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] => [3,2,1] => 0
[1,0,1,1,0,0] => [1,3,2] => [1,3,2] => [2,3,1] => 0
[1,1,0,0,1,0] => [2,1,3] => [2,1,3] => [3,1,2] => 0
[1,1,0,1,0,0] => [2,3,1] => [3,1,2] => [2,1,3] => 0
[1,1,1,0,0,0] => [3,1,2] => [3,2,1] => [1,2,3] => 0
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [3,1,4,2] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,4,3] => [3,2,1,4] => 0
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,3,2,4] => [4,3,2,1] => 0
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,4,2,3] => [2,3,1,4] => 0
[1,0,1,1,1,0,0,0] => [1,4,2,3] => [1,4,3,2] => [2,4,3,1] => 0
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [2,1,3,4] => [3,4,2,1] => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [2,1,4,3] => [3,2,4,1] => 0
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [3,1,2,4] => [1,4,3,2] => 0
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [4,1,2,3] => [2,1,3,4] => 0
[1,1,0,1,1,0,0,0] => [2,4,1,3] => [4,3,1,2] => [1,2,4,3] => 0
[1,1,1,0,0,0,1,0] => [3,1,2,4] => [3,2,1,4] => [4,3,1,2] => 0
[1,1,1,0,0,1,0,0] => [3,1,4,2] => [4,2,1,3] => [2,3,4,1] => 0
[1,1,1,0,1,0,0,0] => [3,4,1,2] => [3,1,4,2] => [4,2,3,1] => 0
[1,1,1,1,0,0,0,0] => [4,1,2,3] => [4,3,2,1] => [2,4,1,3] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [3,1,4,5,2] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => [3,1,4,2,5] => 0
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,4,3,5] => [3,1,5,4,2] => 0
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,5,3,4] => [3,2,1,4,5] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [1,2,5,4,3] => [3,2,1,5,4] => 0
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,3,2,4,5] => [4,3,1,5,2] => 0
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => [4,3,2,1,5] => 0
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,4,2,3,5] => [5,3,1,4,2] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,5,2,3,4] => [2,3,1,4,5] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [1,5,4,2,3] => [2,5,3,1,4] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [1,4,3,2,5] => [5,4,3,2,1] => 0
[1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [1,5,3,2,4] => [2,4,3,1,5] => 0
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [1,4,2,5,3] => [5,3,2,1,4] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [1,5,4,3,2] => [2,5,4,3,1] => 0
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [2,1,3,4,5] => [3,4,1,5,2] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [2,1,3,5,4] => [3,4,2,1,5] => 1
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [2,1,4,3,5] => [3,5,4,2,1] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [2,1,5,3,4] => [3,2,4,1,5] => 0
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [2,1,5,4,3] => [3,2,5,4,1] => 0
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [3,1,2,4,5] => [1,4,3,5,2] => 0
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [3,1,2,5,4] => [1,4,3,2,5] => 0
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [4,1,2,3,5] => [1,5,3,4,2] => 0
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [5,1,2,3,4] => [2,1,3,4,5] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4] => [5,4,1,2,3] => [1,2,5,3,4] => 0
[1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => [4,3,1,2,5] => [5,1,4,3,2] => 0
[1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => [5,3,1,2,4] => [1,2,4,3,5] => 0
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => [4,1,2,5,3] => [1,5,3,2,4] => 0
[1,1,0,1,1,1,0,0,0,0] => [2,5,1,3,4] => [5,4,3,1,2] => [2,5,1,4,3] => 0
[1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => [3,2,1,4,5] => [4,3,5,2,1] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => [3,2,1,5,4] => [4,3,2,5,1] => 0
[1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => [4,2,1,3,5] => [5,3,4,2,1] => 0
[1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => [5,2,1,3,4] => [2,3,4,1,5] => 0
[1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => [5,4,2,1,3] => [2,5,3,4,1] => 0
[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [3,1,4,2,5] => [4,5,3,2,1] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => [3,1,5,2,4] => [4,2,3,1,5] => 0
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => [5,2,4,1,3] => [1,2,3,5,4] => 0
[1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => [3,1,5,4,2] => [4,2,5,3,1] => 1
[1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => [4,3,2,1,5] => [5,4,3,1,2] => 0
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => [5,3,2,1,4] => [2,4,3,5,1] => 0
[1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => [4,2,1,5,3] => [5,3,2,4,1] => 0
[1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => [5,3,1,4,2] => [2,4,5,3,1] => 1
[1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => [5,4,3,2,1] => [2,5,4,1,3] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [3,1,4,5,6,2] => 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] => [3,1,4,5,2,6] => 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] => [3,1,4,6,5,2] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => [3,1,4,2,5,6] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => [1,2,3,6,5,4] => [3,1,4,2,6,5] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [3,1,5,4,6,2] => 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] => [3,1,5,4,2,6] => 0
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => [3,1,6,4,5,2] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => [3,2,1,4,5,6] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => [1,2,6,5,3,4] => [3,2,1,6,4,5] => 0
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => [1,2,5,4,3,6] => [3,1,6,5,4,2] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => [1,2,6,4,3,5] => [3,2,1,5,4,6] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => [1,2,5,3,6,4] => [3,1,6,4,2,5] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => [1,2,6,5,4,3] => [3,2,1,6,5,4] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [4,3,1,5,6,2] => 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] => [4,3,1,5,2,6] => 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] => [4,3,1,6,5,2] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,3,2,6,4,5] => [4,3,2,1,5,6] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => [1,3,2,6,5,4] => [4,3,2,1,6,5] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => [5,3,1,4,6,2] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,4,2,3,6,5] => [5,3,1,4,2,6] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => [6,3,1,4,5,2] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => [2,3,1,4,5,6] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => [1,6,5,2,3,4] => [2,6,3,1,4,5] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => [1,5,4,2,3,6] => [6,5,3,1,4,2] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => [1,6,4,2,3,5] => [2,5,3,1,4,6] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => [1,5,2,3,6,4] => [6,3,1,4,2,5] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => [1,6,5,4,2,3] => [2,6,5,3,1,4] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => [1,4,3,2,5,6] => [5,4,3,1,6,2] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => [1,4,3,2,6,5] => [5,4,3,2,1,6] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => [1,5,3,2,4,6] => [6,4,3,1,5,2] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => [1,6,3,2,4,5] => [2,4,3,1,5,6] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => [1,6,5,3,2,4] => [2,6,4,3,1,5] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [1,4,2,5,3,6] => [5,3,1,6,4,2] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => [1,4,2,6,3,5] => [5,3,2,1,4,6] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [1,6,3,5,2,4] => [2,4,1,6,3,5] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => [1,4,2,6,5,3] => [5,3,2,1,6,4] => 0
>>> Load all 222 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => [1,5,4,3,2,6] => [6,5,4,3,2,1] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => [1,6,4,3,2,5] => [2,5,4,3,1,6] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => [1,5,3,2,6,4] => [6,4,3,2,1,5] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => [1,6,4,2,5,3] => [2,5,3,1,6,4] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => [1,6,5,4,3,2] => [2,6,5,4,3,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [3,4,1,5,6,2] => 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] => [3,4,1,5,2,6] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [3,4,1,6,5,2] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,3,6,4,5] => [3,4,2,1,5,6] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => [2,1,3,6,5,4] => [3,4,2,1,6,5] => 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] => [3,5,4,1,6,2] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [3,5,4,2,1,6] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [2,1,5,3,4,6] => [3,6,4,1,5,2] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,6,3,4,5] => [3,2,4,1,5,6] => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => [2,1,6,5,3,4] => [3,2,6,4,1,5] => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [2,1,5,4,3,6] => [3,6,5,4,2,1] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => [2,1,6,4,3,5] => [3,2,5,4,1,6] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => [2,1,5,3,6,4] => [3,6,4,2,1,5] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => [2,1,6,5,4,3] => [3,2,6,5,4,1] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [1,4,3,5,6,2] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [3,1,2,4,6,5] => [1,4,3,5,2,6] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [3,1,2,5,4,6] => [1,4,3,6,5,2] => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,1,2,6,4,5] => [1,4,3,2,5,6] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => [3,1,2,6,5,4] => [1,4,3,2,6,5] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => [1,5,3,4,6,2] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [4,1,2,3,6,5] => [1,5,3,4,2,6] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => [1,6,3,4,5,2] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [2,1,3,4,5,6] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,1,5] => [6,5,1,2,3,4] => [1,2,6,3,4,5] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => [5,4,1,2,3,6] => [6,1,5,3,4,2] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => [6,4,1,2,3,5] => [1,2,5,3,4,6] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,1,4] => [5,1,2,3,6,4] => [1,6,3,4,2,5] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,1,4,5] => [6,5,4,1,2,3] => [2,6,1,5,3,4] => 0
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => [4,3,1,2,5,6] => [5,1,4,3,6,2] => 0
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,1,3,6,5] => [4,3,1,2,6,5] => [5,1,4,3,2,6] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => [5,3,1,2,4,6] => [6,1,4,3,5,2] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => [6,3,1,2,4,5] => [1,2,4,3,5,6] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => [6,5,3,1,2,4] => [2,6,1,4,3,5] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => [4,1,2,5,3,6] => [1,5,3,6,4,2] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,1,6,3] => [4,1,2,6,3,5] => [1,5,3,2,4,6] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,1,3] => [6,3,5,1,2,4] => [1,2,4,6,3,5] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => [4,1,2,6,5,3] => [1,5,3,2,6,4] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => [5,4,3,1,2,6] => [6,5,1,4,3,2] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,4] => [6,4,3,1,2,5] => [2,5,1,4,3,6] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => [5,3,1,2,6,4] => [6,1,4,3,2,5] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,1,3,4] => [6,4,1,2,5,3] => [1,2,5,3,6,4] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,3,4,5] => [6,5,4,3,1,2] => [2,6,5,1,4,3] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => [4,3,5,1,6,2] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => [3,2,1,4,6,5] => [4,3,5,2,1,6] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => [3,2,1,5,4,6] => [4,3,6,5,2,1] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => [3,2,1,6,4,5] => [4,3,2,5,1,6] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [3,2,1,6,5,4] => [4,3,2,6,5,1] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [4,2,1,3,5,6] => [5,3,4,1,6,2] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => [4,2,1,3,6,5] => [5,3,4,2,1,6] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [5,2,1,3,4,6] => [6,3,4,1,5,2] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => [6,2,1,3,4,5] => [2,3,4,1,5,6] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,4,6,2,5] => [6,5,2,1,3,4] => [2,6,3,4,1,5] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => [5,4,2,1,3,6] => [6,5,3,4,2,1] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => [6,4,2,1,3,5] => [2,5,3,4,1,6] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => [5,2,1,3,6,4] => [6,3,4,2,1,5] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => [6,5,4,2,1,3] => [2,6,5,3,4,1] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [4,5,3,1,6,2] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => [3,1,4,2,6,5] => [4,5,3,2,1,6] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => [3,1,5,2,4,6] => [4,6,3,1,5,2] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => [3,1,6,2,4,5] => [4,2,3,1,5,6] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => [3,1,6,5,2,4] => [4,2,6,3,1,5] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [5,2,4,1,3,6] => [6,1,3,5,4,2] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => [6,2,4,1,3,5] => [1,2,3,5,4,6] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => [5,1,3,6,2,4] => [1,6,4,2,3,5] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => [6,5,2,4,1,3] => [2,6,1,3,5,4] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => [3,1,5,4,2,6] => [4,6,5,3,2,1] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => [3,1,6,4,2,5] => [4,2,5,3,1,6] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => [3,1,5,2,6,4] => [4,6,3,2,1,5] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => [5,2,6,4,1,3] => [6,3,1,2,5,4] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => [3,1,6,5,4,2] => [4,2,6,5,3,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => [5,4,3,6,2,1] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => [4,3,2,1,6,5] => [5,4,3,2,6,1] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => [5,3,2,1,4,6] => [6,4,3,5,2,1] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => [6,3,2,1,4,5] => [2,4,3,5,1,6] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => [6,5,3,2,1,4] => [2,6,4,3,5,1] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [4,2,1,5,3,6] => [5,3,6,4,2,1] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => [4,2,1,6,3,5] => [5,3,2,4,1,6] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,5,6,2,3] => [6,3,5,2,1,4] => [2,4,6,3,5,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => [4,2,1,6,5,3] => [5,3,2,6,4,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => [5,3,1,4,2,6] => [6,4,5,3,2,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => [6,3,1,4,2,5] => [2,4,5,3,1,6] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => [5,2,6,3,1,4] => [6,3,2,4,5,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [5,6,3,2,1,4] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5] => [6,5,3,1,4,2] => [2,6,4,5,3,1] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => [6,5,4,3,1,2] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => [6,4,3,2,1,5] => [2,5,4,3,6,1] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1,2,6,3,4] => [5,3,2,1,6,4] => [6,4,3,2,5,1] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => [6,4,2,1,5,3] => [2,5,3,6,4,1] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => [5,3,1,6,4,2] => [6,4,2,5,3,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => [2,6,5,4,1,3] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => [1,4,3,5,6,7,2] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [3,1,2,4,5,7,6] => [1,4,3,5,6,2,7] => 0
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [3,1,2,4,6,5,7] => [1,4,3,5,7,6,2] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [3,1,2,4,7,5,6] => [1,4,3,5,2,6,7] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,5,6] => [3,1,2,4,7,6,5] => [1,4,3,5,2,7,6] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [3,1,2,5,4,6,7] => [1,4,3,6,5,7,2] => 0
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [3,1,2,5,4,7,6] => [1,4,3,6,5,2,7] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [3,1,2,6,4,5,7] => [1,4,3,7,5,6,2] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [3,1,2,7,4,5,6] => [1,4,3,2,5,6,7] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,4,6] => [3,1,2,7,6,4,5] => [1,4,3,2,7,5,6] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,4,5,7] => [3,1,2,6,5,4,7] => [1,4,3,7,6,5,2] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,4,7,5] => [3,1,2,7,5,4,6] => [1,4,3,2,6,5,7] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,4,5] => [3,1,2,6,4,7,5] => [1,4,3,7,5,2,6] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,4,5,6] => [3,1,2,7,6,5,4] => [1,4,3,2,7,6,5] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,1,6] => [7,6,1,2,3,4,5] => [1,2,7,3,4,5,6] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,1,7,5] => [7,5,1,2,3,4,6] => [1,2,6,3,4,5,7] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,1,6,7,4] => [7,4,1,2,3,5,6] => [1,2,5,3,4,6,7] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,1,4] => [7,4,6,1,2,3,5] => [1,2,5,7,3,4,6] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,1,4,5] => [7,5,1,2,3,6,4] => [1,2,6,3,4,7,5] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,6,7,3] => [7,3,1,2,4,5,6] => [1,2,4,3,5,6,7] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,1,7,3] => [7,3,5,1,2,4,6] => [1,2,4,6,3,5,7] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,1,3,7,4] => [7,4,1,2,5,3,6] => [1,2,5,3,6,4,7] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,1,6,7,2] => [7,2,4,1,3,5,6] => [1,2,3,5,4,6,7] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,1,2] => [7,2,4,6,1,3,5] => [1,2,3,5,7,4,6] => 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,1,2,5] => [7,5,1,3,6,2,4] => [1,2,6,4,7,3,5] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,1,7,2,4] => [7,4,1,3,6,2,5] => [1,2,5,4,7,3,6] => 0
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Description
The number of restricted non-inversions between exceedances.
This is for a permutation $\sigma$ of length $n$ given by
$$\operatorname{nie}(\sigma) = \#\{1 \leq i, j \leq n \mid i < j < \sigma(i) < \sigma(j) \}.$$
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
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
inverse toric promotion
Description
Toric promotion of a permutation.
Let $\sigma\in\mathfrak S_n$ be a permutation and let
$ \tau_{i, j}(\sigma) = \begin{cases} \sigma & \text{if $|\sigma^{-1}(i) - \sigma^{-1}(j)| = 1$}\\ (i, j)\circ\sigma & \text{otherwise}. \end{cases} $
The toric promotion operator is the product $\tau_{n,1}\tau_{n-1,n}\dots\tau_{1,2}$.
This is the special case of toric promotion on graphs for the path graph. Its order is $n-1$.