Identifier
- St000437: Permutations ⟶ ℤ
Values
[1,2] => 0
[2,1] => 0
[1,2,3] => 0
[1,3,2] => 0
[2,1,3] => 0
[2,3,1] => 0
[3,1,2] => 1
[3,2,1] => 1
[1,2,3,4] => 0
[1,2,4,3] => 0
[1,3,2,4] => 0
[1,3,4,2] => 0
[1,4,2,3] => 1
[1,4,3,2] => 1
[2,1,3,4] => 0
[2,1,4,3] => 0
[2,3,1,4] => 0
[2,3,4,1] => 0
[2,4,1,3] => 1
[2,4,3,1] => 1
[3,1,2,4] => 1
[3,1,4,2] => 1
[3,2,1,4] => 1
[3,2,4,1] => 1
[3,4,1,2] => 2
[3,4,2,1] => 2
[4,1,2,3] => 3
[4,1,3,2] => 3
[4,2,1,3] => 3
[4,2,3,1] => 3
[4,3,1,2] => 4
[4,3,2,1] => 4
[1,2,3,4,5] => 0
[1,2,3,5,4] => 0
[1,2,4,3,5] => 0
[1,2,4,5,3] => 0
[1,2,5,3,4] => 1
[1,2,5,4,3] => 1
[1,3,2,4,5] => 0
[1,3,2,5,4] => 0
[1,3,4,2,5] => 0
[1,3,4,5,2] => 0
[1,3,5,2,4] => 1
[1,3,5,4,2] => 1
[1,4,2,3,5] => 1
[1,4,2,5,3] => 1
[1,4,3,2,5] => 1
[1,4,3,5,2] => 1
[1,4,5,2,3] => 2
[1,4,5,3,2] => 2
[1,5,2,3,4] => 3
[1,5,2,4,3] => 3
[1,5,3,2,4] => 3
[1,5,3,4,2] => 3
[1,5,4,2,3] => 4
[1,5,4,3,2] => 4
[2,1,3,4,5] => 0
[2,1,3,5,4] => 0
[2,1,4,3,5] => 0
[2,1,4,5,3] => 0
[2,1,5,3,4] => 1
[2,1,5,4,3] => 1
[2,3,1,4,5] => 0
[2,3,1,5,4] => 0
[2,3,4,1,5] => 0
[2,3,4,5,1] => 0
[2,3,5,1,4] => 1
[2,3,5,4,1] => 1
[2,4,1,3,5] => 1
[2,4,1,5,3] => 1
[2,4,3,1,5] => 1
[2,4,3,5,1] => 1
[2,4,5,1,3] => 2
[2,4,5,3,1] => 2
[2,5,1,3,4] => 3
[2,5,1,4,3] => 3
[2,5,3,1,4] => 3
[2,5,3,4,1] => 3
[2,5,4,1,3] => 4
[2,5,4,3,1] => 4
[3,1,2,4,5] => 1
[3,1,2,5,4] => 1
[3,1,4,2,5] => 1
[3,1,4,5,2] => 1
[3,1,5,2,4] => 2
[3,1,5,4,2] => 2
[3,2,1,4,5] => 1
[3,2,1,5,4] => 1
[3,2,4,1,5] => 1
[3,2,4,5,1] => 1
[3,2,5,1,4] => 2
[3,2,5,4,1] => 2
[3,4,1,2,5] => 2
[3,4,1,5,2] => 2
[3,4,2,1,5] => 2
[3,4,2,5,1] => 2
[3,4,5,1,2] => 3
[3,4,5,2,1] => 3
[3,5,1,2,4] => 4
[3,5,1,4,2] => 4
[3,5,2,1,4] => 4
>>> Load all 1200 entries. <<<[3,5,2,4,1] => 4
[3,5,4,1,2] => 5
[3,5,4,2,1] => 5
[4,1,2,3,5] => 3
[4,1,2,5,3] => 3
[4,1,3,2,5] => 3
[4,1,3,5,2] => 3
[4,1,5,2,3] => 4
[4,1,5,3,2] => 4
[4,2,1,3,5] => 3
[4,2,1,5,3] => 3
[4,2,3,1,5] => 3
[4,2,3,5,1] => 3
[4,2,5,1,3] => 4
[4,2,5,3,1] => 4
[4,3,1,2,5] => 4
[4,3,1,5,2] => 4
[4,3,2,1,5] => 4
[4,3,2,5,1] => 4
[4,3,5,1,2] => 5
[4,3,5,2,1] => 5
[4,5,1,2,3] => 6
[4,5,1,3,2] => 6
[4,5,2,1,3] => 6
[4,5,2,3,1] => 6
[4,5,3,1,2] => 7
[4,5,3,2,1] => 7
[5,1,2,3,4] => 6
[5,1,2,4,3] => 6
[5,1,3,2,4] => 6
[5,1,3,4,2] => 6
[5,1,4,2,3] => 7
[5,1,4,3,2] => 7
[5,2,1,3,4] => 6
[5,2,1,4,3] => 6
[5,2,3,1,4] => 6
[5,2,3,4,1] => 6
[5,2,4,1,3] => 7
[5,2,4,3,1] => 7
[5,3,1,2,4] => 7
[5,3,1,4,2] => 7
[5,3,2,1,4] => 7
[5,3,2,4,1] => 7
[5,3,4,1,2] => 8
[5,3,4,2,1] => 8
[5,4,1,2,3] => 9
[5,4,1,3,2] => 9
[5,4,2,1,3] => 9
[5,4,2,3,1] => 9
[5,4,3,1,2] => 10
[5,4,3,2,1] => 10
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 0
[1,2,3,5,4,6] => 0
[1,2,3,5,6,4] => 0
[1,2,3,6,4,5] => 1
[1,2,3,6,5,4] => 1
[1,2,4,3,5,6] => 0
[1,2,4,3,6,5] => 0
[1,2,4,5,3,6] => 0
[1,2,4,5,6,3] => 0
[1,2,4,6,3,5] => 1
[1,2,4,6,5,3] => 1
[1,2,5,3,4,6] => 1
[1,2,5,3,6,4] => 1
[1,2,5,4,3,6] => 1
[1,2,5,4,6,3] => 1
[1,2,5,6,3,4] => 2
[1,2,5,6,4,3] => 2
[1,2,6,3,4,5] => 3
[1,2,6,3,5,4] => 3
[1,2,6,4,3,5] => 3
[1,2,6,4,5,3] => 3
[1,2,6,5,3,4] => 4
[1,2,6,5,4,3] => 4
[1,3,2,4,5,6] => 0
[1,3,2,4,6,5] => 0
[1,3,2,5,4,6] => 0
[1,3,2,5,6,4] => 0
[1,3,2,6,4,5] => 1
[1,3,2,6,5,4] => 1
[1,3,4,2,5,6] => 0
[1,3,4,2,6,5] => 0
[1,3,4,5,2,6] => 0
[1,3,4,5,6,2] => 0
[1,3,4,6,2,5] => 1
[1,3,4,6,5,2] => 1
[1,3,5,2,4,6] => 1
[1,3,5,2,6,4] => 1
[1,3,5,4,2,6] => 1
[1,3,5,4,6,2] => 1
[1,3,5,6,2,4] => 2
[1,3,5,6,4,2] => 2
[1,3,6,2,4,5] => 3
[1,3,6,2,5,4] => 3
[1,3,6,4,2,5] => 3
[1,3,6,4,5,2] => 3
[1,3,6,5,2,4] => 4
[1,3,6,5,4,2] => 4
[1,4,2,3,5,6] => 1
[1,4,2,3,6,5] => 1
[1,4,2,5,3,6] => 1
[1,4,2,5,6,3] => 1
[1,4,2,6,3,5] => 2
[1,4,2,6,5,3] => 2
[1,4,3,2,5,6] => 1
[1,4,3,2,6,5] => 1
[1,4,3,5,2,6] => 1
[1,4,3,5,6,2] => 1
[1,4,3,6,2,5] => 2
[1,4,3,6,5,2] => 2
[1,4,5,2,3,6] => 2
[1,4,5,2,6,3] => 2
[1,4,5,3,2,6] => 2
[1,4,5,3,6,2] => 2
[1,4,5,6,2,3] => 3
[1,4,5,6,3,2] => 3
[1,4,6,2,3,5] => 4
[1,4,6,2,5,3] => 4
[1,4,6,3,2,5] => 4
[1,4,6,3,5,2] => 4
[1,4,6,5,2,3] => 5
[1,4,6,5,3,2] => 5
[1,5,2,3,4,6] => 3
[1,5,2,3,6,4] => 3
[1,5,2,4,3,6] => 3
[1,5,2,4,6,3] => 3
[1,5,2,6,3,4] => 4
[1,5,2,6,4,3] => 4
[1,5,3,2,4,6] => 3
[1,5,3,2,6,4] => 3
[1,5,3,4,2,6] => 3
[1,5,3,4,6,2] => 3
[1,5,3,6,2,4] => 4
[1,5,3,6,4,2] => 4
[1,5,4,2,3,6] => 4
[1,5,4,2,6,3] => 4
[1,5,4,3,2,6] => 4
[1,5,4,3,6,2] => 4
[1,5,4,6,2,3] => 5
[1,5,4,6,3,2] => 5
[1,5,6,2,3,4] => 6
[1,5,6,2,4,3] => 6
[1,5,6,3,2,4] => 6
[1,5,6,3,4,2] => 6
[1,5,6,4,2,3] => 7
[1,5,6,4,3,2] => 7
[1,6,2,3,4,5] => 6
[1,6,2,3,5,4] => 6
[1,6,2,4,3,5] => 6
[1,6,2,4,5,3] => 6
[1,6,2,5,3,4] => 7
[1,6,2,5,4,3] => 7
[1,6,3,2,4,5] => 6
[1,6,3,2,5,4] => 6
[1,6,3,4,2,5] => 6
[1,6,3,4,5,2] => 6
[1,6,3,5,2,4] => 7
[1,6,3,5,4,2] => 7
[1,6,4,2,3,5] => 7
[1,6,4,2,5,3] => 7
[1,6,4,3,2,5] => 7
[1,6,4,3,5,2] => 7
[1,6,4,5,2,3] => 8
[1,6,4,5,3,2] => 8
[1,6,5,2,3,4] => 9
[1,6,5,2,4,3] => 9
[1,6,5,3,2,4] => 9
[1,6,5,3,4,2] => 9
[1,6,5,4,2,3] => 10
[1,6,5,4,3,2] => 10
[2,1,3,4,5,6] => 0
[2,1,3,4,6,5] => 0
[2,1,3,5,4,6] => 0
[2,1,3,5,6,4] => 0
[2,1,3,6,4,5] => 1
[2,1,3,6,5,4] => 1
[2,1,4,3,5,6] => 0
[2,1,4,3,6,5] => 0
[2,1,4,5,3,6] => 0
[2,1,4,5,6,3] => 0
[2,1,4,6,3,5] => 1
[2,1,4,6,5,3] => 1
[2,1,5,3,4,6] => 1
[2,1,5,3,6,4] => 1
[2,1,5,4,3,6] => 1
[2,1,5,4,6,3] => 1
[2,1,5,6,3,4] => 2
[2,1,5,6,4,3] => 2
[2,1,6,3,4,5] => 3
[2,1,6,3,5,4] => 3
[2,1,6,4,3,5] => 3
[2,1,6,4,5,3] => 3
[2,1,6,5,3,4] => 4
[2,1,6,5,4,3] => 4
[2,3,1,4,5,6] => 0
[2,3,1,4,6,5] => 0
[2,3,1,5,4,6] => 0
[2,3,1,5,6,4] => 0
[2,3,1,6,4,5] => 1
[2,3,1,6,5,4] => 1
[2,3,4,1,5,6] => 0
[2,3,4,1,6,5] => 0
[2,3,4,5,1,6] => 0
[2,3,4,5,6,1] => 0
[2,3,4,6,1,5] => 1
[2,3,4,6,5,1] => 1
[2,3,5,1,4,6] => 1
[2,3,5,1,6,4] => 1
[2,3,5,4,1,6] => 1
[2,3,5,4,6,1] => 1
[2,3,5,6,1,4] => 2
[2,3,5,6,4,1] => 2
[2,3,6,1,4,5] => 3
[2,3,6,1,5,4] => 3
[2,3,6,4,1,5] => 3
[2,3,6,4,5,1] => 3
[2,3,6,5,1,4] => 4
[2,3,6,5,4,1] => 4
[2,4,1,3,5,6] => 1
[2,4,1,3,6,5] => 1
[2,4,1,5,3,6] => 1
[2,4,1,5,6,3] => 1
[2,4,1,6,3,5] => 2
[2,4,1,6,5,3] => 2
[2,4,3,1,5,6] => 1
[2,4,3,1,6,5] => 1
[2,4,3,5,1,6] => 1
[2,4,3,5,6,1] => 1
[2,4,3,6,1,5] => 2
[2,4,3,6,5,1] => 2
[2,4,5,1,3,6] => 2
[2,4,5,1,6,3] => 2
[2,4,5,3,1,6] => 2
[2,4,5,3,6,1] => 2
[2,4,5,6,1,3] => 3
[2,4,5,6,3,1] => 3
[2,4,6,1,3,5] => 4
[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] => 5
[2,4,6,5,3,1] => 5
[2,5,1,3,4,6] => 3
[2,5,1,3,6,4] => 3
[2,5,1,4,3,6] => 3
[2,5,1,4,6,3] => 3
[2,5,1,6,3,4] => 4
[2,5,1,6,4,3] => 4
[2,5,3,1,4,6] => 3
[2,5,3,1,6,4] => 3
[2,5,3,4,1,6] => 3
[2,5,3,4,6,1] => 3
[2,5,3,6,1,4] => 4
[2,5,3,6,4,1] => 4
[2,5,4,1,3,6] => 4
[2,5,4,1,6,3] => 4
[2,5,4,3,1,6] => 4
[2,5,4,3,6,1] => 4
[2,5,4,6,1,3] => 5
[2,5,4,6,3,1] => 5
[2,5,6,1,3,4] => 6
[2,5,6,1,4,3] => 6
[2,5,6,3,1,4] => 6
[2,5,6,3,4,1] => 6
[2,5,6,4,1,3] => 7
[2,5,6,4,3,1] => 7
[2,6,1,3,4,5] => 6
[2,6,1,3,5,4] => 6
[2,6,1,4,3,5] => 6
[2,6,1,4,5,3] => 6
[2,6,1,5,3,4] => 7
[2,6,1,5,4,3] => 7
[2,6,3,1,4,5] => 6
[2,6,3,1,5,4] => 6
[2,6,3,4,1,5] => 6
[2,6,3,4,5,1] => 6
[2,6,3,5,1,4] => 7
[2,6,3,5,4,1] => 7
[2,6,4,1,3,5] => 7
[2,6,4,1,5,3] => 7
[2,6,4,3,1,5] => 7
[2,6,4,3,5,1] => 7
[2,6,4,5,1,3] => 8
[2,6,4,5,3,1] => 8
[2,6,5,1,3,4] => 9
[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] => 10
[3,1,2,4,5,6] => 1
[3,1,2,4,6,5] => 1
[3,1,2,5,4,6] => 1
[3,1,2,5,6,4] => 1
[3,1,2,6,4,5] => 2
[3,1,2,6,5,4] => 2
[3,1,4,2,5,6] => 1
[3,1,4,2,6,5] => 1
[3,1,4,5,2,6] => 1
[3,1,4,5,6,2] => 1
[3,1,4,6,2,5] => 2
[3,1,4,6,5,2] => 2
[3,1,5,2,4,6] => 2
[3,1,5,2,6,4] => 2
[3,1,5,4,2,6] => 2
[3,1,5,4,6,2] => 2
[3,1,5,6,2,4] => 3
[3,1,5,6,4,2] => 3
[3,1,6,2,4,5] => 4
[3,1,6,2,5,4] => 4
[3,1,6,4,2,5] => 4
[3,1,6,4,5,2] => 4
[3,1,6,5,2,4] => 5
[3,1,6,5,4,2] => 5
[3,2,1,4,5,6] => 1
[3,2,1,4,6,5] => 1
[3,2,1,5,4,6] => 1
[3,2,1,5,6,4] => 1
[3,2,1,6,4,5] => 2
[3,2,1,6,5,4] => 2
[3,2,4,1,5,6] => 1
[3,2,4,1,6,5] => 1
[3,2,4,5,1,6] => 1
[3,2,4,5,6,1] => 1
[3,2,4,6,1,5] => 2
[3,2,4,6,5,1] => 2
[3,2,5,1,4,6] => 2
[3,2,5,1,6,4] => 2
[3,2,5,4,1,6] => 2
[3,2,5,4,6,1] => 2
[3,2,5,6,1,4] => 3
[3,2,5,6,4,1] => 3
[3,2,6,1,4,5] => 4
[3,2,6,1,5,4] => 4
[3,2,6,4,1,5] => 4
[3,2,6,4,5,1] => 4
[3,2,6,5,1,4] => 5
[3,2,6,5,4,1] => 5
[3,4,1,2,5,6] => 2
[3,4,1,2,6,5] => 2
[3,4,1,5,2,6] => 2
[3,4,1,5,6,2] => 2
[3,4,1,6,2,5] => 3
[3,4,1,6,5,2] => 3
[3,4,2,1,5,6] => 2
[3,4,2,1,6,5] => 2
[3,4,2,5,1,6] => 2
[3,4,2,5,6,1] => 2
[3,4,2,6,1,5] => 3
[3,4,2,6,5,1] => 3
[3,4,5,1,2,6] => 3
[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] => 4
[3,4,5,6,2,1] => 4
[3,4,6,1,2,5] => 5
[3,4,6,1,5,2] => 5
[3,4,6,2,1,5] => 5
[3,4,6,2,5,1] => 5
[3,4,6,5,1,2] => 6
[3,4,6,5,2,1] => 6
[3,5,1,2,4,6] => 4
[3,5,1,2,6,4] => 4
[3,5,1,4,2,6] => 4
[3,5,1,4,6,2] => 4
[3,5,1,6,2,4] => 5
[3,5,1,6,4,2] => 5
[3,5,2,1,4,6] => 4
[3,5,2,1,6,4] => 4
[3,5,2,4,1,6] => 4
[3,5,2,4,6,1] => 4
[3,5,2,6,1,4] => 5
[3,5,2,6,4,1] => 5
[3,5,4,1,2,6] => 5
[3,5,4,1,6,2] => 5
[3,5,4,2,1,6] => 5
[3,5,4,2,6,1] => 5
[3,5,4,6,1,2] => 6
[3,5,4,6,2,1] => 6
[3,5,6,1,2,4] => 7
[3,5,6,1,4,2] => 7
[3,5,6,2,1,4] => 7
[3,5,6,2,4,1] => 7
[3,5,6,4,1,2] => 8
[3,5,6,4,2,1] => 8
[3,6,1,2,4,5] => 7
[3,6,1,2,5,4] => 7
[3,6,1,4,2,5] => 7
[3,6,1,4,5,2] => 7
[3,6,1,5,2,4] => 8
[3,6,1,5,4,2] => 8
[3,6,2,1,4,5] => 7
[3,6,2,1,5,4] => 7
[3,6,2,4,1,5] => 7
[3,6,2,4,5,1] => 7
[3,6,2,5,1,4] => 8
[3,6,2,5,4,1] => 8
[3,6,4,1,2,5] => 8
[3,6,4,1,5,2] => 8
[3,6,4,2,1,5] => 8
[3,6,4,2,5,1] => 8
[3,6,4,5,1,2] => 9
[3,6,4,5,2,1] => 9
[3,6,5,1,2,4] => 10
[3,6,5,1,4,2] => 10
[3,6,5,2,1,4] => 10
[3,6,5,2,4,1] => 10
[3,6,5,4,1,2] => 11
[3,6,5,4,2,1] => 11
[4,1,2,3,5,6] => 3
[4,1,2,3,6,5] => 3
[4,1,2,5,3,6] => 3
[4,1,2,5,6,3] => 3
[4,1,2,6,3,5] => 4
[4,1,2,6,5,3] => 4
[4,1,3,2,5,6] => 3
[4,1,3,2,6,5] => 3
[4,1,3,5,2,6] => 3
[4,1,3,5,6,2] => 3
[4,1,3,6,2,5] => 4
[4,1,3,6,5,2] => 4
[4,1,5,2,3,6] => 4
[4,1,5,2,6,3] => 4
[4,1,5,3,2,6] => 4
[4,1,5,3,6,2] => 4
[4,1,5,6,2,3] => 5
[4,1,5,6,3,2] => 5
[4,1,6,2,3,5] => 6
[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] => 7
[4,1,6,5,3,2] => 7
[4,2,1,3,5,6] => 3
[4,2,1,3,6,5] => 3
[4,2,1,5,3,6] => 3
[4,2,1,5,6,3] => 3
[4,2,1,6,3,5] => 4
[4,2,1,6,5,3] => 4
[4,2,3,1,5,6] => 3
[4,2,3,1,6,5] => 3
[4,2,3,5,1,6] => 3
[4,2,3,5,6,1] => 3
[4,2,3,6,1,5] => 4
[4,2,3,6,5,1] => 4
[4,2,5,1,3,6] => 4
[4,2,5,1,6,3] => 4
[4,2,5,3,1,6] => 4
[4,2,5,3,6,1] => 4
[4,2,5,6,1,3] => 5
[4,2,5,6,3,1] => 5
[4,2,6,1,3,5] => 6
[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] => 7
[4,2,6,5,3,1] => 7
[4,3,1,2,5,6] => 4
[4,3,1,2,6,5] => 4
[4,3,1,5,2,6] => 4
[4,3,1,5,6,2] => 4
[4,3,1,6,2,5] => 5
[4,3,1,6,5,2] => 5
[4,3,2,1,5,6] => 4
[4,3,2,1,6,5] => 4
[4,3,2,5,1,6] => 4
[4,3,2,5,6,1] => 4
[4,3,2,6,1,5] => 5
[4,3,2,6,5,1] => 5
[4,3,5,1,2,6] => 5
[4,3,5,1,6,2] => 5
[4,3,5,2,1,6] => 5
[4,3,5,2,6,1] => 5
[4,3,5,6,1,2] => 6
[4,3,5,6,2,1] => 6
[4,3,6,1,2,5] => 7
[4,3,6,1,5,2] => 7
[4,3,6,2,1,5] => 7
[4,3,6,2,5,1] => 7
[4,3,6,5,1,2] => 8
[4,3,6,5,2,1] => 8
[4,5,1,2,3,6] => 6
[4,5,1,2,6,3] => 6
[4,5,1,3,2,6] => 6
[4,5,1,3,6,2] => 6
[4,5,1,6,2,3] => 7
[4,5,1,6,3,2] => 7
[4,5,2,1,3,6] => 6
[4,5,2,1,6,3] => 6
[4,5,2,3,1,6] => 6
[4,5,2,3,6,1] => 6
[4,5,2,6,1,3] => 7
[4,5,2,6,3,1] => 7
[4,5,3,1,2,6] => 7
[4,5,3,1,6,2] => 7
[4,5,3,2,1,6] => 7
[4,5,3,2,6,1] => 7
[4,5,3,6,1,2] => 8
[4,5,3,6,2,1] => 8
[4,5,6,1,2,3] => 9
[4,5,6,1,3,2] => 9
[4,5,6,2,1,3] => 9
[4,5,6,2,3,1] => 9
[4,5,6,3,1,2] => 10
[4,5,6,3,2,1] => 10
[4,6,1,2,3,5] => 9
[4,6,1,2,5,3] => 9
[4,6,1,3,2,5] => 9
[4,6,1,3,5,2] => 9
[4,6,1,5,2,3] => 10
[4,6,1,5,3,2] => 10
[4,6,2,1,3,5] => 9
[4,6,2,1,5,3] => 9
[4,6,2,3,1,5] => 9
[4,6,2,3,5,1] => 9
[4,6,2,5,1,3] => 10
[4,6,2,5,3,1] => 10
[4,6,3,1,2,5] => 10
[4,6,3,1,5,2] => 10
[4,6,3,2,1,5] => 10
[4,6,3,2,5,1] => 10
[4,6,3,5,1,2] => 11
[4,6,3,5,2,1] => 11
[4,6,5,1,2,3] => 12
[4,6,5,1,3,2] => 12
[4,6,5,2,1,3] => 12
[4,6,5,2,3,1] => 12
[4,6,5,3,1,2] => 13
[4,6,5,3,2,1] => 13
[5,1,2,3,4,6] => 6
[5,1,2,3,6,4] => 6
[5,1,2,4,3,6] => 6
[5,1,2,4,6,3] => 6
[5,1,2,6,3,4] => 7
[5,1,2,6,4,3] => 7
[5,1,3,2,4,6] => 6
[5,1,3,2,6,4] => 6
[5,1,3,4,2,6] => 6
[5,1,3,4,6,2] => 6
[5,1,3,6,2,4] => 7
[5,1,3,6,4,2] => 7
[5,1,4,2,3,6] => 7
[5,1,4,2,6,3] => 7
[5,1,4,3,2,6] => 7
[5,1,4,3,6,2] => 7
[5,1,4,6,2,3] => 8
[5,1,4,6,3,2] => 8
[5,1,6,2,3,4] => 9
[5,1,6,2,4,3] => 9
[5,1,6,3,2,4] => 9
[5,1,6,3,4,2] => 9
[5,1,6,4,2,3] => 10
[5,1,6,4,3,2] => 10
[5,2,1,3,4,6] => 6
[5,2,1,3,6,4] => 6
[5,2,1,4,3,6] => 6
[5,2,1,4,6,3] => 6
[5,2,1,6,3,4] => 7
[5,2,1,6,4,3] => 7
[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] => 7
[5,2,3,6,4,1] => 7
[5,2,4,1,3,6] => 7
[5,2,4,1,6,3] => 7
[5,2,4,3,1,6] => 7
[5,2,4,3,6,1] => 7
[5,2,4,6,1,3] => 8
[5,2,4,6,3,1] => 8
[5,2,6,1,3,4] => 9
[5,2,6,1,4,3] => 9
[5,2,6,3,1,4] => 9
[5,2,6,3,4,1] => 9
[5,2,6,4,1,3] => 10
[5,2,6,4,3,1] => 10
[5,3,1,2,4,6] => 7
[5,3,1,2,6,4] => 7
[5,3,1,4,2,6] => 7
[5,3,1,4,6,2] => 7
[5,3,1,6,2,4] => 8
[5,3,1,6,4,2] => 8
[5,3,2,1,4,6] => 7
[5,3,2,1,6,4] => 7
[5,3,2,4,1,6] => 7
[5,3,2,4,6,1] => 7
[5,3,2,6,1,4] => 8
[5,3,2,6,4,1] => 8
[5,3,4,1,2,6] => 8
[5,3,4,1,6,2] => 8
[5,3,4,2,1,6] => 8
[5,3,4,2,6,1] => 8
[5,3,4,6,1,2] => 9
[5,3,4,6,2,1] => 9
[5,3,6,1,2,4] => 10
[5,3,6,1,4,2] => 10
[5,3,6,2,1,4] => 10
[5,3,6,2,4,1] => 10
[5,3,6,4,1,2] => 11
[5,3,6,4,2,1] => 11
[5,4,1,2,3,6] => 9
[5,4,1,2,6,3] => 9
[5,4,1,3,2,6] => 9
[5,4,1,3,6,2] => 9
[5,4,1,6,2,3] => 10
[5,4,1,6,3,2] => 10
[5,4,2,1,3,6] => 9
[5,4,2,1,6,3] => 9
[5,4,2,3,1,6] => 9
[5,4,2,3,6,1] => 9
[5,4,2,6,1,3] => 10
[5,4,2,6,3,1] => 10
[5,4,3,1,2,6] => 10
[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] => 11
[5,4,3,6,2,1] => 11
[5,4,6,1,2,3] => 12
[5,4,6,1,3,2] => 12
[5,4,6,2,1,3] => 12
[5,4,6,2,3,1] => 12
[5,4,6,3,1,2] => 13
[5,4,6,3,2,1] => 13
[5,6,1,2,3,4] => 12
[5,6,1,2,4,3] => 12
[5,6,1,3,2,4] => 12
[5,6,1,3,4,2] => 12
[5,6,1,4,2,3] => 13
[5,6,1,4,3,2] => 13
[5,6,2,1,3,4] => 12
[5,6,2,1,4,3] => 12
[5,6,2,3,1,4] => 12
[5,6,2,3,4,1] => 12
[5,6,2,4,1,3] => 13
[5,6,2,4,3,1] => 13
[5,6,3,1,2,4] => 13
[5,6,3,1,4,2] => 13
[5,6,3,2,1,4] => 13
[5,6,3,2,4,1] => 13
[5,6,3,4,1,2] => 14
[5,6,3,4,2,1] => 14
[5,6,4,1,2,3] => 15
[5,6,4,1,3,2] => 15
[5,6,4,2,1,3] => 15
[5,6,4,2,3,1] => 15
[5,6,4,3,1,2] => 16
[5,6,4,3,2,1] => 16
[6,1,2,3,4,5] => 10
[6,1,2,3,5,4] => 10
[6,1,2,4,3,5] => 10
[6,1,2,4,5,3] => 10
[6,1,2,5,3,4] => 11
[6,1,2,5,4,3] => 11
[6,1,3,2,4,5] => 10
[6,1,3,2,5,4] => 10
[6,1,3,4,2,5] => 10
[6,1,3,4,5,2] => 10
[6,1,3,5,2,4] => 11
[6,1,3,5,4,2] => 11
[6,1,4,2,3,5] => 11
[6,1,4,2,5,3] => 11
[6,1,4,3,2,5] => 11
[6,1,4,3,5,2] => 11
[6,1,4,5,2,3] => 12
[6,1,4,5,3,2] => 12
[6,1,5,2,3,4] => 13
[6,1,5,2,4,3] => 13
[6,1,5,3,2,4] => 13
[6,1,5,3,4,2] => 13
[6,1,5,4,2,3] => 14
[6,1,5,4,3,2] => 14
[6,2,1,3,4,5] => 10
[6,2,1,3,5,4] => 10
[6,2,1,4,3,5] => 10
[6,2,1,4,5,3] => 10
[6,2,1,5,3,4] => 11
[6,2,1,5,4,3] => 11
[6,2,3,1,4,5] => 10
[6,2,3,1,5,4] => 10
[6,2,3,4,1,5] => 10
[6,2,3,4,5,1] => 10
[6,2,3,5,1,4] => 11
[6,2,3,5,4,1] => 11
[6,2,4,1,3,5] => 11
[6,2,4,1,5,3] => 11
[6,2,4,3,1,5] => 11
[6,2,4,3,5,1] => 11
[6,2,4,5,1,3] => 12
[6,2,4,5,3,1] => 12
[6,2,5,1,3,4] => 13
[6,2,5,1,4,3] => 13
[6,2,5,3,1,4] => 13
[6,2,5,3,4,1] => 13
[6,2,5,4,1,3] => 14
[6,2,5,4,3,1] => 14
[6,3,1,2,4,5] => 11
[6,3,1,2,5,4] => 11
[6,3,1,4,2,5] => 11
[6,3,1,4,5,2] => 11
[6,3,1,5,2,4] => 12
[6,3,1,5,4,2] => 12
[6,3,2,1,4,5] => 11
[6,3,2,1,5,4] => 11
[6,3,2,4,1,5] => 11
[6,3,2,4,5,1] => 11
[6,3,2,5,1,4] => 12
[6,3,2,5,4,1] => 12
[6,3,4,1,2,5] => 12
[6,3,4,1,5,2] => 12
[6,3,4,2,1,5] => 12
[6,3,4,2,5,1] => 12
[6,3,4,5,1,2] => 13
[6,3,4,5,2,1] => 13
[6,3,5,1,2,4] => 14
[6,3,5,1,4,2] => 14
[6,3,5,2,1,4] => 14
[6,3,5,2,4,1] => 14
[6,3,5,4,1,2] => 15
[6,3,5,4,2,1] => 15
[6,4,1,2,3,5] => 13
[6,4,1,2,5,3] => 13
[6,4,1,3,2,5] => 13
[6,4,1,3,5,2] => 13
[6,4,1,5,2,3] => 14
[6,4,1,5,3,2] => 14
[6,4,2,1,3,5] => 13
[6,4,2,1,5,3] => 13
[6,4,2,3,1,5] => 13
[6,4,2,3,5,1] => 13
[6,4,2,5,1,3] => 14
[6,4,2,5,3,1] => 14
[6,4,3,1,2,5] => 14
[6,4,3,1,5,2] => 14
[6,4,3,2,1,5] => 14
[6,4,3,2,5,1] => 14
[6,4,3,5,1,2] => 15
[6,4,3,5,2,1] => 15
[6,4,5,1,2,3] => 16
[6,4,5,1,3,2] => 16
[6,4,5,2,1,3] => 16
[6,4,5,2,3,1] => 16
[6,4,5,3,1,2] => 17
[6,4,5,3,2,1] => 17
[6,5,1,2,3,4] => 16
[6,5,1,2,4,3] => 16
[6,5,1,3,2,4] => 16
[6,5,1,3,4,2] => 16
[6,5,1,4,2,3] => 17
[6,5,1,4,3,2] => 17
[6,5,2,1,3,4] => 16
[6,5,2,1,4,3] => 16
[6,5,2,3,1,4] => 16
[6,5,2,3,4,1] => 16
[6,5,2,4,1,3] => 17
[6,5,2,4,3,1] => 17
[6,5,3,1,2,4] => 17
[6,5,3,1,4,2] => 17
[6,5,3,2,1,4] => 17
[6,5,3,2,4,1] => 17
[6,5,3,4,1,2] => 18
[6,5,3,4,2,1] => 18
[6,5,4,1,2,3] => 19
[6,5,4,1,3,2] => 19
[6,5,4,2,1,3] => 19
[6,5,4,2,3,1] => 19
[6,5,4,3,1,2] => 20
[6,5,4,3,2,1] => 20
[1,2,3,4,5,6,7] => 0
[1,2,3,4,5,7,6] => 0
[1,2,3,4,6,5,7] => 0
[1,2,3,4,6,7,5] => 0
[1,2,3,4,7,5,6] => 1
[1,2,3,4,7,6,5] => 1
[1,2,3,5,4,6,7] => 0
[1,2,3,5,4,7,6] => 0
[1,2,3,5,6,4,7] => 0
[1,2,3,5,6,7,4] => 0
[1,2,3,5,7,4,6] => 1
[1,2,3,5,7,6,4] => 1
[1,2,3,6,4,5,7] => 1
[1,2,3,6,4,7,5] => 1
[1,2,3,6,5,4,7] => 1
[1,2,3,6,5,7,4] => 1
[1,2,3,6,7,4,5] => 2
[1,2,3,6,7,5,4] => 2
[1,2,3,7,4,5,6] => 3
[1,2,3,7,4,6,5] => 3
[1,2,3,7,5,4,6] => 3
[1,2,3,7,5,6,4] => 3
[1,2,3,7,6,4,5] => 4
[1,2,3,7,6,5,4] => 4
[1,2,4,3,5,6,7] => 0
[1,2,4,3,5,7,6] => 0
[1,2,4,3,6,5,7] => 0
[1,2,4,3,6,7,5] => 0
[1,2,4,3,7,5,6] => 1
[1,2,4,3,7,6,5] => 1
[1,2,4,5,3,6,7] => 0
[1,2,4,5,3,7,6] => 0
[1,2,4,5,6,3,7] => 0
[1,2,4,5,6,7,3] => 0
[1,2,4,5,7,3,6] => 1
[1,2,4,5,7,6,3] => 1
[1,2,4,6,3,5,7] => 1
[1,2,4,6,3,7,5] => 1
[1,2,4,6,5,3,7] => 1
[1,2,4,6,5,7,3] => 1
[1,2,4,6,7,3,5] => 2
[1,2,4,6,7,5,3] => 2
[1,2,4,7,3,5,6] => 3
[1,2,4,7,3,6,5] => 3
[1,2,4,7,5,3,6] => 3
[1,2,4,7,5,6,3] => 3
[1,2,4,7,6,3,5] => 4
[1,2,4,7,6,5,3] => 4
[1,2,5,3,4,6,7] => 1
[1,2,5,3,4,7,6] => 1
[1,2,5,3,6,4,7] => 1
[1,2,5,3,6,7,4] => 1
[1,2,5,3,7,4,6] => 2
[1,2,5,3,7,6,4] => 2
[1,2,5,4,3,6,7] => 1
[1,2,5,4,3,7,6] => 1
[1,2,5,4,6,3,7] => 1
[1,2,5,4,6,7,3] => 1
[1,2,5,4,7,3,6] => 2
[1,2,5,4,7,6,3] => 2
[1,2,5,6,3,4,7] => 2
[1,2,5,6,3,7,4] => 2
[1,2,5,6,4,3,7] => 2
[1,2,5,6,4,7,3] => 2
[1,2,5,6,7,3,4] => 3
[1,2,5,6,7,4,3] => 3
[1,2,5,7,3,4,6] => 4
[1,2,5,7,3,6,4] => 4
[1,2,5,7,4,3,6] => 4
[1,2,5,7,4,6,3] => 4
[1,2,5,7,6,3,4] => 5
[1,2,5,7,6,4,3] => 5
[1,2,6,3,4,5,7] => 3
[1,2,6,3,4,7,5] => 3
[1,2,6,3,5,4,7] => 3
[1,2,6,3,5,7,4] => 3
[1,2,6,3,7,4,5] => 4
[1,2,6,3,7,5,4] => 4
[1,2,6,4,3,5,7] => 3
[1,2,6,4,3,7,5] => 3
[1,2,6,4,5,3,7] => 3
[1,2,6,4,5,7,3] => 3
[1,2,6,4,7,3,5] => 4
[1,2,6,4,7,5,3] => 4
[1,2,6,5,3,4,7] => 4
[1,2,6,5,3,7,4] => 4
[1,2,6,5,4,3,7] => 4
[1,2,6,5,4,7,3] => 4
[1,2,6,5,7,3,4] => 5
[1,2,6,5,7,4,3] => 5
[1,2,6,7,3,4,5] => 6
[1,2,6,7,3,5,4] => 6
[1,2,6,7,4,3,5] => 6
[1,2,6,7,4,5,3] => 6
[1,2,6,7,5,3,4] => 7
[1,2,6,7,5,4,3] => 7
[1,2,7,3,4,5,6] => 6
[1,2,7,3,4,6,5] => 6
[1,2,7,3,5,4,6] => 6
[1,2,7,3,5,6,4] => 6
[1,2,7,3,6,4,5] => 7
[1,2,7,3,6,5,4] => 7
[1,2,7,4,3,5,6] => 6
[1,2,7,4,3,6,5] => 6
[1,2,7,4,5,3,6] => 6
[1,2,7,4,5,6,3] => 6
[1,2,7,4,6,3,5] => 7
[1,2,7,4,6,5,3] => 7
[1,2,7,5,3,4,6] => 7
[1,2,7,5,3,6,4] => 7
[1,2,7,5,4,3,6] => 7
[1,2,7,5,4,6,3] => 7
[1,2,7,5,6,3,4] => 8
[1,2,7,5,6,4,3] => 8
[1,2,7,6,3,4,5] => 9
[1,2,7,6,3,5,4] => 9
[1,2,7,6,4,3,5] => 9
[1,2,7,6,4,5,3] => 9
[1,2,7,6,5,3,4] => 10
[1,2,7,6,5,4,3] => 10
[1,3,2,4,5,6,7] => 0
[1,3,2,4,5,7,6] => 0
[1,3,2,4,6,5,7] => 0
[1,3,2,4,6,7,5] => 0
[1,3,2,4,7,5,6] => 1
[1,3,2,4,7,6,5] => 1
[1,3,2,5,4,6,7] => 0
[1,3,2,5,4,7,6] => 0
[1,3,2,5,6,4,7] => 0
[1,3,2,5,6,7,4] => 0
[1,3,2,5,7,4,6] => 1
[1,3,2,5,7,6,4] => 1
[1,3,2,6,4,5,7] => 1
[1,3,2,6,4,7,5] => 1
[1,3,2,6,5,4,7] => 1
[1,3,2,6,5,7,4] => 1
[1,3,2,6,7,4,5] => 2
[1,3,2,6,7,5,4] => 2
[1,3,2,7,4,5,6] => 3
[1,3,2,7,4,6,5] => 3
[1,3,2,7,5,4,6] => 3
[1,3,2,7,5,6,4] => 3
[1,3,2,7,6,4,5] => 4
[1,3,2,7,6,5,4] => 4
[1,3,4,2,5,6,7] => 0
[1,3,4,2,5,7,6] => 0
[1,3,4,2,6,5,7] => 0
[1,3,4,2,6,7,5] => 0
[1,3,4,2,7,5,6] => 1
[1,3,4,2,7,6,5] => 1
[1,3,4,5,2,6,7] => 0
[1,3,4,5,2,7,6] => 0
[1,3,4,5,6,2,7] => 0
[1,3,4,5,6,7,2] => 0
[1,3,4,5,7,2,6] => 1
[1,3,4,5,7,6,2] => 1
[1,3,4,6,2,5,7] => 1
[1,3,4,6,2,7,5] => 1
[1,3,4,6,5,2,7] => 1
[1,3,4,6,5,7,2] => 1
[1,3,4,6,7,2,5] => 2
[1,3,4,6,7,5,2] => 2
[1,3,4,7,2,5,6] => 3
[1,3,4,7,2,6,5] => 3
[1,3,4,7,5,2,6] => 3
[1,3,4,7,5,6,2] => 3
[1,3,4,7,6,2,5] => 4
[1,3,4,7,6,5,2] => 4
[1,3,5,2,4,6,7] => 1
[1,3,5,2,4,7,6] => 1
[1,3,5,2,6,4,7] => 1
[1,3,5,2,6,7,4] => 1
[1,3,5,2,7,4,6] => 2
[1,3,5,2,7,6,4] => 2
[1,3,5,4,2,6,7] => 1
[1,3,5,4,2,7,6] => 1
[1,3,5,4,6,2,7] => 1
[1,3,5,4,6,7,2] => 1
[1,3,5,4,7,2,6] => 2
[1,3,5,4,7,6,2] => 2
[1,3,5,6,2,4,7] => 2
[1,3,5,6,2,7,4] => 2
[1,3,5,6,4,2,7] => 2
[1,3,5,6,4,7,2] => 2
[1,3,5,6,7,2,4] => 3
[1,3,5,6,7,4,2] => 3
[1,3,5,7,2,4,6] => 4
[1,3,5,7,2,6,4] => 4
[1,3,5,7,4,2,6] => 4
[1,3,5,7,4,6,2] => 4
[1,3,5,7,6,2,4] => 5
[1,3,5,7,6,4,2] => 5
[1,3,6,2,4,5,7] => 3
[1,3,6,2,4,7,5] => 3
[1,3,6,2,5,4,7] => 3
[1,3,6,2,5,7,4] => 3
[1,3,6,2,7,4,5] => 4
[1,3,6,2,7,5,4] => 4
[1,3,6,4,2,5,7] => 3
[1,3,6,4,2,7,5] => 3
[1,3,6,4,5,2,7] => 3
[1,3,6,4,5,7,2] => 3
[1,3,6,4,7,2,5] => 4
[1,3,6,4,7,5,2] => 4
[1,3,6,5,2,4,7] => 4
[1,3,6,5,2,7,4] => 4
[1,3,6,5,4,2,7] => 4
[1,3,6,5,4,7,2] => 4
[1,3,6,5,7,2,4] => 5
[1,3,6,5,7,4,2] => 5
[1,3,6,7,2,4,5] => 6
[1,3,6,7,2,5,4] => 6
[1,3,6,7,4,2,5] => 6
[1,3,6,7,4,5,2] => 6
[1,3,6,7,5,2,4] => 7
[1,3,6,7,5,4,2] => 7
[1,3,7,2,4,5,6] => 6
[1,3,7,2,4,6,5] => 6
[1,3,7,2,5,4,6] => 6
[1,3,7,2,5,6,4] => 6
[1,3,7,2,6,4,5] => 7
[1,3,7,2,6,5,4] => 7
[1,3,7,4,2,5,6] => 6
[1,3,7,4,2,6,5] => 6
[1,3,7,4,5,2,6] => 6
[1,3,7,4,5,6,2] => 6
[1,3,7,4,6,2,5] => 7
[1,3,7,4,6,5,2] => 7
[1,3,7,5,2,4,6] => 7
[1,3,7,5,2,6,4] => 7
[1,3,7,5,4,2,6] => 7
[1,3,7,5,4,6,2] => 7
[1,3,7,5,6,2,4] => 8
[1,3,7,5,6,4,2] => 8
[1,3,7,6,2,4,5] => 9
[1,3,7,6,2,5,4] => 9
[1,3,7,6,4,2,5] => 9
[1,3,7,6,4,5,2] => 9
[1,3,7,6,5,2,4] => 10
[1,3,7,6,5,4,2] => 10
[1,4,2,3,5,6,7] => 1
[1,4,2,3,5,7,6] => 1
[1,4,2,3,6,5,7] => 1
[1,4,2,3,6,7,5] => 1
[1,4,2,3,7,5,6] => 2
[1,4,2,3,7,6,5] => 2
[1,4,2,5,3,6,7] => 1
[1,4,2,5,3,7,6] => 1
[1,4,2,5,6,3,7] => 1
[1,4,2,5,6,7,3] => 1
[1,4,2,5,7,3,6] => 2
[1,4,2,5,7,6,3] => 2
[1,4,2,6,3,5,7] => 2
[1,4,2,6,3,7,5] => 2
[1,4,2,6,5,3,7] => 2
[1,4,2,6,5,7,3] => 2
[1,4,2,6,7,3,5] => 3
[1,4,2,6,7,5,3] => 3
[1,4,2,7,3,5,6] => 4
[1,4,2,7,3,6,5] => 4
[1,4,2,7,5,3,6] => 4
[1,4,2,7,5,6,3] => 4
[1,4,2,7,6,3,5] => 5
[1,4,2,7,6,5,3] => 5
[1,4,3,2,5,6,7] => 1
[1,4,3,2,5,7,6] => 1
[1,4,3,2,6,5,7] => 1
[1,4,3,2,6,7,5] => 1
[1,4,3,2,7,5,6] => 2
[1,4,3,2,7,6,5] => 2
[1,4,3,5,2,6,7] => 1
[1,4,3,5,2,7,6] => 1
[1,4,3,5,6,2,7] => 1
[1,4,3,5,6,7,2] => 1
[1,4,3,5,7,2,6] => 2
[1,4,3,5,7,6,2] => 2
[1,4,3,6,2,5,7] => 2
[1,4,3,6,2,7,5] => 2
[1,4,3,6,5,2,7] => 2
[1,4,3,6,5,7,2] => 2
[1,4,3,6,7,2,5] => 3
[1,4,3,6,7,5,2] => 3
[1,4,3,7,2,5,6] => 4
[1,4,3,7,2,6,5] => 4
[1,4,3,7,5,2,6] => 4
[1,4,3,7,5,6,2] => 4
[1,4,3,7,6,2,5] => 5
[1,4,3,7,6,5,2] => 5
[1,4,5,2,3,6,7] => 2
[1,4,5,2,3,7,6] => 2
[1,4,5,2,6,3,7] => 2
[1,4,5,2,6,7,3] => 2
[1,4,5,2,7,3,6] => 3
[1,4,5,2,7,6,3] => 3
[1,4,5,3,2,6,7] => 2
[1,4,5,3,2,7,6] => 2
[1,4,5,3,6,2,7] => 2
[1,4,5,3,6,7,2] => 2
[1,4,5,3,7,2,6] => 3
[1,4,5,3,7,6,2] => 3
[1,4,5,6,2,3,7] => 3
[1,4,5,6,2,7,3] => 3
[1,4,5,6,3,2,7] => 3
[1,4,5,6,3,7,2] => 3
[1,4,5,6,7,2,3] => 4
[1,4,5,6,7,3,2] => 4
[1,4,5,7,2,3,6] => 5
[1,4,5,7,2,6,3] => 5
[1,4,5,7,3,2,6] => 5
[1,4,5,7,3,6,2] => 5
[1,4,5,7,6,2,3] => 6
[1,4,5,7,6,3,2] => 6
[1,4,6,2,3,5,7] => 4
[1,4,6,2,3,7,5] => 4
[1,4,6,2,5,3,7] => 4
[1,4,6,2,5,7,3] => 4
[1,4,6,2,7,3,5] => 5
[1,4,6,2,7,5,3] => 5
[1,4,6,3,2,5,7] => 4
[1,4,6,3,2,7,5] => 4
[1,4,6,3,5,2,7] => 4
[1,4,6,3,5,7,2] => 4
[1,4,6,3,7,2,5] => 5
[1,4,6,3,7,5,2] => 5
[1,4,6,5,2,3,7] => 5
[1,4,6,5,2,7,3] => 5
[1,4,6,5,3,2,7] => 5
[1,4,6,5,3,7,2] => 5
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Generating function
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Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,2 8,8,2,4,2 16,24,12,18,16,4,12,10,2,4,2 32,64,48,64,74,36,62,72,30,40,50,32,28,30,18,8,14,10,2,4,2
$F_{2} = 2$
$F_{3} = 4 + 2\ q$
$F_{4} = 8 + 8\ q + 2\ q^{2} + 4\ q^{3} + 2\ q^{4}$
$F_{5} = 16 + 24\ q + 12\ q^{2} + 18\ q^{3} + 16\ q^{4} + 4\ q^{5} + 12\ q^{6} + 10\ q^{7} + 2\ q^{8} + 4\ q^{9} + 2\ q^{10}$
$F_{6} = 32 + 64\ q + 48\ q^{2} + 64\ q^{3} + 74\ q^{4} + 36\ q^{5} + 62\ q^{6} + 72\ q^{7} + 30\ q^{8} + 40\ q^{9} + 50\ q^{10} + 32\ q^{11} + 28\ q^{12} + 30\ q^{13} + 18\ q^{14} + 8\ q^{15} + 14\ q^{16} + 10\ q^{17} + 2\ q^{18} + 4\ q^{19} + 2\ q^{20}$
Description
The number of occurrences of the pattern 312 or of the pattern 321 in a permutation.
Code
def statistic(pi):
return len(pi.pattern_positions([3, 1, 2]))+len(pi.pattern_positions([3, 2, 1]))
Created
Feb 26, 2016 at 12:47 by Martin Rubey
Updated
Feb 26, 2016 at 12:47 by Martin Rubey
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