Identifier
Values
[1,0] => [1] => [1] => [1] => 0
[1,0,1,0] => [1,2] => [1,2] => [1,2] => 0
[1,1,0,0] => [2,1] => [2,1] => [2,1] => 0
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,0,1,1,0,0] => [1,3,2] => [1,3,2] => [1,3,2] => 0
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [2,1,3] => 0
[1,1,0,1,0,0] => [2,3,1] => [3,2,1] => [2,3,1] => 0
[1,1,1,0,0,0] => [3,1,2] => [3,1,2] => [3,1,2] => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [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] => [1,2,4,3] => 0
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 0
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,3,2] => [1,3,4,2] => 0
[1,0,1,1,1,0,0,0] => [1,4,2,3] => [1,4,2,3] => [1,4,2,3] => 1
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 0
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 0
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,2,1,4] => [2,3,1,4] => 0
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4,2,3,1] => [2,3,4,1] => 0
[1,1,0,1,1,0,0,0] => [2,4,1,3] => [4,2,1,3] => [2,4,1,3] => 1
[1,1,1,0,0,0,1,0] => [3,1,2,4] => [3,1,2,4] => [3,1,2,4] => 1
[1,1,1,0,0,1,0,0] => [3,1,4,2] => [4,3,1,2] => [3,4,2,1] => 1
[1,1,1,0,1,0,0,0] => [3,4,1,2] => [4,1,3,2] => [3,1,4,2] => 1
[1,1,1,1,0,0,0,0] => [4,1,2,3] => [4,1,2,3] => [4,1,2,3] => 2
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [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] => [1,2,3,5,4] => 0
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 0
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,5,4,3] => [1,2,4,5,3] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 0
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,3,4,2] => [1,3,4,5,2] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [1,5,3,2,4] => [1,3,5,2,4] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [1,4,2,3,5] => [1,4,2,3,5] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [1,5,4,2,3] => [1,4,5,3,2] => 1
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [1,5,2,4,3] => [1,4,2,5,3] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [1,5,2,3,4] => [1,5,2,3,4] => 2
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => 0
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => 0
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 0
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,4,3] => [2,1,4,5,3] => 0
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [2,1,5,3,4] => [2,1,5,3,4] => 1
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,2,1,4,5] => [2,3,1,4,5] => 0
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,2,1,5,4] => [2,3,1,5,4] => 0
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,2,3,1,5] => [2,3,4,1,5] => 0
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5,2,3,4,1] => [2,3,4,5,1] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4] => [5,2,3,1,4] => [2,3,5,1,4] => 1
[1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,1,3,5] => 1
[1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => [5,2,4,1,3] => [2,4,5,3,1] => 1
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => [5,2,1,4,3] => [2,4,1,5,3] => 1
[1,1,0,1,1,1,0,0,0,0] => [2,5,1,3,4] => [5,2,1,3,4] => [2,5,1,3,4] => 2
[1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => [3,1,2,4,5] => [3,1,2,4,5] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => [3,1,2,5,4] => [3,1,2,5,4] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => [4,3,1,2,5] => [3,4,2,1,5] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => [5,3,1,4,2] => [3,4,2,5,1] => 1
[1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => [5,3,1,2,4] => [3,5,2,1,4] => 2
[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [4,1,3,2,5] => [3,1,4,2,5] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => [5,4,3,1,2] => [3,4,5,2,1] => 0
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => [5,1,3,4,2] => [3,1,4,5,2] => 1
[1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => [5,1,3,2,4] => [3,1,5,2,4] => 2
[1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => [4,1,2,3,5] => [4,1,2,3,5] => 2
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => [5,1,4,2,3] => [4,1,5,3,2] => 2
[1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => [5,4,1,2,3] => [4,5,2,3,1] => 2
[1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => [5,1,2,4,3] => [4,1,2,5,3] => 2
[1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => [5,1,2,3,4] => [5,1,2,3,4] => 3
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [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] => [1,2,3,4,6,5] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [1,2,3,5,6,4] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => [1,2,3,6,4,5] => [1,2,3,6,4,5] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => [1,2,4,5,6,3] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => [1,2,6,4,3,5] => [1,2,4,6,3,5] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => [1,2,5,3,4,6] => [1,2,5,3,4,6] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => [1,2,6,5,3,4] => [1,2,5,6,4,3] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => [1,2,6,3,5,4] => [1,2,5,3,6,4] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => [1,2,6,3,4,5] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [1,3,2,5,6,4] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => [1,3,2,6,4,5] => [1,3,2,6,4,5] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [1,3,4,2,6,5] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => [1,3,4,5,2,6] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => [1,3,4,5,6,2] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => [1,6,3,4,2,5] => [1,3,4,6,2,5] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => [1,5,3,2,4,6] => [1,3,5,2,4,6] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => [1,6,3,5,2,4] => [1,3,5,6,4,2] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => [1,6,3,2,5,4] => [1,3,5,2,6,4] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => [1,6,3,2,4,5] => [1,3,6,2,4,5] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => [1,4,2,3,5,6] => [1,4,2,3,5,6] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => [1,4,2,3,6,5] => [1,4,2,3,6,5] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => [1,5,4,2,3,6] => [1,4,5,3,2,6] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => [1,6,4,2,5,3] => [1,4,5,3,6,2] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => [1,6,4,2,3,5] => [1,4,6,3,2,5] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [1,5,2,4,3,6] => [1,4,2,5,3,6] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => [1,6,5,4,2,3] => [1,4,5,6,3,2] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [1,6,2,4,5,3] => [1,4,2,5,6,3] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => [1,6,2,4,3,5] => [1,4,2,6,3,5] => 2
>>> Load all 196 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => [1,5,2,3,4,6] => [1,5,2,3,4,6] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => [1,6,2,5,3,4] => [1,5,2,6,4,3] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => [1,6,5,2,3,4] => [1,5,6,3,4,2] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => [1,6,2,3,5,4] => [1,5,2,3,6,4] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => [1,6,2,3,4,5] => [1,6,2,3,4,5] => 3
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 0
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 0
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [2,1,3,5,6,4] => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => [2,1,3,6,4,5] => [2,1,3,6,4,5] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => 0
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [2,1,4,5,3,6] => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => [2,1,4,5,6,3] => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => [2,1,6,4,3,5] => [2,1,4,6,3,5] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [2,1,5,3,4,6] => [2,1,5,3,4,6] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => [2,1,6,5,3,4] => [2,1,5,6,4,3] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => [2,1,6,3,5,4] => [2,1,5,3,6,4] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => [2,1,6,3,4,5] => [2,1,6,3,4,5] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [2,3,1,4,6,5] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => [3,2,1,6,4,5] => [2,3,1,6,4,5] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [2,3,4,1,5,6] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => [2,3,4,1,6,5] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [2,3,4,5,1,6] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,1,5] => [6,2,3,4,1,5] => [2,3,4,6,1,5] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => [5,2,3,1,4,6] => [2,3,5,1,4,6] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => [6,2,3,5,1,4] => [2,3,5,6,4,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,1,4] => [6,2,3,1,5,4] => [2,3,5,1,6,4] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,1,4,5] => [6,2,3,1,4,5] => [2,3,6,1,4,5] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => [4,2,1,3,6,5] => [2,4,1,3,6,5] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => [5,2,4,1,3,6] => [2,4,5,3,1,6] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => [6,2,4,1,5,3] => [2,4,5,3,6,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => [6,2,4,1,3,5] => [2,4,6,3,1,5] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => [5,2,1,4,3,6] => [2,4,1,5,3,6] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => [6,2,5,4,1,3] => [2,4,5,6,3,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,1,3] => [6,2,1,4,5,3] => [2,4,1,5,6,3] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => [6,2,1,4,3,5] => [2,4,1,6,3,5] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => [2,5,1,3,4,6] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,4] => [6,2,1,5,3,4] => [2,5,1,6,4,3] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => [6,2,5,1,3,4] => [2,5,6,3,4,1] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,1,3,4] => [6,2,1,3,5,4] => [2,5,1,3,6,4] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => [2,6,1,3,4,5] => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => [3,1,2,4,6,5] => [3,1,2,4,6,5] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => [3,1,2,5,4,6] => [3,1,2,5,4,6] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => [3,1,2,6,5,4] => [3,1,2,5,6,4] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [3,1,2,6,4,5] => [3,1,2,6,4,5] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [4,3,1,2,5,6] => [3,4,2,1,5,6] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => [4,3,1,2,6,5] => [3,4,2,1,6,5] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [5,3,1,4,2,6] => [3,4,2,5,1,6] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => [6,3,1,4,5,2] => [3,4,2,5,6,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,4,6,2,5] => [6,3,1,4,2,5] => [3,4,2,6,1,5] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => [5,3,1,2,4,6] => [3,5,2,1,4,6] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => [6,3,1,5,2,4] => [3,5,2,6,4,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => [6,3,1,2,5,4] => [3,5,2,1,6,4] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => [6,3,1,2,4,5] => [3,6,2,1,4,5] => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => [4,1,3,2,5,6] => [3,1,4,2,5,6] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => [4,1,3,2,6,5] => [3,1,4,2,6,5] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => [5,4,3,1,2,6] => [3,4,5,2,1,6] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => [6,4,3,1,5,2] => [3,4,5,2,6,1] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => [6,4,3,1,2,5] => [3,4,6,2,1,5] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [5,1,3,4,2,6] => [3,1,4,5,2,6] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => [6,5,3,4,1,2] => [3,4,5,6,2,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => [6,1,3,4,5,2] => [3,1,4,5,6,2] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => [6,1,3,4,2,5] => [3,1,4,6,2,5] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => [5,1,3,2,4,6] => [3,1,5,2,4,6] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => [6,1,3,5,2,4] => [3,1,5,6,4,2] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => [6,5,3,1,2,4] => [3,5,6,2,4,1] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => [6,1,3,2,5,4] => [3,1,5,2,6,4] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => [6,1,3,2,4,5] => [3,1,6,2,4,5] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => [4,1,2,3,6,5] => [4,1,2,3,6,5] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => [5,1,4,2,3,6] => [4,1,5,3,2,6] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => [6,1,4,2,5,3] => [4,1,5,3,6,2] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => [6,1,4,2,3,5] => [4,1,6,3,2,5] => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [5,4,1,2,3,6] => [4,5,2,3,1,6] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => [6,5,4,1,2,3] => [4,5,6,3,2,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,5,6,2,3] => [6,4,1,2,5,3] => [4,5,2,3,6,1] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => [6,4,1,2,3,5] => [4,6,2,3,1,5] => 3
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => [5,1,2,4,3,6] => [4,1,2,5,3,6] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => [6,1,5,4,2,3] => [4,1,5,6,3,2] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => [6,5,1,4,2,3] => [4,5,2,6,3,1] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => [4,1,2,5,6,3] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5] => [6,1,2,4,3,5] => [4,1,2,6,3,5] => 3
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => 3
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => [6,1,2,5,3,4] => [5,1,2,6,4,3] => 3
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1,2,6,3,4] => [6,1,5,2,3,4] => [5,1,6,3,4,2] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => [6,5,1,2,3,4] => [5,6,2,3,4,1] => 3
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => [6,1,2,3,5,4] => [5,1,2,3,6,4] => 3
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => 4
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Description
The cycle descent number of a permutation.
Let $(i_1,\ldots,i_k)$ be a cycle of a permutation $\pi$ such that $i_1$ is its smallest element. A **cycle descent** of $(i_1,\ldots,i_k)$ is an $i_a$ for $1 \leq a < k$ such that $i_a > i_{a+1}$. The **cycle descent set** of $\pi$ is then the set of descents in all the cycles of $\pi$, and the **cycle descent number** is its cardinality.
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.
Map
Clarke-Steingrimsson-Zeng
Description
The Clarke-Steingrimsson-Zeng map sending descents to excedances.
This is the map $\Phi$ in [1, sec.3]. In particular, it satisfies
$$ (des, Dbot, Ddif, Res)\pi = (exc, Ebot, Edif, Ine)\Phi(\pi), $$
where
  • $des$ is the number of descents, St000021The number of descents of a permutation.,
  • $exc$ is the number of (strict) excedances, St000155The number of exceedances (also excedences) of a permutation.,
  • $Dbot$ is the sum of the descent bottoms, St000154The sum of the descent bottoms of a permutation.,
  • $Ebot$ is the sum of the excedance bottoms,
  • $Ddif$ is the sum of the descent differences, St000030The sum of the descent differences of a permutations.,
  • $Edif$ is the sum of the excedance differences (or depth), St000029The depth of a permutation.,
  • $Res$ is the sum of the (right) embracing numbers,
  • $Ine$ is the sum of the side numbers.
Map
Corteel
Description
Corteel's map interchanging the number of crossings and the number of nestings of a permutation.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.