3,2] => 5
[6,1,5,2,3,4] => 6
[6,1,5,2,4,3] => 3
[6,1,5,3,2,4] => 3
[6,1,5,3,4,2] => 4
[6,1,5,4,2,3] => 3
[6,1,5,4,3,2] => 1
[6,2,1,3,4,5] => 8
[6,2,1,3,5,4] => 4
[6,2,1,4,3,5] => 4
[6,2,1,4,5,3] => 5
[6,2,1,5,3,4] => 4
[6,2,1,5,4,3] => 1
[6,2,3,1,4,5] => 7
[6,2,3,1,5,4] => 3
[6,2,3,4,1,5] => 6
[6,2,3,4,5,1] => 9
[6,2,3,5,1,4] => 6
[6,2,3,5,4,1] => 5
[6,2,4,1,3,5] => 6
[6,2,4,1,5,3] => 3
[6,2,4,3,1,5] => 3
[6,2,4,3,5,1] => 5
[6,2,4,5,1,3] => 7
[6,2,4,5,3,1] => 6
[6,2,5,1,3,4] => 6
[6,2,5,1,4,3] => 3
[6,2,5,3,1,4] => 3
[6,2,5,3,4,1] => 5
[6,2,5,4,1,3] => 3
[6,2,5,4,3,1] => 2
[6,3,1,2,4,5] => 7
[6,3,1,2,5,4] => 3
[6,3,1,4,2,5] => 3
[6,3,1,4,5,2] => 5
[6,3,1,5,2,4] => 3
[6,3,1,5,4,2] => 1
[6,3,2,1,4,5] => 5
[6,3,2,1,5,4] => 1
[6,3,2,4,1,5] => 3
[6,3,2,4,5,1] => 6
[6,3,2,5,1,4] => 3
[6,3,2,5,4,1] => 2
[6,3,4,1,2,5] => 6
[6,3,4,1,5,2] => 4
[6,3,4,2,1,5] => 4
[6,3,4,2,5,1] => 5
[6,3,4,5,1,2] => 8
[6,3,4,5,2,1] => 7
[6,3,5,1,2,4] => 6
[6,3,5,1,4,2] => 4
[6,3,5,2,1,4] => 4
[6,3,5,2,4,1] => 5
[6,3,5,4,1,2] => 4
[6,3,5,4,2,1] => 3
[6,4,1,2,3,5] => 6
[6,4,1,2,5,3] => 3
[6,4,1,3,2,5] => 3
[6,4,1,3,5,2] => 4
[6,4,1,5,2,3] => 3
[6,4,1,5,3,2] => 1
[6,4,2,1,3,5] => 4
[6,4,2,1,5,3] => 1
[6,4,2,3,1,5] => 3
[6,4,2,3,5,1] => 5
[6,4,2,5,1,3] => 3
[6,4,2,5,3,1] => 2
[6,4,3,1,2,5] => 3
[6,4,3,1,5,2] => 1
[6,4,3,2,1,5] => 1
[6,4,3,2,5,1] => 2
[6,4,3,5,1,2] => 4
[6,4,3,5,2,1] => 3
[6,4,5,1,2,3] => 7
[6,4,5,1,3,2] => 5
[6,4,5,2,1,3] => 5
[6,4,5,2,3,1] => 6
[6,4,5,3,1,2] => 5
[6,4,5,3,2,1] => 4
[6,5,1,2,3,4] => 6
[6,5,1,2,4,3] => 3
[6,5,1,3,2,4] => 3
[6,5,1,3,4,2] => 4
[6,5,1,4,2,3] => 3
[6,5,1,4,3,2] => 1
[6,5,2,1,3,4] => 4
[6,5,2,1,4,3] => 1
[6,5,2,3,1,4] => 3
[6,5,2,3,4,1] => 5
[6,5,2,4,1,3] => 3
[6,5,2,4,3,1] => 2
[6,5,3,1,2,4] => 3
[6,5,3,1,4,2] => 1
[6,5,3,2,1,4] => 1
[6,5,3,2,4,1] => 2
[6,5,3,4,1,2] => 4
[6,5,3,4,2,1] => 3
[6,5,4,1,2,3] => 3
[6,5,4,1,3,2] => 1
[6,5,4,2,1,3] => 1
[6,5,4,2,3,1] => 2
[6,5,4,3,1,2] => 1
[6,5,4,3,2,1] => 0
[1,2,3,4,5,6,7] => 21
[1,2,3,4,5,7,6] => 15
[1,2,3,4,6,5,7] => 15
[1,2,3,4,6,7,5] => 16
[1,2,3,4,7,5,6] => 15
[1,2,3,4,7,6,5] => 10
[1,2,3,5,4,6,7] => 16
[1,2,3,5,4,7,6] => 10
[1,2,3,5,6,4,7] => 15
[1,2,3,5,6,7,4] => 17
[1,2,3,5,7,4,6] => 15
[1,2,3,5,7,6,4] => 11
[1,2,3,6,4,5,7] => 15
[1,2,3,6,4,7,5] => 10
[1,2,3,6,5,4,7] => 10
[1,2,3,6,5,7,4] => 11
[1,2,3,6,7,4,5] => 16
[1,2,3,6,7,5,4] => 12
[1,2,3,7,4,5,6] => 15
[1,2,3,7,4,6,5] => 10
[1,2,3,7,5,4,6] => 10
[1,2,3,7,5,6,4] => 11
[1,2,3,7,6,4,5] => 10
[1,2,3,7,6,5,4] => 6
[1,2,4,3,5,6,7] => 17
[1,2,4,3,5,7,6] => 11
[1,2,4,3,6,5,7] => 11
[1,2,4,3,6,7,5] => 12
[1,2,4,3,7,5,6] => 11
[1,2,4,3,7,6,5] => 6
[1,2,4,5,3,6,7] => 16
[1,2,4,5,3,7,6] => 10
[1,2,4,5,6,3,7] => 15
[1,2,4,5,6,7,3] => 18
[1,2,4,5,7,3,6] => 15
[1,2,4,5,7,6,3] => 12
[1,2,4,6,3,5,7] => 15
[1,2,4,6,3,7,5] => 10
[1,2,4,6,5,3,7] => 10
[1,2,4,6,5,7,3] => 12
[1,2,4,6,7,3,5] => 16
[1,2,4,6,7,5,3] => 13
[1,2,4,7,3,5,6] => 15
[1,2,4,7,3,6,5] => 10
[1,2,4,7,5,3,6] => 10
[1,2,4,7,5,6,3] => 12
[1,2,4,7,6,3,5] => 10
[1,2,4,7,6,5,3] => 7
[1,2,5,3,4,6,7] => 16
[1,2,5,3,4,7,6] => 10
[1,2,5,3,6,4,7] => 10
[1,2,5,3,6,7,4] => 12
[1,2,5,3,7,4,6] => 10
[1,2,5,3,7,6,4] => 6
[1,2,5,4,3,6,7] => 12
[1,2,5,4,3,7,6] => 6
[1,2,5,4,6,3,7] => 10
[1,2,5,4,6,7,3] => 13
[1,2,5,4,7,3,6] => 10
[1,2,5,4,7,6,3] => 7
[1,2,5,6,3,4,7] => 15
[1,2,5,6,3,7,4] => 11
[1,2,5,6,4,3,7] => 11
[1,2,5,6,4,7,3] => 12
[1,2,5,6,7,3,4] => 17
[1,2,5,6,7,4,3] => 14
[1,2,5,7,3,4,6] => 15
[1,2,5,7,3,6,4] => 11
[1,2,5,7,4,3,6] => 11
[1,2,5,7,4,6,3] => 12
[1,2,5,7,6,3,4] => 11
[1,2,5,7,6,4,3] => 8
[1,2,6,3,4,5,7] => 15
[1,2,6,3,4,7,5] => 10
[1,2,6,3,5,4,7] => 10
[1,2,6,3,5,7,4] => 11
[1,2,6,3,7,4,5] => 10
[1,2,6,3,7,5,4] => 6
[1,2,6,4,3,5,7] => 11
[1,2,6,4,3,7,5] => 6
[1,2,6,4,5,3,7] => 10
[1,2,6,4,5,7,3] => 12
[1,2,6,4,7,3,5] => 10
[1,2,6,4,7,5,3] => 7
[1,2,6,5,3,4,7] => 10
[1,2,6,5,3,7,4] => 6
[1,2,6,5,4,3,7] => 6
[1,2,6,5,4,7,3] => 7
[1,2,6,5,7,3,4] => 11
[1,2,6,5,7,4,3] => 8
[1,2,6,7,3,4,5] => 16
[1,2,6,7,3,5,4] => 12
[1,2,6,7,4,3,5] => 12
[1,2,6,7,4,5,3] => 13
[1,2,6,7,5,3,4] => 12
[1,2,6,7,5,4,3] => 9
[1,2,7,3,4,5,6] => 15
[1,2,7,3,4,6,5] => 10
[1,2,7,3,5,4,6] => 10
[1,2,7,3,5,6,4] => 11
[1,2,7,3,6,4,5] => 10
[1,2,7,3,6,5,4] => 6
[1,2,7,4,3,5,6] => 11
[1,2,7,4,3,6,5] => 6
[1,2,7,4,5,3,6] => 10
[1,2,7,4,5,6,3] => 12
[1,2,7,4,6,3,5] => 10
[1,2,7,4,6,5,3] => 7
[1,2,7,5,3,4,6] => 10
[1,2,7,5,3,6,4] => 6
[1,2,7,5,4,3,6] => 6
[1,2,7,5,4,6,3] => 7
[1,2,7,5,6,3,4] => 11
[1,2,7,5,6,4,3] => 8
[1,2,7,6,3,4,5] => 10
[1,2,7,6,3,5,4] => 6
[1,2,7,6,4,3,5] => 6
[1,2,7,6,4,5,3] => 7
[1,2,7,6,5,3,4] => 6
[1,2,7,6,5,4,3] => 3
[1,3,2,4,5,6,7] => 18
[1,3,2,4,5,7,6] => 12
[1,3,2,4,6,5,7] => 12
[1,3,2,4,6,7,5] => 13
[1,3,2,4,7,5,6] => 12
[1,3,2,4,7,6,5] => 7
[1,3,2,5,4,6,7] => 13
[1,3,2,5,4,7,6] => 7
[1,3,2,5,6,4,7] => 12
[1,3,2,5,6,7,4] => 14
[1,3,2,5,7,4,6] => 12
[1,3,2,5,7,6,4] => 8
[1,3,2,6,4,5,7] => 12
[1,3,2,6,4,7,5] => 7
[1,3,2,6,5,4,7] => 7
[1,3,2,6,5,7,4] => 8
[1,3,2,6,7,4,5] => 13
[1,3,2,6,7,5,4] => 9
[1,3,2,7,4,5,6] => 12
[1,3,2,7,4,6,5] => 7
[1,3,2,7,5,4,6] => 7
[1,3,2,7,5,6,4] => 8
[1,3,2,7,6,4,5] => 7
[1,3,2,7,6,5,4] => 3
[1,3,4,2,5,6,7] => 17
[1,3,4,2,5,7,6] => 11
[1,3,4,2,6,5,7] => 11
[1,3,4,2,6,7,5] => 12
[1,3,4,2,7,5,6] => 11
[1,3,4,2,7,6,5] => 6
[1,3,4,5,2,6,7] => 16
[1,3,4,5,2,7,6] => 10
[1,3,4,5,6,2,7] => 15
[1,3,4,5,6,7,2] => 19
[1,3,4,5,7,2,6] => 15
[1,3,4,5,7,6,2] => 13
[1,3,4,6,2,5,7] => 15
[1,3,4,6,2,7,5] => 10
[1,3,4,6,5,2,7] => 10
[1,3,4,6,5,7,2] => 13
[1,3,4,6,7,2,5] => 16
[1,3,4,6,7,5,2] => 14
[1,3,4,7,2,5,6] => 15
[1,3,4,7,2,6,5] => 10
[1,3,4,7,5,2,6] => 10
[1,3,4,7,5,6,2] => 13
[1,3,4,7,6,2,5] => 10
[1,3,4,7,6,5,2] => 8
[1,3,5,2,4,6,7] => 16
[1,3,5,2,4,7,6] => 10
[1,3,5,2,6,4,7] => 10
[1,3,5,2,6,7,4] => 12
[1,3,5,2,7,4,6] => 10
[1,3,5,2,7,6,4] => 6
[1,3,5,4,2,6,7] => 12
[1,3,5,4,2,7,6] => 6
[1,3,5,4,6,2,7] => 10
[1,3,5,4,6,7,2] => 14
[1,3,5,4,7,2,6] => 10
[1,3,5,4,7,6,2] => 8
[1,3,5,6,2,4,7] => 15
[1,3,5,6,2,7,4] => 11
[1,3,5,6,4,2,7] => 11
[1,3,5,6,4,7,2] => 13
[1,3,5,6,7,2,4] => 17
[1,3,5,6,7,4,2] => 15
[1,3,5,7,2,4,6] => 15
[1,3,5,7,2,6,4] => 11
[1,3,5,7,4,2,6] => 11
[1,3,5,7,4,6,2] => 13
[1,3,5,7,6,2,4] => 11
[1,3,5,7,6,4,2] => 9
[1,3,6,2,4,5,7] => 15
[1,3,6,2,4,7,5] => 10
[1,3,6,2,5,4,7] => 10
[1,3,6,2,5,7,4] => 11
[1,3,6,2,7,4,5] => 10
[1,3,6,2,7,5,4] => 6
[1,3,6,4,2,5,7] => 11
[1,3,6,4,2,7,5] => 6
[1,3,6,4,5,2,7] => 10
[1,3,6,4,5,7,2] => 13
[1,3,6,4,7,2,5] => 10
[1,3,6,4,7,5,2] => 8
[1,3,6,5,2,4,7] => 10
[1,3,6,5,2,7,4] => 6
[1,3,6,5,4,2,7] => 6
[1,3,6,5,4,7,2] => 8
[1,3,6,5,7,2,4] => 11
[1,3,6,5,7,4,2] => 9
[1,3,6,7,2,4,5] => 16
[1,3,6,7,2,5,4] => 12
[1,3,6,7,4,2,5] => 12
[1,3,6,7,4,5,2] => 14
[1,3,6,7,5,2,4] => 12
[1,3,6,7,5,4,2] => 10
[1,3,7,2,4,5,6] => 15
[1,3,7,2,4,6,5] => 10
[1,3,7,2,5,4,6] => 10
[1,3,7,2,5,6,4] => 11
[1,3,7,2,6,4,5] => 10
[1,3,7,2,6,5,4] => 6
[1,3,7,4,2,5,6] => 11
[1,3,7,4,2,6,5] => 6
[1,3,7,4,5,2,6] => 10
[1,3,7,4,5,6,2] => 13
[1,3,7,4,6,2,5] => 10
[1,3,7,4,6,5,2] => 8
[1,3,7,5,2,4,6] => 10
[1,3,7,5,2,6,4] => 6
[1,3,7,5,4,2,6] => 6
[1,3,7,5,4,6,2] => 8
[1,3,7,5,6,2,4] => 11
[1,3,7,5,6,4,2] => 9
[1,3,7,6,2,4,5] => 10
[1,3,7,6,2,5,4] => 6
[1,3,7,6,4,2,5] => 6
[1,3,7,6,4,5,2] => 8
[1,3,7,6,5,2,4] => 6
[1,3,7,6,5,4,2] => 4
[1,4,2,3,5,6,7] => 17
[1,4,2,3,5,7,6] => 11
[1,4,2,3,6,5,7] => 11
[1,4,2,3,6,7,5] => 12
[1,4,2,3,7,5,6] => 11
[1,4,2,3,7,6,5] => 6
[1,4,2,5,3,6,7] => 12
[1,4,2,5,3,7,6] => 6
[1,4,2,5,6,3,7] => 11
[1,4,2,5,6,7,3] => 14
[1,4,2,5,7,3,6] => 11
[1,4,2,5,7,6,3] => 8
[1,4,2,6,3,5,7] => 11
[1,4,2,6,3,7,5] => 6
[1,4,2,6,5,3,7] => 6
[1,4,2,6,5,7,3] => 8
[1,4,2,6,7,3,5] => 12
[1,4,2,6,7,5,3] => 9
[1,4,2,7,3,5,6] => 11
[1,4,2,7,3,6,5] => 6
[1,4,2,7,5,3,6] => 6
[1,4,2,7,5,6,3] => 8
[1,4,2,7,6,3,5] => 6
[1,4,2,7,6,5,3] => 3
[1,4,3,2,5,6,7] => 14
[1,4,3,2,5,7,6] => 8
[1,4,3,2,6,5,7] => 8
[1,4,3,2,6,7,5] => 9
[1,4,3,2,7,5,6] => 8
[1,4,3,2,7,6,5] => 3
[1,4,3,5,2,6,7] => 12
[1,4,3,5,2,7,6] => 6
[1,4,3,5,6,2,7] => 11
[1,4,3,5,6,7,2] => 15
[1,4,3,5,7,2,6] => 11
[1,4,3,5,7,6,2] => 9
[1,4,3,6,2,5,7] => 11
[1,4,3,6,2,7,5] => 6
[1,4,3,6,5,2,7] => 6
[1,4,3,6,5,7,2] => 9
[1,4,3,6,7,2,5] => 12
[1,4,3,6,7,5,2] => 10
[1,4,3,7,2,5,6] => 11
[1,4,3,7,2,6,5] => 6
[1,4,3,7,5,2,6] => 6
[1,4,3,7,5,6,2] => 9
[1,4,3,7,6,2,5] => 6
[1,4,3,7,6,5,2] => 4
[1,4,5,2,3,6,7] => 16
[1,4,5,2,3,7,6] => 10
[1,4,5,2,6,3,7] => 10
[1,4,5,2,6,7,3] => 13
[1,4,5,2,7,3,6] => 10
[1,4,5,2,7,6,3] => 7
[1,4,5,3,2,6,7] => 13
[1,4,5,3,2,7,6] => 7
[1,4,5,3,6,2,7] => 10
[1,4,5,3,6,7,2] => 14
[1,4,5,3,7,2,6] => 10
[1,4,5,3,7,6,2] => 8
[1,4,5,6,2,3,7] => 15
[1,4,5,6,2,7,3] => 12
[1,4,5,6,3,2,7] => 12
[1,4,5,6,3,7,2] => 13
[1,4,5,6,7,2,3] => 18
[1,4,5,6,7,3,2] => 16
[1,4,5,7,2,3,6] => 15
[1,4,5,7,2,6,3] => 12
[1,4,5,7,3,2,6] => 12
[1,4,5,7,3,6,2] => 13
[1,4,5,7,6,2,3] => 12
[1,4,5,7,6,3,2] => 10
[1,4,6,2,3,5,7] => 15
[1,4,6,2,3,7,5] => 10
[1,4,6,2,5,3,7] => 10
[1,4,6,2,5,7,3] => 12
[1,4,6,2,7,3,5] => 10
[1,4,6,2,7,5,3] => 7
[1,4,6,3,2,5,7] => 12
[1,4,6,3,2,7,5] => 7
[1,4,6,3,5,2,7] => 10
[1,4,6,3,5,7,2] => 13
[1,4,6,3,7,2,5] => 10
[1,4,6,3,7,5,2] => 8
[1,4,6,5,2,3,7] => 10
[1,4,6,5,2,7,3] => 7
[1,4,6,5,3,2,7] => 7
[1,4,6,5,3,7,2] => 8
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,3,1,1 1,7,3,8,3,1,1 1,15,7,34,18,14,18,8,3,1,1 1,31,15,122,72,69,147,83,71,33,45,18,8,3,1,1
$F_{2} = 1 + q$
$F_{3} = 1 + 3\ q + q^{2} + q^{3}$
$F_{4} = 1 + 7\ q + 3\ q^{2} + 8\ q^{3} + 3\ q^{4} + q^{5} + q^{6}$
$F_{5} = 1 + 15\ q + 7\ q^{2} + 34\ q^{3} + 18\ q^{4} + 14\ q^{5} + 18\ q^{6} + 8\ q^{7} + 3\ q^{8} + q^{9} + q^{10}$
$F_{6} = 1 + 31\ q + 15\ q^{2} + 122\ q^{3} + 72\ q^{4} + 69\ q^{5} + 147\ q^{6} + 83\ q^{7} + 71\ q^{8} + 33\ q^{9} + 45\ q^{10} + 18\ q^{11} + 8\ q^{12} + 3\ q^{13} + q^{14} + q^{15}$
Description
The sum of the ascent bottoms of a permutation.
Code
def statistic(pi):
return sum( pi[i-1] for i in range(1,len(pi)) if pi[i-1]
Created
Apr 15, 2016 at 14:18 by Christian Stump
Updated
Apr 15, 2016 at 14:18 by Christian Stump
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