Identifier
- St001379: Permutations ⟶ ℤ
Values
[1] => 0
[1,2] => 0
[2,1] => 2
[1,2,3] => 0
[1,3,2] => 3
[2,1,3] => 2
[2,3,1] => 4
[3,1,2] => 3
[3,2,1] => 6
[1,2,3,4] => 0
[1,2,4,3] => 4
[1,3,2,4] => 3
[1,3,4,2] => 5
[1,4,2,3] => 4
[1,4,3,2] => 8
[2,1,3,4] => 2
[2,1,4,3] => 6
[2,3,1,4] => 4
[2,3,4,1] => 6
[2,4,1,3] => 5
[2,4,3,1] => 9
[3,1,2,4] => 3
[3,1,4,2] => 7
[3,2,1,4] => 6
[3,2,4,1] => 8
[3,4,1,2] => 6
[3,4,2,1] => 10
[4,1,2,3] => 4
[4,1,3,2] => 8
[4,2,1,3] => 7
[4,2,3,1] => 9
[4,3,1,2] => 8
[4,3,2,1] => 12
[1,2,3,4,5] => 0
[1,2,3,5,4] => 5
[1,2,4,3,5] => 4
[1,2,4,5,3] => 6
[1,2,5,3,4] => 5
[1,2,5,4,3] => 10
[1,3,2,4,5] => 3
[1,3,2,5,4] => 8
[1,3,4,2,5] => 5
[1,3,4,5,2] => 7
[1,3,5,2,4] => 6
[1,3,5,4,2] => 11
[1,4,2,3,5] => 4
[1,4,2,5,3] => 9
[1,4,3,2,5] => 8
[1,4,3,5,2] => 10
[1,4,5,2,3] => 7
[1,4,5,3,2] => 12
[1,5,2,3,4] => 5
[1,5,2,4,3] => 10
[1,5,3,2,4] => 9
[1,5,3,4,2] => 11
[1,5,4,2,3] => 10
[1,5,4,3,2] => 15
[2,1,3,4,5] => 2
[2,1,3,5,4] => 7
[2,1,4,3,5] => 6
[2,1,4,5,3] => 8
[2,1,5,3,4] => 7
[2,1,5,4,3] => 12
[2,3,1,4,5] => 4
[2,3,1,5,4] => 9
[2,3,4,1,5] => 6
[2,3,4,5,1] => 8
[2,3,5,1,4] => 7
[2,3,5,4,1] => 12
[2,4,1,3,5] => 5
[2,4,1,5,3] => 10
[2,4,3,1,5] => 9
[2,4,3,5,1] => 11
[2,4,5,1,3] => 8
[2,4,5,3,1] => 13
[2,5,1,3,4] => 6
[2,5,1,4,3] => 11
[2,5,3,1,4] => 10
[2,5,3,4,1] => 12
[2,5,4,1,3] => 11
[2,5,4,3,1] => 16
[3,1,2,4,5] => 3
[3,1,2,5,4] => 8
[3,1,4,2,5] => 7
[3,1,4,5,2] => 9
[3,1,5,2,4] => 8
[3,1,5,4,2] => 13
[3,2,1,4,5] => 6
[3,2,1,5,4] => 11
[3,2,4,1,5] => 8
[3,2,4,5,1] => 10
[3,2,5,1,4] => 9
[3,2,5,4,1] => 14
[3,4,1,2,5] => 6
[3,4,1,5,2] => 11
[3,4,2,1,5] => 10
[3,4,2,5,1] => 12
[3,4,5,1,2] => 9
[3,4,5,2,1] => 14
[3,5,1,2,4] => 7
[3,5,1,4,2] => 12
>>> Load all 1200 entries. <<<[3,5,2,1,4] => 11
[3,5,2,4,1] => 13
[3,5,4,1,2] => 12
[3,5,4,2,1] => 17
[4,1,2,3,5] => 4
[4,1,2,5,3] => 9
[4,1,3,2,5] => 8
[4,1,3,5,2] => 10
[4,1,5,2,3] => 9
[4,1,5,3,2] => 14
[4,2,1,3,5] => 7
[4,2,1,5,3] => 12
[4,2,3,1,5] => 9
[4,2,3,5,1] => 11
[4,2,5,1,3] => 10
[4,2,5,3,1] => 15
[4,3,1,2,5] => 8
[4,3,1,5,2] => 13
[4,3,2,1,5] => 12
[4,3,2,5,1] => 14
[4,3,5,1,2] => 11
[4,3,5,2,1] => 16
[4,5,1,2,3] => 8
[4,5,1,3,2] => 13
[4,5,2,1,3] => 12
[4,5,2,3,1] => 14
[4,5,3,1,2] => 13
[4,5,3,2,1] => 18
[5,1,2,3,4] => 5
[5,1,2,4,3] => 10
[5,1,3,2,4] => 9
[5,1,3,4,2] => 11
[5,1,4,2,3] => 10
[5,1,4,3,2] => 15
[5,2,1,3,4] => 8
[5,2,1,4,3] => 13
[5,2,3,1,4] => 10
[5,2,3,4,1] => 12
[5,2,4,1,3] => 11
[5,2,4,3,1] => 16
[5,3,1,2,4] => 9
[5,3,1,4,2] => 14
[5,3,2,1,4] => 13
[5,3,2,4,1] => 15
[5,3,4,1,2] => 12
[5,3,4,2,1] => 17
[5,4,1,2,3] => 10
[5,4,1,3,2] => 15
[5,4,2,1,3] => 14
[5,4,2,3,1] => 16
[5,4,3,1,2] => 15
[5,4,3,2,1] => 20
[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] => 7
[1,2,3,6,4,5] => 6
[1,2,3,6,5,4] => 12
[1,2,4,3,5,6] => 4
[1,2,4,3,6,5] => 10
[1,2,4,5,3,6] => 6
[1,2,4,5,6,3] => 8
[1,2,4,6,3,5] => 7
[1,2,4,6,5,3] => 13
[1,2,5,3,4,6] => 5
[1,2,5,3,6,4] => 11
[1,2,5,4,3,6] => 10
[1,2,5,4,6,3] => 12
[1,2,5,6,3,4] => 8
[1,2,5,6,4,3] => 14
[1,2,6,3,4,5] => 6
[1,2,6,3,5,4] => 12
[1,2,6,4,3,5] => 11
[1,2,6,4,5,3] => 13
[1,2,6,5,3,4] => 12
[1,2,6,5,4,3] => 18
[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] => 10
[1,3,2,6,4,5] => 9
[1,3,2,6,5,4] => 15
[1,3,4,2,5,6] => 5
[1,3,4,2,6,5] => 11
[1,3,4,5,2,6] => 7
[1,3,4,5,6,2] => 9
[1,3,4,6,2,5] => 8
[1,3,4,6,5,2] => 14
[1,3,5,2,4,6] => 6
[1,3,5,2,6,4] => 12
[1,3,5,4,2,6] => 11
[1,3,5,4,6,2] => 13
[1,3,5,6,2,4] => 9
[1,3,5,6,4,2] => 15
[1,3,6,2,4,5] => 7
[1,3,6,2,5,4] => 13
[1,3,6,4,2,5] => 12
[1,3,6,4,5,2] => 14
[1,3,6,5,2,4] => 13
[1,3,6,5,4,2] => 19
[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] => 11
[1,4,2,6,3,5] => 10
[1,4,2,6,5,3] => 16
[1,4,3,2,5,6] => 8
[1,4,3,2,6,5] => 14
[1,4,3,5,2,6] => 10
[1,4,3,5,6,2] => 12
[1,4,3,6,2,5] => 11
[1,4,3,6,5,2] => 17
[1,4,5,2,3,6] => 7
[1,4,5,2,6,3] => 13
[1,4,5,3,2,6] => 12
[1,4,5,3,6,2] => 14
[1,4,5,6,2,3] => 10
[1,4,5,6,3,2] => 16
[1,4,6,2,3,5] => 8
[1,4,6,2,5,3] => 14
[1,4,6,3,2,5] => 13
[1,4,6,3,5,2] => 15
[1,4,6,5,2,3] => 14
[1,4,6,5,3,2] => 20
[1,5,2,3,4,6] => 5
[1,5,2,3,6,4] => 11
[1,5,2,4,3,6] => 10
[1,5,2,4,6,3] => 12
[1,5,2,6,3,4] => 11
[1,5,2,6,4,3] => 17
[1,5,3,2,4,6] => 9
[1,5,3,2,6,4] => 15
[1,5,3,4,2,6] => 11
[1,5,3,4,6,2] => 13
[1,5,3,6,2,4] => 12
[1,5,3,6,4,2] => 18
[1,5,4,2,3,6] => 10
[1,5,4,2,6,3] => 16
[1,5,4,3,2,6] => 15
[1,5,4,3,6,2] => 17
[1,5,4,6,2,3] => 13
[1,5,4,6,3,2] => 19
[1,5,6,2,3,4] => 9
[1,5,6,2,4,3] => 15
[1,5,6,3,2,4] => 14
[1,5,6,3,4,2] => 16
[1,5,6,4,2,3] => 15
[1,5,6,4,3,2] => 21
[1,6,2,3,4,5] => 6
[1,6,2,3,5,4] => 12
[1,6,2,4,3,5] => 11
[1,6,2,4,5,3] => 13
[1,6,2,5,3,4] => 12
[1,6,2,5,4,3] => 18
[1,6,3,2,4,5] => 10
[1,6,3,2,5,4] => 16
[1,6,3,4,2,5] => 12
[1,6,3,4,5,2] => 14
[1,6,3,5,2,4] => 13
[1,6,3,5,4,2] => 19
[1,6,4,2,3,5] => 11
[1,6,4,2,5,3] => 17
[1,6,4,3,2,5] => 16
[1,6,4,3,5,2] => 18
[1,6,4,5,2,3] => 14
[1,6,4,5,3,2] => 20
[1,6,5,2,3,4] => 12
[1,6,5,2,4,3] => 18
[1,6,5,3,2,4] => 17
[1,6,5,3,4,2] => 19
[1,6,5,4,2,3] => 18
[1,6,5,4,3,2] => 24
[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] => 9
[2,1,3,6,4,5] => 8
[2,1,3,6,5,4] => 14
[2,1,4,3,5,6] => 6
[2,1,4,3,6,5] => 12
[2,1,4,5,3,6] => 8
[2,1,4,5,6,3] => 10
[2,1,4,6,3,5] => 9
[2,1,4,6,5,3] => 15
[2,1,5,3,4,6] => 7
[2,1,5,3,6,4] => 13
[2,1,5,4,3,6] => 12
[2,1,5,4,6,3] => 14
[2,1,5,6,3,4] => 10
[2,1,5,6,4,3] => 16
[2,1,6,3,4,5] => 8
[2,1,6,3,5,4] => 14
[2,1,6,4,3,5] => 13
[2,1,6,4,5,3] => 15
[2,1,6,5,3,4] => 14
[2,1,6,5,4,3] => 20
[2,3,1,4,5,6] => 4
[2,3,1,4,6,5] => 10
[2,3,1,5,4,6] => 9
[2,3,1,5,6,4] => 11
[2,3,1,6,4,5] => 10
[2,3,1,6,5,4] => 16
[2,3,4,1,5,6] => 6
[2,3,4,1,6,5] => 12
[2,3,4,5,1,6] => 8
[2,3,4,5,6,1] => 10
[2,3,4,6,1,5] => 9
[2,3,4,6,5,1] => 15
[2,3,5,1,4,6] => 7
[2,3,5,1,6,4] => 13
[2,3,5,4,1,6] => 12
[2,3,5,4,6,1] => 14
[2,3,5,6,1,4] => 10
[2,3,5,6,4,1] => 16
[2,3,6,1,4,5] => 8
[2,3,6,1,5,4] => 14
[2,3,6,4,1,5] => 13
[2,3,6,4,5,1] => 15
[2,3,6,5,1,4] => 14
[2,3,6,5,4,1] => 20
[2,4,1,3,5,6] => 5
[2,4,1,3,6,5] => 11
[2,4,1,5,3,6] => 10
[2,4,1,5,6,3] => 12
[2,4,1,6,3,5] => 11
[2,4,1,6,5,3] => 17
[2,4,3,1,5,6] => 9
[2,4,3,1,6,5] => 15
[2,4,3,5,1,6] => 11
[2,4,3,5,6,1] => 13
[2,4,3,6,1,5] => 12
[2,4,3,6,5,1] => 18
[2,4,5,1,3,6] => 8
[2,4,5,1,6,3] => 14
[2,4,5,3,1,6] => 13
[2,4,5,3,6,1] => 15
[2,4,5,6,1,3] => 11
[2,4,5,6,3,1] => 17
[2,4,6,1,3,5] => 9
[2,4,6,1,5,3] => 15
[2,4,6,3,1,5] => 14
[2,4,6,3,5,1] => 16
[2,4,6,5,1,3] => 15
[2,4,6,5,3,1] => 21
[2,5,1,3,4,6] => 6
[2,5,1,3,6,4] => 12
[2,5,1,4,3,6] => 11
[2,5,1,4,6,3] => 13
[2,5,1,6,3,4] => 12
[2,5,1,6,4,3] => 18
[2,5,3,1,4,6] => 10
[2,5,3,1,6,4] => 16
[2,5,3,4,1,6] => 12
[2,5,3,4,6,1] => 14
[2,5,3,6,1,4] => 13
[2,5,3,6,4,1] => 19
[2,5,4,1,3,6] => 11
[2,5,4,1,6,3] => 17
[2,5,4,3,1,6] => 16
[2,5,4,3,6,1] => 18
[2,5,4,6,1,3] => 14
[2,5,4,6,3,1] => 20
[2,5,6,1,3,4] => 10
[2,5,6,1,4,3] => 16
[2,5,6,3,1,4] => 15
[2,5,6,3,4,1] => 17
[2,5,6,4,1,3] => 16
[2,5,6,4,3,1] => 22
[2,6,1,3,4,5] => 7
[2,6,1,3,5,4] => 13
[2,6,1,4,3,5] => 12
[2,6,1,4,5,3] => 14
[2,6,1,5,3,4] => 13
[2,6,1,5,4,3] => 19
[2,6,3,1,4,5] => 11
[2,6,3,1,5,4] => 17
[2,6,3,4,1,5] => 13
[2,6,3,4,5,1] => 15
[2,6,3,5,1,4] => 14
[2,6,3,5,4,1] => 20
[2,6,4,1,3,5] => 12
[2,6,4,1,5,3] => 18
[2,6,4,3,1,5] => 17
[2,6,4,3,5,1] => 19
[2,6,4,5,1,3] => 15
[2,6,4,5,3,1] => 21
[2,6,5,1,3,4] => 13
[2,6,5,1,4,3] => 19
[2,6,5,3,1,4] => 18
[2,6,5,3,4,1] => 20
[2,6,5,4,1,3] => 19
[2,6,5,4,3,1] => 25
[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] => 10
[3,1,2,6,4,5] => 9
[3,1,2,6,5,4] => 15
[3,1,4,2,5,6] => 7
[3,1,4,2,6,5] => 13
[3,1,4,5,2,6] => 9
[3,1,4,5,6,2] => 11
[3,1,4,6,2,5] => 10
[3,1,4,6,5,2] => 16
[3,1,5,2,4,6] => 8
[3,1,5,2,6,4] => 14
[3,1,5,4,2,6] => 13
[3,1,5,4,6,2] => 15
[3,1,5,6,2,4] => 11
[3,1,5,6,4,2] => 17
[3,1,6,2,4,5] => 9
[3,1,6,2,5,4] => 15
[3,1,6,4,2,5] => 14
[3,1,6,4,5,2] => 16
[3,1,6,5,2,4] => 15
[3,1,6,5,4,2] => 21
[3,2,1,4,5,6] => 6
[3,2,1,4,6,5] => 12
[3,2,1,5,4,6] => 11
[3,2,1,5,6,4] => 13
[3,2,1,6,4,5] => 12
[3,2,1,6,5,4] => 18
[3,2,4,1,5,6] => 8
[3,2,4,1,6,5] => 14
[3,2,4,5,1,6] => 10
[3,2,4,5,6,1] => 12
[3,2,4,6,1,5] => 11
[3,2,4,6,5,1] => 17
[3,2,5,1,4,6] => 9
[3,2,5,1,6,4] => 15
[3,2,5,4,1,6] => 14
[3,2,5,4,6,1] => 16
[3,2,5,6,1,4] => 12
[3,2,5,6,4,1] => 18
[3,2,6,1,4,5] => 10
[3,2,6,1,5,4] => 16
[3,2,6,4,1,5] => 15
[3,2,6,4,5,1] => 17
[3,2,6,5,1,4] => 16
[3,2,6,5,4,1] => 22
[3,4,1,2,5,6] => 6
[3,4,1,2,6,5] => 12
[3,4,1,5,2,6] => 11
[3,4,1,5,6,2] => 13
[3,4,1,6,2,5] => 12
[3,4,1,6,5,2] => 18
[3,4,2,1,5,6] => 10
[3,4,2,1,6,5] => 16
[3,4,2,5,1,6] => 12
[3,4,2,5,6,1] => 14
[3,4,2,6,1,5] => 13
[3,4,2,6,5,1] => 19
[3,4,5,1,2,6] => 9
[3,4,5,1,6,2] => 15
[3,4,5,2,1,6] => 14
[3,4,5,2,6,1] => 16
[3,4,5,6,1,2] => 12
[3,4,5,6,2,1] => 18
[3,4,6,1,2,5] => 10
[3,4,6,1,5,2] => 16
[3,4,6,2,1,5] => 15
[3,4,6,2,5,1] => 17
[3,4,6,5,1,2] => 16
[3,4,6,5,2,1] => 22
[3,5,1,2,4,6] => 7
[3,5,1,2,6,4] => 13
[3,5,1,4,2,6] => 12
[3,5,1,4,6,2] => 14
[3,5,1,6,2,4] => 13
[3,5,1,6,4,2] => 19
[3,5,2,1,4,6] => 11
[3,5,2,1,6,4] => 17
[3,5,2,4,1,6] => 13
[3,5,2,4,6,1] => 15
[3,5,2,6,1,4] => 14
[3,5,2,6,4,1] => 20
[3,5,4,1,2,6] => 12
[3,5,4,1,6,2] => 18
[3,5,4,2,1,6] => 17
[3,5,4,2,6,1] => 19
[3,5,4,6,1,2] => 15
[3,5,4,6,2,1] => 21
[3,5,6,1,2,4] => 11
[3,5,6,1,4,2] => 17
[3,5,6,2,1,4] => 16
[3,5,6,2,4,1] => 18
[3,5,6,4,1,2] => 17
[3,5,6,4,2,1] => 23
[3,6,1,2,4,5] => 8
[3,6,1,2,5,4] => 14
[3,6,1,4,2,5] => 13
[3,6,1,4,5,2] => 15
[3,6,1,5,2,4] => 14
[3,6,1,5,4,2] => 20
[3,6,2,1,4,5] => 12
[3,6,2,1,5,4] => 18
[3,6,2,4,1,5] => 14
[3,6,2,4,5,1] => 16
[3,6,2,5,1,4] => 15
[3,6,2,5,4,1] => 21
[3,6,4,1,2,5] => 13
[3,6,4,1,5,2] => 19
[3,6,4,2,1,5] => 18
[3,6,4,2,5,1] => 20
[3,6,4,5,1,2] => 16
[3,6,4,5,2,1] => 22
[3,6,5,1,2,4] => 14
[3,6,5,1,4,2] => 20
[3,6,5,2,1,4] => 19
[3,6,5,2,4,1] => 21
[3,6,5,4,1,2] => 20
[3,6,5,4,2,1] => 26
[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] => 11
[4,1,2,6,3,5] => 10
[4,1,2,6,5,3] => 16
[4,1,3,2,5,6] => 8
[4,1,3,2,6,5] => 14
[4,1,3,5,2,6] => 10
[4,1,3,5,6,2] => 12
[4,1,3,6,2,5] => 11
[4,1,3,6,5,2] => 17
[4,1,5,2,3,6] => 9
[4,1,5,2,6,3] => 15
[4,1,5,3,2,6] => 14
[4,1,5,3,6,2] => 16
[4,1,5,6,2,3] => 12
[4,1,5,6,3,2] => 18
[4,1,6,2,3,5] => 10
[4,1,6,2,5,3] => 16
[4,1,6,3,2,5] => 15
[4,1,6,3,5,2] => 17
[4,1,6,5,2,3] => 16
[4,1,6,5,3,2] => 22
[4,2,1,3,5,6] => 7
[4,2,1,3,6,5] => 13
[4,2,1,5,3,6] => 12
[4,2,1,5,6,3] => 14
[4,2,1,6,3,5] => 13
[4,2,1,6,5,3] => 19
[4,2,3,1,5,6] => 9
[4,2,3,1,6,5] => 15
[4,2,3,5,1,6] => 11
[4,2,3,5,6,1] => 13
[4,2,3,6,1,5] => 12
[4,2,3,6,5,1] => 18
[4,2,5,1,3,6] => 10
[4,2,5,1,6,3] => 16
[4,2,5,3,1,6] => 15
[4,2,5,3,6,1] => 17
[4,2,5,6,1,3] => 13
[4,2,5,6,3,1] => 19
[4,2,6,1,3,5] => 11
[4,2,6,1,5,3] => 17
[4,2,6,3,1,5] => 16
[4,2,6,3,5,1] => 18
[4,2,6,5,1,3] => 17
[4,2,6,5,3,1] => 23
[4,3,1,2,5,6] => 8
[4,3,1,2,6,5] => 14
[4,3,1,5,2,6] => 13
[4,3,1,5,6,2] => 15
[4,3,1,6,2,5] => 14
[4,3,1,6,5,2] => 20
[4,3,2,1,5,6] => 12
[4,3,2,1,6,5] => 18
[4,3,2,5,1,6] => 14
[4,3,2,5,6,1] => 16
[4,3,2,6,1,5] => 15
[4,3,2,6,5,1] => 21
[4,3,5,1,2,6] => 11
[4,3,5,1,6,2] => 17
[4,3,5,2,1,6] => 16
[4,3,5,2,6,1] => 18
[4,3,5,6,1,2] => 14
[4,3,5,6,2,1] => 20
[4,3,6,1,2,5] => 12
[4,3,6,1,5,2] => 18
[4,3,6,2,1,5] => 17
[4,3,6,2,5,1] => 19
[4,3,6,5,1,2] => 18
[4,3,6,5,2,1] => 24
[4,5,1,2,3,6] => 8
[4,5,1,2,6,3] => 14
[4,5,1,3,2,6] => 13
[4,5,1,3,6,2] => 15
[4,5,1,6,2,3] => 14
[4,5,1,6,3,2] => 20
[4,5,2,1,3,6] => 12
[4,5,2,1,6,3] => 18
[4,5,2,3,1,6] => 14
[4,5,2,3,6,1] => 16
[4,5,2,6,1,3] => 15
[4,5,2,6,3,1] => 21
[4,5,3,1,2,6] => 13
[4,5,3,1,6,2] => 19
[4,5,3,2,1,6] => 18
[4,5,3,2,6,1] => 20
[4,5,3,6,1,2] => 16
[4,5,3,6,2,1] => 22
[4,5,6,1,2,3] => 12
[4,5,6,1,3,2] => 18
[4,5,6,2,1,3] => 17
[4,5,6,2,3,1] => 19
[4,5,6,3,1,2] => 18
[4,5,6,3,2,1] => 24
[4,6,1,2,3,5] => 9
[4,6,1,2,5,3] => 15
[4,6,1,3,2,5] => 14
[4,6,1,3,5,2] => 16
[4,6,1,5,2,3] => 15
[4,6,1,5,3,2] => 21
[4,6,2,1,3,5] => 13
[4,6,2,1,5,3] => 19
[4,6,2,3,1,5] => 15
[4,6,2,3,5,1] => 17
[4,6,2,5,1,3] => 16
[4,6,2,5,3,1] => 22
[4,6,3,1,2,5] => 14
[4,6,3,1,5,2] => 20
[4,6,3,2,1,5] => 19
[4,6,3,2,5,1] => 21
[4,6,3,5,1,2] => 17
[4,6,3,5,2,1] => 23
[4,6,5,1,2,3] => 15
[4,6,5,1,3,2] => 21
[4,6,5,2,1,3] => 20
[4,6,5,2,3,1] => 22
[4,6,5,3,1,2] => 21
[4,6,5,3,2,1] => 27
[5,1,2,3,4,6] => 5
[5,1,2,3,6,4] => 11
[5,1,2,4,3,6] => 10
[5,1,2,4,6,3] => 12
[5,1,2,6,3,4] => 11
[5,1,2,6,4,3] => 17
[5,1,3,2,4,6] => 9
[5,1,3,2,6,4] => 15
[5,1,3,4,2,6] => 11
[5,1,3,4,6,2] => 13
[5,1,3,6,2,4] => 12
[5,1,3,6,4,2] => 18
[5,1,4,2,3,6] => 10
[5,1,4,2,6,3] => 16
[5,1,4,3,2,6] => 15
[5,1,4,3,6,2] => 17
[5,1,4,6,2,3] => 13
[5,1,4,6,3,2] => 19
[5,1,6,2,3,4] => 11
[5,1,6,2,4,3] => 17
[5,1,6,3,2,4] => 16
[5,1,6,3,4,2] => 18
[5,1,6,4,2,3] => 17
[5,1,6,4,3,2] => 23
[5,2,1,3,4,6] => 8
[5,2,1,3,6,4] => 14
[5,2,1,4,3,6] => 13
[5,2,1,4,6,3] => 15
[5,2,1,6,3,4] => 14
[5,2,1,6,4,3] => 20
[5,2,3,1,4,6] => 10
[5,2,3,1,6,4] => 16
[5,2,3,4,1,6] => 12
[5,2,3,4,6,1] => 14
[5,2,3,6,1,4] => 13
[5,2,3,6,4,1] => 19
[5,2,4,1,3,6] => 11
[5,2,4,1,6,3] => 17
[5,2,4,3,1,6] => 16
[5,2,4,3,6,1] => 18
[5,2,4,6,1,3] => 14
[5,2,4,6,3,1] => 20
[5,2,6,1,3,4] => 12
[5,2,6,1,4,3] => 18
[5,2,6,3,1,4] => 17
[5,2,6,3,4,1] => 19
[5,2,6,4,1,3] => 18
[5,2,6,4,3,1] => 24
[5,3,1,2,4,6] => 9
[5,3,1,2,6,4] => 15
[5,3,1,4,2,6] => 14
[5,3,1,4,6,2] => 16
[5,3,1,6,2,4] => 15
[5,3,1,6,4,2] => 21
[5,3,2,1,4,6] => 13
[5,3,2,1,6,4] => 19
[5,3,2,4,1,6] => 15
[5,3,2,4,6,1] => 17
[5,3,2,6,1,4] => 16
[5,3,2,6,4,1] => 22
[5,3,4,1,2,6] => 12
[5,3,4,1,6,2] => 18
[5,3,4,2,1,6] => 17
[5,3,4,2,6,1] => 19
[5,3,4,6,1,2] => 15
[5,3,4,6,2,1] => 21
[5,3,6,1,2,4] => 13
[5,3,6,1,4,2] => 19
[5,3,6,2,1,4] => 18
[5,3,6,2,4,1] => 20
[5,3,6,4,1,2] => 19
[5,3,6,4,2,1] => 25
[5,4,1,2,3,6] => 10
[5,4,1,2,6,3] => 16
[5,4,1,3,2,6] => 15
[5,4,1,3,6,2] => 17
[5,4,1,6,2,3] => 16
[5,4,1,6,3,2] => 22
[5,4,2,1,3,6] => 14
[5,4,2,1,6,3] => 20
[5,4,2,3,1,6] => 16
[5,4,2,3,6,1] => 18
[5,4,2,6,1,3] => 17
[5,4,2,6,3,1] => 23
[5,4,3,1,2,6] => 15
[5,4,3,1,6,2] => 21
[5,4,3,2,1,6] => 20
[5,4,3,2,6,1] => 22
[5,4,3,6,1,2] => 18
[5,4,3,6,2,1] => 24
[5,4,6,1,2,3] => 14
[5,4,6,1,3,2] => 20
[5,4,6,2,1,3] => 19
[5,4,6,2,3,1] => 21
[5,4,6,3,1,2] => 20
[5,4,6,3,2,1] => 26
[5,6,1,2,3,4] => 10
[5,6,1,2,4,3] => 16
[5,6,1,3,2,4] => 15
[5,6,1,3,4,2] => 17
[5,6,1,4,2,3] => 16
[5,6,1,4,3,2] => 22
[5,6,2,1,3,4] => 14
[5,6,2,1,4,3] => 20
[5,6,2,3,1,4] => 16
[5,6,2,3,4,1] => 18
[5,6,2,4,1,3] => 17
[5,6,2,4,3,1] => 23
[5,6,3,1,2,4] => 15
[5,6,3,1,4,2] => 21
[5,6,3,2,1,4] => 20
[5,6,3,2,4,1] => 22
[5,6,3,4,1,2] => 18
[5,6,3,4,2,1] => 24
[5,6,4,1,2,3] => 16
[5,6,4,1,3,2] => 22
[5,6,4,2,1,3] => 21
[5,6,4,2,3,1] => 23
[5,6,4,3,1,2] => 22
[5,6,4,3,2,1] => 28
[6,1,2,3,4,5] => 6
[6,1,2,3,5,4] => 12
[6,1,2,4,3,5] => 11
[6,1,2,4,5,3] => 13
[6,1,2,5,3,4] => 12
[6,1,2,5,4,3] => 18
[6,1,3,2,4,5] => 10
[6,1,3,2,5,4] => 16
[6,1,3,4,2,5] => 12
[6,1,3,4,5,2] => 14
[6,1,3,5,2,4] => 13
[6,1,3,5,4,2] => 19
[6,1,4,2,3,5] => 11
[6,1,4,2,5,3] => 17
[6,1,4,3,2,5] => 16
[6,1,4,3,5,2] => 18
[6,1,4,5,2,3] => 14
[6,1,4,5,3,2] => 20
[6,1,5,2,3,4] => 12
[6,1,5,2,4,3] => 18
[6,1,5,3,2,4] => 17
[6,1,5,3,4,2] => 19
[6,1,5,4,2,3] => 18
[6,1,5,4,3,2] => 24
[6,2,1,3,4,5] => 9
[6,2,1,3,5,4] => 15
[6,2,1,4,3,5] => 14
[6,2,1,4,5,3] => 16
[6,2,1,5,3,4] => 15
[6,2,1,5,4,3] => 21
[6,2,3,1,4,5] => 11
[6,2,3,1,5,4] => 17
[6,2,3,4,1,5] => 13
[6,2,3,4,5,1] => 15
[6,2,3,5,1,4] => 14
[6,2,3,5,4,1] => 20
[6,2,4,1,3,5] => 12
[6,2,4,1,5,3] => 18
[6,2,4,3,1,5] => 17
[6,2,4,3,5,1] => 19
[6,2,4,5,1,3] => 15
[6,2,4,5,3,1] => 21
[6,2,5,1,3,4] => 13
[6,2,5,1,4,3] => 19
[6,2,5,3,1,4] => 18
[6,2,5,3,4,1] => 20
[6,2,5,4,1,3] => 19
[6,2,5,4,3,1] => 25
[6,3,1,2,4,5] => 10
[6,3,1,2,5,4] => 16
[6,3,1,4,2,5] => 15
[6,3,1,4,5,2] => 17
[6,3,1,5,2,4] => 16
[6,3,1,5,4,2] => 22
[6,3,2,1,4,5] => 14
[6,3,2,1,5,4] => 20
[6,3,2,4,1,5] => 16
[6,3,2,4,5,1] => 18
[6,3,2,5,1,4] => 17
[6,3,2,5,4,1] => 23
[6,3,4,1,2,5] => 13
[6,3,4,1,5,2] => 19
[6,3,4,2,1,5] => 18
[6,3,4,2,5,1] => 20
[6,3,4,5,1,2] => 16
[6,3,4,5,2,1] => 22
[6,3,5,1,2,4] => 14
[6,3,5,1,4,2] => 20
[6,3,5,2,1,4] => 19
[6,3,5,2,4,1] => 21
[6,3,5,4,1,2] => 20
[6,3,5,4,2,1] => 26
[6,4,1,2,3,5] => 11
[6,4,1,2,5,3] => 17
[6,4,1,3,2,5] => 16
[6,4,1,3,5,2] => 18
[6,4,1,5,2,3] => 17
[6,4,1,5,3,2] => 23
[6,4,2,1,3,5] => 15
[6,4,2,1,5,3] => 21
[6,4,2,3,1,5] => 17
[6,4,2,3,5,1] => 19
[6,4,2,5,1,3] => 18
[6,4,2,5,3,1] => 24
[6,4,3,1,2,5] => 16
[6,4,3,1,5,2] => 22
[6,4,3,2,1,5] => 21
[6,4,3,2,5,1] => 23
[6,4,3,5,1,2] => 19
[6,4,3,5,2,1] => 25
[6,4,5,1,2,3] => 15
[6,4,5,1,3,2] => 21
[6,4,5,2,1,3] => 20
[6,4,5,2,3,1] => 22
[6,4,5,3,1,2] => 21
[6,4,5,3,2,1] => 27
[6,5,1,2,3,4] => 12
[6,5,1,2,4,3] => 18
[6,5,1,3,2,4] => 17
[6,5,1,3,4,2] => 19
[6,5,1,4,2,3] => 18
[6,5,1,4,3,2] => 24
[6,5,2,1,3,4] => 16
[6,5,2,1,4,3] => 22
[6,5,2,3,1,4] => 18
[6,5,2,3,4,1] => 20
[6,5,2,4,1,3] => 19
[6,5,2,4,3,1] => 25
[6,5,3,1,2,4] => 17
[6,5,3,1,4,2] => 23
[6,5,3,2,1,4] => 22
[6,5,3,2,4,1] => 24
[6,5,3,4,1,2] => 20
[6,5,3,4,2,1] => 26
[6,5,4,1,2,3] => 18
[6,5,4,1,3,2] => 24
[6,5,4,2,1,3] => 23
[6,5,4,2,3,1] => 25
[6,5,4,3,1,2] => 24
[6,5,4,3,2,1] => 30
[1,2,3,4,5,6,7] => 0
[1,2,3,4,5,7,6] => 7
[1,2,3,4,6,5,7] => 6
[1,2,3,4,6,7,5] => 8
[1,2,3,4,7,5,6] => 7
[1,2,3,4,7,6,5] => 14
[1,2,3,5,4,6,7] => 5
[1,2,3,5,4,7,6] => 12
[1,2,3,5,6,4,7] => 7
[1,2,3,5,6,7,4] => 9
[1,2,3,5,7,4,6] => 8
[1,2,3,5,7,6,4] => 15
[1,2,3,6,4,5,7] => 6
[1,2,3,6,4,7,5] => 13
[1,2,3,6,5,4,7] => 12
[1,2,3,6,5,7,4] => 14
[1,2,3,6,7,4,5] => 9
[1,2,3,6,7,5,4] => 16
[1,2,3,7,4,5,6] => 7
[1,2,3,7,4,6,5] => 14
[1,2,3,7,5,4,6] => 13
[1,2,3,7,5,6,4] => 15
[1,2,3,7,6,4,5] => 14
[1,2,3,7,6,5,4] => 21
[1,2,4,3,5,6,7] => 4
[1,2,4,3,5,7,6] => 11
[1,2,4,3,6,5,7] => 10
[1,2,4,3,6,7,5] => 12
[1,2,4,3,7,5,6] => 11
[1,2,4,3,7,6,5] => 18
[1,2,4,5,3,6,7] => 6
[1,2,4,5,3,7,6] => 13
[1,2,4,5,6,3,7] => 8
[1,2,4,5,6,7,3] => 10
[1,2,4,5,7,3,6] => 9
[1,2,4,5,7,6,3] => 16
[1,2,4,6,3,5,7] => 7
[1,2,4,6,3,7,5] => 14
[1,2,4,6,5,3,7] => 13
[1,2,4,6,5,7,3] => 15
[1,2,4,6,7,3,5] => 10
[1,2,4,6,7,5,3] => 17
[1,2,4,7,3,5,6] => 8
[1,2,4,7,3,6,5] => 15
[1,2,4,7,5,3,6] => 14
[1,2,4,7,5,6,3] => 16
[1,2,4,7,6,3,5] => 15
[1,2,4,7,6,5,3] => 22
[1,2,5,3,4,6,7] => 5
[1,2,5,3,4,7,6] => 12
[1,2,5,3,6,4,7] => 11
[1,2,5,3,6,7,4] => 13
[1,2,5,3,7,4,6] => 12
[1,2,5,3,7,6,4] => 19
[1,2,5,4,3,6,7] => 10
[1,2,5,4,3,7,6] => 17
[1,2,5,4,6,3,7] => 12
[1,2,5,4,6,7,3] => 14
[1,2,5,4,7,3,6] => 13
[1,2,5,4,7,6,3] => 20
[1,2,5,6,3,4,7] => 8
[1,2,5,6,3,7,4] => 15
[1,2,5,6,4,3,7] => 14
[1,2,5,6,4,7,3] => 16
[1,2,5,6,7,3,4] => 11
[1,2,5,6,7,4,3] => 18
[1,2,5,7,3,4,6] => 9
[1,2,5,7,3,6,4] => 16
[1,2,5,7,4,3,6] => 15
[1,2,5,7,4,6,3] => 17
[1,2,5,7,6,3,4] => 16
[1,2,5,7,6,4,3] => 23
[1,2,6,3,4,5,7] => 6
[1,2,6,3,4,7,5] => 13
[1,2,6,3,5,4,7] => 12
[1,2,6,3,5,7,4] => 14
[1,2,6,3,7,4,5] => 13
[1,2,6,3,7,5,4] => 20
[1,2,6,4,3,5,7] => 11
[1,2,6,4,3,7,5] => 18
[1,2,6,4,5,3,7] => 13
[1,2,6,4,5,7,3] => 15
[1,2,6,4,7,3,5] => 14
[1,2,6,4,7,5,3] => 21
[1,2,6,5,3,4,7] => 12
[1,2,6,5,3,7,4] => 19
[1,2,6,5,4,3,7] => 18
[1,2,6,5,4,7,3] => 20
[1,2,6,5,7,3,4] => 15
[1,2,6,5,7,4,3] => 22
[1,2,6,7,3,4,5] => 10
[1,2,6,7,3,5,4] => 17
[1,2,6,7,4,3,5] => 16
[1,2,6,7,4,5,3] => 18
[1,2,6,7,5,3,4] => 17
[1,2,6,7,5,4,3] => 24
[1,2,7,3,4,5,6] => 7
[1,2,7,3,4,6,5] => 14
[1,2,7,3,5,4,6] => 13
[1,2,7,3,5,6,4] => 15
[1,2,7,3,6,4,5] => 14
[1,2,7,3,6,5,4] => 21
[1,2,7,4,3,5,6] => 12
[1,2,7,4,3,6,5] => 19
[1,2,7,4,5,3,6] => 14
[1,2,7,4,5,6,3] => 16
[1,2,7,4,6,3,5] => 15
[1,2,7,4,6,5,3] => 22
[1,2,7,5,3,4,6] => 13
[1,2,7,5,3,6,4] => 20
[1,2,7,5,4,3,6] => 19
[1,2,7,5,4,6,3] => 21
[1,2,7,5,6,3,4] => 16
[1,2,7,5,6,4,3] => 23
[1,2,7,6,3,4,5] => 14
[1,2,7,6,3,5,4] => 21
[1,2,7,6,4,3,5] => 20
[1,2,7,6,4,5,3] => 22
[1,2,7,6,5,3,4] => 21
[1,2,7,6,5,4,3] => 28
[1,3,2,4,5,6,7] => 3
[1,3,2,4,5,7,6] => 10
[1,3,2,4,6,5,7] => 9
[1,3,2,4,6,7,5] => 11
[1,3,2,4,7,5,6] => 10
[1,3,2,4,7,6,5] => 17
[1,3,2,5,4,6,7] => 8
[1,3,2,5,4,7,6] => 15
[1,3,2,5,6,4,7] => 10
[1,3,2,5,6,7,4] => 12
[1,3,2,5,7,4,6] => 11
[1,3,2,5,7,6,4] => 18
[1,3,2,6,4,5,7] => 9
[1,3,2,6,4,7,5] => 16
[1,3,2,6,5,4,7] => 15
[1,3,2,6,5,7,4] => 17
[1,3,2,6,7,4,5] => 12
[1,3,2,6,7,5,4] => 19
[1,3,2,7,4,5,6] => 10
[1,3,2,7,4,6,5] => 17
[1,3,2,7,5,4,6] => 16
[1,3,2,7,5,6,4] => 18
[1,3,2,7,6,4,5] => 17
[1,3,2,7,6,5,4] => 24
[1,3,4,2,5,6,7] => 5
[1,3,4,2,5,7,6] => 12
[1,3,4,2,6,5,7] => 11
[1,3,4,2,6,7,5] => 13
[1,3,4,2,7,5,6] => 12
[1,3,4,2,7,6,5] => 19
[1,3,4,5,2,6,7] => 7
[1,3,4,5,2,7,6] => 14
[1,3,4,5,6,2,7] => 9
[1,3,4,5,6,7,2] => 11
[1,3,4,5,7,2,6] => 10
[1,3,4,5,7,6,2] => 17
[1,3,4,6,2,5,7] => 8
[1,3,4,6,2,7,5] => 15
[1,3,4,6,5,2,7] => 14
[1,3,4,6,5,7,2] => 16
[1,3,4,6,7,2,5] => 11
[1,3,4,6,7,5,2] => 18
[1,3,4,7,2,5,6] => 9
[1,3,4,7,2,6,5] => 16
[1,3,4,7,5,2,6] => 15
[1,3,4,7,5,6,2] => 17
[1,3,4,7,6,2,5] => 16
[1,3,4,7,6,5,2] => 23
[1,3,5,2,4,6,7] => 6
[1,3,5,2,4,7,6] => 13
[1,3,5,2,6,4,7] => 12
[1,3,5,2,6,7,4] => 14
[1,3,5,2,7,4,6] => 13
[1,3,5,2,7,6,4] => 20
[1,3,5,4,2,6,7] => 11
[1,3,5,4,2,7,6] => 18
[1,3,5,4,6,2,7] => 13
[1,3,5,4,6,7,2] => 15
[1,3,5,4,7,2,6] => 14
[1,3,5,4,7,6,2] => 21
[1,3,5,6,2,4,7] => 9
[1,3,5,6,2,7,4] => 16
[1,3,5,6,4,2,7] => 15
[1,3,5,6,4,7,2] => 17
[1,3,5,6,7,2,4] => 12
[1,3,5,6,7,4,2] => 19
[1,3,5,7,2,4,6] => 10
[1,3,5,7,2,6,4] => 17
[1,3,5,7,4,2,6] => 16
[1,3,5,7,4,6,2] => 18
[1,3,5,7,6,2,4] => 17
[1,3,5,7,6,4,2] => 24
[1,3,6,2,4,5,7] => 7
[1,3,6,2,4,7,5] => 14
[1,3,6,2,5,4,7] => 13
[1,3,6,2,5,7,4] => 15
[1,3,6,2,7,4,5] => 14
[1,3,6,2,7,5,4] => 21
[1,3,6,4,2,5,7] => 12
[1,3,6,4,2,7,5] => 19
[1,3,6,4,5,2,7] => 14
[1,3,6,4,5,7,2] => 16
[1,3,6,4,7,2,5] => 15
[1,3,6,4,7,5,2] => 22
[1,3,6,5,2,4,7] => 13
[1,3,6,5,2,7,4] => 20
[1,3,6,5,4,2,7] => 19
[1,3,6,5,4,7,2] => 21
[1,3,6,5,7,2,4] => 16
[1,3,6,5,7,4,2] => 23
[1,3,6,7,2,4,5] => 11
[1,3,6,7,2,5,4] => 18
[1,3,6,7,4,2,5] => 17
[1,3,6,7,4,5,2] => 19
[1,3,6,7,5,2,4] => 18
[1,3,6,7,5,4,2] => 25
[1,3,7,2,4,5,6] => 8
[1,3,7,2,4,6,5] => 15
[1,3,7,2,5,4,6] => 14
[1,3,7,2,5,6,4] => 16
[1,3,7,2,6,4,5] => 15
[1,3,7,2,6,5,4] => 22
[1,3,7,4,2,5,6] => 13
[1,3,7,4,2,6,5] => 20
[1,3,7,4,5,2,6] => 15
[1,3,7,4,5,6,2] => 17
[1,3,7,4,6,2,5] => 16
[1,3,7,4,6,5,2] => 23
[1,3,7,5,2,4,6] => 14
[1,3,7,5,2,6,4] => 21
[1,3,7,5,4,2,6] => 20
[1,3,7,5,4,6,2] => 22
[1,3,7,5,6,2,4] => 17
[1,3,7,5,6,4,2] => 24
[1,3,7,6,2,4,5] => 15
[1,3,7,6,2,5,4] => 22
[1,3,7,6,4,2,5] => 21
[1,3,7,6,4,5,2] => 23
[1,3,7,6,5,2,4] => 22
[1,3,7,6,5,4,2] => 29
[1,4,2,3,5,6,7] => 4
[1,4,2,3,5,7,6] => 11
[1,4,2,3,6,5,7] => 10
[1,4,2,3,6,7,5] => 12
[1,4,2,3,7,5,6] => 11
[1,4,2,3,7,6,5] => 18
[1,4,2,5,3,6,7] => 9
[1,4,2,5,3,7,6] => 16
[1,4,2,5,6,3,7] => 11
[1,4,2,5,6,7,3] => 13
[1,4,2,5,7,3,6] => 12
[1,4,2,5,7,6,3] => 19
[1,4,2,6,3,5,7] => 10
[1,4,2,6,3,7,5] => 17
[1,4,2,6,5,3,7] => 16
[1,4,2,6,5,7,3] => 18
[1,4,2,6,7,3,5] => 13
[1,4,2,6,7,5,3] => 20
[1,4,2,7,3,5,6] => 11
[1,4,2,7,3,6,5] => 18
[1,4,2,7,5,3,6] => 17
[1,4,2,7,5,6,3] => 19
[1,4,2,7,6,3,5] => 18
[1,4,2,7,6,5,3] => 25
[1,4,3,2,5,6,7] => 8
[1,4,3,2,5,7,6] => 15
[1,4,3,2,6,5,7] => 14
[1,4,3,2,6,7,5] => 16
[1,4,3,2,7,5,6] => 15
[1,4,3,2,7,6,5] => 22
[1,4,3,5,2,6,7] => 10
[1,4,3,5,2,7,6] => 17
[1,4,3,5,6,2,7] => 12
[1,4,3,5,6,7,2] => 14
[1,4,3,5,7,2,6] => 13
[1,4,3,5,7,6,2] => 20
[1,4,3,6,2,5,7] => 11
[1,4,3,6,2,7,5] => 18
[1,4,3,6,5,2,7] => 17
[1,4,3,6,5,7,2] => 19
[1,4,3,6,7,2,5] => 14
[1,4,3,6,7,5,2] => 21
[1,4,3,7,2,5,6] => 12
[1,4,3,7,2,6,5] => 19
[1,4,3,7,5,2,6] => 18
[1,4,3,7,5,6,2] => 20
[1,4,3,7,6,2,5] => 19
[1,4,3,7,6,5,2] => 26
[1,4,5,2,3,6,7] => 7
[1,4,5,2,3,7,6] => 14
[1,4,5,2,6,3,7] => 13
[1,4,5,2,6,7,3] => 15
[1,4,5,2,7,3,6] => 14
[1,4,5,2,7,6,3] => 21
[1,4,5,3,2,6,7] => 12
[1,4,5,3,2,7,6] => 19
[1,4,5,3,6,2,7] => 14
[1,4,5,3,6,7,2] => 16
[1,4,5,3,7,2,6] => 15
[1,4,5,3,7,6,2] => 22
[1,4,5,6,2,3,7] => 10
[1,4,5,6,2,7,3] => 17
[1,4,5,6,3,2,7] => 16
[1,4,5,6,3,7,2] => 18
[1,4,5,6,7,2,3] => 13
[1,4,5,6,7,3,2] => 20
[1,4,5,7,2,3,6] => 11
[1,4,5,7,2,6,3] => 18
[1,4,5,7,3,2,6] => 17
[1,4,5,7,3,6,2] => 19
[1,4,5,7,6,2,3] => 18
[1,4,5,7,6,3,2] => 25
[1,4,6,2,3,5,7] => 8
[1,4,6,2,3,7,5] => 15
[1,4,6,2,5,3,7] => 14
[1,4,6,2,5,7,3] => 16
[1,4,6,2,7,3,5] => 15
[1,4,6,2,7,5,3] => 22
[1,4,6,3,2,5,7] => 13
[1,4,6,3,2,7,5] => 20
[1,4,6,3,5,2,7] => 15
[1,4,6,3,5,7,2] => 17
[1,4,6,3,7,2,5] => 16
[1,4,6,3,7,5,2] => 23
[1,4,6,5,2,3,7] => 14
[1,4,6,5,2,7,3] => 21
[1,4,6,5,3,2,7] => 20
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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:
1,0,1 1,0,1,2,1,0,1 1,0,1,2,4,2,4,2,4,2,1,0,1 1,0,1,2,4,6,7,8,12,12,14,12,12,8,7,6,4,2,1,0,1 1,0,1,2,4,6,12,12,21,26,37,40,55,52,61,60,61,52,55,40,37,26,21,12,12,6,4,2,1,0,1
$F_{1} = 1$
$F_{2} = 1 + q^{2}$
$F_{3} = 1 + q^{2} + 2\ q^{3} + q^{4} + q^{6}$
$F_{4} = 1 + q^{2} + 2\ q^{3} + 4\ q^{4} + 2\ q^{5} + 4\ q^{6} + 2\ q^{7} + 4\ q^{8} + 2\ q^{9} + q^{10} + q^{12}$
$F_{5} = 1 + q^{2} + 2\ q^{3} + 4\ q^{4} + 6\ q^{5} + 7\ q^{6} + 8\ q^{7} + 12\ q^{8} + 12\ q^{9} + 14\ q^{10} + 12\ q^{11} + 12\ q^{12} + 8\ q^{13} + 7\ q^{14} + 6\ q^{15} + 4\ q^{16} + 2\ q^{17} + q^{18} + q^{20}$
$F_{6} = 1 + q^{2} + 2\ q^{3} + 4\ q^{4} + 6\ q^{5} + 12\ q^{6} + 12\ q^{7} + 21\ q^{8} + 26\ q^{9} + 37\ q^{10} + 40\ q^{11} + 55\ q^{12} + 52\ q^{13} + 61\ q^{14} + 60\ q^{15} + 61\ q^{16} + 52\ q^{17} + 55\ q^{18} + 40\ q^{19} + 37\ q^{20} + 26\ q^{21} + 21\ q^{22} + 12\ q^{23} + 12\ q^{24} + 6\ q^{25} + 4\ q^{26} + 2\ q^{27} + q^{28} + q^{30}$
Description
References
[1] Wachs, M. L. An involution for signed Eulerian numbers MathSciNet:1158780
Code
def statistic(pi):
return pi.major_index() + pi.number_of_inversions()
Created
Mar 30, 2019 at 08:54 by Christian Stump
Updated
Mar 30, 2019 at 08:54 by Christian Stump
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