Identifier
Values
[1,0] => [1] => [1] => 0
[1,0,1,0] => [1,2] => [1,2] => 0
[1,1,0,0] => [2,1] => [2,1] => 1
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => 0
[1,0,1,1,0,0] => [1,3,2] => [1,3,2] => 2
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => 1
[1,1,0,1,0,0] => [2,3,1] => [3,1,2] => 1
[1,1,1,0,0,0] => [3,1,2] => [2,3,1] => 2
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,4,3] => 3
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2,4] => 2
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,2,3] => 2
[1,0,1,1,1,0,0,0] => [1,4,2,3] => [1,3,4,2] => 3
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => 4
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,1,2,4] => 1
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4,1,2,3] => 1
[1,1,0,1,1,0,0,0] => [2,4,1,3] => [3,1,4,2] => 4
[1,1,1,0,0,0,1,0] => [3,1,2,4] => [2,3,1,4] => 2
[1,1,1,0,0,1,0,0] => [3,1,4,2] => [2,4,1,3] => 2
[1,1,1,0,1,0,0,0] => [3,4,1,2] => [3,4,1,2] => 2
[1,1,1,1,0,0,0,0] => [4,1,2,3] => [2,3,4,1] => 3
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => 4
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,4,3,5] => 3
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,5,3,4] => 3
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [1,2,4,5,3] => 4
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,3,2,4,5] => 2
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => 6
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,4,2,3,5] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,2,3,4] => 2
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [1,4,2,5,3] => 6
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [1,3,4,2,5] => 3
[1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [1,3,5,2,4] => 3
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [1,4,5,2,3] => 3
[1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [1,3,4,5,2] => 4
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,3,5,4] => 5
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,4,3,5] => 4
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,3,4] => 4
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [2,1,4,5,3] => 5
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,1,2,4,5] => 1
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,1,2,5,4] => 5
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,1,2,3,5] => 1
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5,1,2,3,4] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4] => [4,1,2,5,3] => 5
[1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => [3,1,4,2,5] => 4
[1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => [3,1,5,2,4] => 4
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => [4,1,5,2,3] => 4
[1,1,0,1,1,1,0,0,0,0] => [2,5,1,3,4] => [3,1,4,5,2] => 5
[1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => [2,3,1,4,5] => 2
[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => [2,3,1,5,4] => 6
[1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => [2,4,1,3,5] => 2
[1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => [2,5,1,3,4] => 2
[1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => [2,4,1,5,3] => 6
[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [3,4,1,2,5] => 2
[1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => [3,5,1,2,4] => 2
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => [4,5,1,2,3] => 2
[1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => [3,4,1,5,2] => 6
[1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => [2,3,4,1,5] => 3
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => [2,3,5,1,4] => 3
[1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => [2,4,5,1,3] => 3
[1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => [3,4,5,1,2] => 3
[1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => [2,3,4,5,1] => 4
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 4
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 5
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 8
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => 3
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => 8
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => 4
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => [1,2,4,6,3,5] => 4
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => [1,2,5,6,3,4] => 4
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 5
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 7
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 6
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,4,5] => 6
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => [1,3,2,5,6,4] => 7
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,4,2,3,6,5] => 7
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => [1,5,2,3,6,4] => 7
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => [1,4,2,5,3,6] => 6
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => [1,4,2,6,3,5] => 6
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => [1,5,2,6,3,4] => 6
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => [1,4,2,5,6,3] => 7
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => 8
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => [1,3,5,2,4,6] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => [1,3,6,2,4,5] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => [1,3,5,2,6,4] => 8
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [1,4,5,2,3,6] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => [1,4,6,2,3,5] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [1,5,6,2,3,4] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => [1,4,5,2,6,3] => 8
>>> Load all 197 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => [1,3,4,6,2,5] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => [1,3,5,6,2,4] => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => [1,4,5,6,2,3] => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 6
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 5
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,3,6,4,5] => 5
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => [2,1,3,5,6,4] => 6
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 9
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,3,4,6] => 4
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,3,4,5] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => [2,1,5,3,6,4] => 9
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [2,1,4,5,3,6] => 5
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => [2,1,4,6,3,5] => 5
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => [2,1,5,6,3,4] => 5
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => [2,1,4,5,6,3] => 6
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,1,2,4,6,5] => 6
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,1,2,5,4,6] => 5
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,1,2,6,4,5] => 5
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => [3,1,2,5,6,4] => 6
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,1,2,3,6,5] => 6
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,1,5] => [5,1,2,3,6,4] => 6
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => [4,1,2,5,3,6] => 5
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => [4,1,2,6,3,5] => 5
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,1,4] => [5,1,2,6,3,4] => 5
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,1,4,5] => [4,1,2,5,6,3] => 6
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => [3,1,4,2,5,6] => 4
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => [3,1,4,2,6,5] => 9
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => [3,1,5,2,4,6] => 4
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => [3,1,6,2,4,5] => 4
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => [3,1,5,2,6,4] => 9
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => [4,1,5,2,3,6] => 4
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => [4,1,6,2,3,5] => 4
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,1,3] => [5,1,6,2,3,4] => 4
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => [4,1,5,2,6,3] => 9
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => [3,1,4,5,2,6] => 5
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,4] => [3,1,4,6,2,5] => 5
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => [3,1,5,6,2,4] => 5
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,1,3,4] => [4,1,5,6,2,3] => 5
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,3,4,5] => [3,1,4,5,6,2] => 6
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => [2,3,1,4,6,5] => 7
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => [2,3,1,5,4,6] => 6
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => [2,3,1,6,4,5] => 6
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [2,3,1,5,6,4] => 7
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [2,4,1,3,5,6] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => [2,4,1,3,6,5] => 7
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [2,5,1,3,4,6] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => [2,6,1,3,4,5] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,4,6,2,5] => [2,5,1,3,6,4] => 7
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => [2,4,1,5,3,6] => 6
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => [2,4,1,6,3,5] => 6
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => [2,5,1,6,3,4] => 6
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => [2,4,1,5,6,3] => 7
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => [3,4,1,2,5,6] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => [3,4,1,2,6,5] => 7
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => [3,5,1,2,4,6] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => [3,6,1,2,4,5] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => [3,5,1,2,6,4] => 7
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [4,5,1,2,3,6] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => [4,6,1,2,3,5] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => [5,6,1,2,3,4] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => [4,5,1,2,6,3] => 7
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => [3,4,1,5,2,6] => 6
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => [3,4,1,6,2,5] => 6
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => [3,5,1,6,2,4] => 6
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => [4,5,1,6,2,3] => 6
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => [3,4,1,5,6,2] => 7
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => [2,3,4,1,6,5] => 8
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => [2,3,5,1,4,6] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => [2,3,6,1,4,5] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => [2,3,5,1,6,4] => 8
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [2,4,5,1,3,6] => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => [2,4,6,1,3,5] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,5,6,2,3] => [2,5,6,1,3,4] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => [2,4,5,1,6,3] => 8
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => [3,4,5,1,2,6] => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => [3,4,6,1,2,5] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => [3,5,6,1,2,4] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => [4,5,6,1,2,3] => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5] => [3,4,5,1,6,2] => 8
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => 4
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => [2,3,4,6,1,5] => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1,2,6,3,4] => [2,3,5,6,1,4] => 4
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => [2,4,5,6,1,3] => 4
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => [3,4,5,6,1,2] => 4
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => 5
[] => [] => [] => 0
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Description
The major index of a permutation.
This is the sum of the positions of its descents,
$$\operatorname{maj}(\sigma) = \sum_{\sigma(i) > \sigma(i+1)} i.$$
Its generating function is $[n]_q! = [1]_q \cdot [2]_q \dots [n]_q$ for $[k]_q = 1 + q + q^2 + \dots q^{k-1}$.
A statistic equidistributed with the major index is called Mahonian statistic.
Map
inverse
Description
Sends a permutation to its inverse.
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.