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] => [3,1,2] => [3,2,1] => 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] => 1
[1,1,1,0,0,0] => [3,1,2] => [1,3,2] => [1,3,2] => 0
[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] => [3,1,2,4] => [3,2,1,4] => 0
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [3,1,4,2] => [4,2,1,3] => 0
[1,0,1,1,1,0,0,0] => [1,4,2,3] => [4,1,2,3] => [4,3,2,1] => 0
[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] => 1
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [3,2,4,1] => [2,4,1,3] => 1
[1,1,0,1,1,0,0,0] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => 1
[1,1,1,0,0,0,1,0] => [3,1,2,4] => [1,3,2,4] => [1,3,2,4] => 0
[1,1,1,0,0,1,0,0] => [3,1,4,2] => [1,3,4,2] => [1,4,2,3] => 0
[1,1,1,0,1,0,0,0] => [3,4,1,2] => [4,3,1,2] => [4,2,3,1] => 1
[1,1,1,1,0,0,0,0] => [4,1,2,3] => [1,4,2,3] => [1,4,3,2] => 0
[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] => [1,2,5,3,4] => [1,2,5,4,3] => 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] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,3,4] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [3,1,2,4,5] => [3,2,1,4,5] => 0
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [3,1,2,5,4] => [3,2,1,5,4] => 0
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [3,1,4,2,5] => [4,2,1,3,5] => 0
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [3,1,4,5,2] => [5,2,1,3,4] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,2,4] => [3,1,5,2,4] => [5,4,2,1,3] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,4,2,3,5] => [4,1,2,3,5] => [4,3,2,1,5] => 0
[1,0,1,1,1,0,0,1,0,0] => [1,4,2,5,3] => [4,1,2,5,3] => [5,3,2,1,4] => 0
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,2,3] => [4,1,5,2,3] => [4,2,1,5,3] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,5,2,3,4] => [5,1,2,3,4] => [5,4,3,2,1] => 0
[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] => [2,1,5,3,4] => [2,1,5,4,3] => 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] => 1
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,3,4] => [2,1,3,5,4] => [2,1,3,5,4] => 0
[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] => 1
[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] => 1
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [3,2,4,1,5] => [2,4,1,3,5] => 1
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [3,2,4,5,1] => [2,5,1,3,4] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4] => [3,2,5,1,4] => [2,5,4,1,3] => 1
[1,1,0,1,1,0,0,0,1,0] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,3,1,5] => 1
[1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,3] => [4,2,1,5,3] => [2,5,3,1,4] => 1
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,3] => [4,2,5,1,3] => [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] => [2,5,4,3,1] => 1
[1,1,1,0,0,0,1,0,1,0] => [3,1,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 0
[1,1,1,0,0,0,1,1,0,0] => [3,1,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[1,1,1,0,0,1,0,0,1,0] => [3,1,4,2,5] => [1,3,4,2,5] => [1,4,2,3,5] => 0
[1,1,1,0,0,1,0,1,0,0] => [3,1,4,5,2] => [1,3,4,5,2] => [1,5,2,3,4] => 0
[1,1,1,0,0,1,1,0,0,0] => [3,1,5,2,4] => [1,3,5,2,4] => [1,5,4,2,3] => 0
[1,1,1,0,1,0,0,0,1,0] => [3,4,1,2,5] => [4,3,1,2,5] => [4,2,3,1,5] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,2] => [4,3,1,5,2] => [5,2,3,1,4] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,2] => [4,3,5,1,2] => [4,1,5,2,3] => 0
[1,1,1,0,1,1,0,0,0,0] => [3,5,1,2,4] => [5,3,1,2,4] => [5,4,2,3,1] => 1
[1,1,1,1,0,0,0,0,1,0] => [4,1,2,3,5] => [1,4,2,3,5] => [1,4,3,2,5] => 0
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,5,3] => [1,4,2,5,3] => [1,5,3,2,4] => 0
[1,1,1,1,0,0,1,0,0,0] => [4,1,5,2,3] => [1,4,5,2,3] => [1,4,2,5,3] => 0
[1,1,1,1,0,1,0,0,0,0] => [4,5,1,2,3] => [5,4,1,2,3] => [4,2,5,3,1] => 1
[1,1,1,1,1,0,0,0,0,0] => [5,1,2,3,4] => [1,5,2,3,4] => [1,5,4,3,2] => 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] => [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] => [1,2,5,3,4,6] => [1,2,5,4,3,6] => 0
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,5,3,6,4] => [1,2,6,4,3,5] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,4,5] => [1,2,6,3,4,5] => [1,2,6,5,4,3] => 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] => [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] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,5,4,6,3] => [1,2,4,6,3,5] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,3,5] => [1,2,6,4,3,5] => [1,2,4,6,5,3] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,3,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,3,6,4] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,3,4] => [1,2,6,5,3,4] => [1,2,6,4,5,3] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,3,4,5] => [1,2,3,6,4,5] => [1,2,3,6,5,4] => 0
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => [3,2,1,4,5,6] => 0
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [3,1,2,4,6,5] => [3,2,1,4,6,5] => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [3,1,2,5,4,6] => [3,2,1,5,4,6] => 0
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [3,1,2,5,6,4] => [3,2,1,6,4,5] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,4,5] => [3,1,2,6,4,5] => [3,2,1,6,5,4] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [3,1,4,2,5,6] => [4,2,1,3,5,6] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [3,1,4,2,6,5] => [4,2,1,3,6,5] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [3,1,4,5,2,6] => [5,2,1,3,4,6] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [3,1,4,5,6,2] => [6,2,1,3,4,5] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,2,5] => [3,1,4,6,2,5] => [6,5,2,1,3,4] => 0
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,2,4,6] => [3,1,5,2,4,6] => [5,4,2,1,3,6] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,2,6,4] => [3,1,5,2,6,4] => [6,4,2,1,3,5] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,2,4] => [3,1,5,6,2,4] => [5,2,1,3,6,4] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,2,4,5] => [3,1,6,2,4,5] => [6,5,4,2,1,3] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,2,3,5,6] => [4,1,2,3,5,6] => [4,3,2,1,5,6] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,2,3,6,5] => [4,1,2,3,6,5] => [4,3,2,1,6,5] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,2,5,3,6] => [4,1,2,5,3,6] => [5,3,2,1,4,6] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,6,3] => [4,1,2,5,6,3] => [6,3,2,1,4,5] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,2,6,3,5] => [4,1,2,6,3,5] => [6,5,3,2,1,4] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,2,3,6] => [4,1,5,2,3,6] => [4,2,1,5,3,6] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,2,6,3] => [4,1,5,2,6,3] => [4,2,1,6,3,5] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,2,3] => [4,1,5,6,2,3] => [6,3,5,2,1,4] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,2,3,5] => [4,1,6,2,3,5] => [4,2,1,6,5,3] => 0
>>> Load all 234 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,2,3,4,6] => [5,1,2,3,4,6] => [5,4,3,2,1,6] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,6,4] => [5,1,2,3,6,4] => [6,4,3,2,1,5] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,2,6,3,4] => [5,1,2,6,3,4] => [5,3,2,1,6,4] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,2,3,4] => [5,1,6,2,3,4] => [6,4,2,1,5,3] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,2,3,4,5] => [6,1,2,3,4,5] => [6,5,4,3,2,1] => 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] => [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] => [2,1,5,3,4,6] => [2,1,5,4,3,6] => 0
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [2,1,5,3,6,4] => [2,1,6,4,3,5] => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,4,5] => [2,1,6,3,4,5] => [2,1,6,5,4,3] => 0
[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] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [2,1,5,4,6,3] => [2,1,4,6,3,5] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,3,5] => [2,1,6,4,3,5] => [2,1,4,6,5,3] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,3,4,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,3,6,4] => [2,1,3,5,6,4] => [2,1,3,6,4,5] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,3,4] => [2,1,6,5,3,4] => [2,1,6,4,5,3] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,3,4,5] => [2,1,3,6,4,5] => [2,1,3,6,5,4] => 0
[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] => 1
[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] => 1
[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] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [3,2,1,5,6,4] => [2,3,1,6,4,5] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,4,5] => [3,2,1,6,4,5] => [2,3,1,6,5,4] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [3,2,4,1,5,6] => [2,4,1,3,5,6] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [3,2,4,1,6,5] => [2,4,1,3,6,5] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [3,2,4,5,1,6] => [2,5,1,3,4,6] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [3,2,4,5,6,1] => [2,6,1,3,4,5] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,1,5] => [3,2,4,6,1,5] => [2,6,5,1,3,4] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,1,4,6] => [3,2,5,1,4,6] => [2,5,4,1,3,6] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,1,6,4] => [3,2,5,1,6,4] => [2,6,4,1,3,5] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,1,4] => [3,2,5,6,1,4] => [2,5,1,3,6,4] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,1,4,5] => [3,2,6,1,4,5] => [2,6,5,4,1,3] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,3,5,6] => [4,2,1,3,5,6] => [2,4,3,1,5,6] => 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] => [2,4,3,1,6,5] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,1,5,3,6] => [4,2,1,5,3,6] => [2,5,3,1,4,6] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,1,5,6,3] => [4,2,1,5,6,3] => [2,6,3,1,4,5] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,1,6,3,5] => [4,2,1,6,3,5] => [2,6,5,3,1,4] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,1,3,6] => [4,2,5,1,3,6] => [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] => [4,2,5,1,6,3] => [2,4,1,6,3,5] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,1,3] => [4,2,5,6,1,3] => [2,6,3,5,1,4] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,1,3,5] => [4,2,6,1,3,5] => [2,4,1,6,5,3] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1,3,4,6] => [5,2,1,3,4,6] => [2,5,4,3,1,6] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,1,3,6,4] => [5,2,1,3,6,4] => [2,6,4,3,1,5] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,1,6,3,4] => [5,2,1,6,3,4] => [2,5,3,1,6,4] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,1,3,4] => [5,2,6,1,3,4] => [2,6,4,1,5,3] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,1,3,4,5] => [6,2,1,3,4,5] => [2,6,5,4,3,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 0
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,1,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,1,2,5,6,4] => [1,3,2,5,6,4] => [1,3,2,6,4,5] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,1,2,6,4,5] => [1,3,2,6,4,5] => [1,3,2,6,5,4] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,1,4,2,6,5] => [1,3,4,2,6,5] => [1,4,2,3,6,5] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,4,5,6,2] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,1,4,6,2,5] => [1,3,4,6,2,5] => [1,6,5,2,3,4] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,5,2,4,6] => [1,3,5,2,4,6] => [1,5,4,2,3,6] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,1,5,2,6,4] => [1,3,5,2,6,4] => [1,6,4,2,3,5] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,5,6,2,4] => [1,3,5,6,2,4] => [1,5,2,3,6,4] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,1,6,2,4,5] => [1,3,6,2,4,5] => [1,6,5,4,2,3] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,1,2,5,6] => [4,3,1,2,5,6] => [4,2,3,1,5,6] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,1,2,6,5] => [4,3,1,2,6,5] => [4,2,3,1,6,5] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,1,5,2,6] => [4,3,1,5,2,6] => [5,2,3,1,4,6] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,1,5,6,2] => [4,3,1,5,6,2] => [6,2,3,1,4,5] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,1,6,2,5] => [4,3,1,6,2,5] => [6,5,2,3,1,4] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,1,2,6] => [4,3,5,1,2,6] => [4,1,5,2,3,6] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,1,6,2] => [4,3,5,1,6,2] => [4,1,6,2,3,5] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,1,2] => [4,3,5,6,1,2] => [6,2,3,5,1,4] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,1,2,5] => [4,3,6,1,2,5] => [4,1,6,5,2,3] => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,1,2,4,6] => [5,3,1,2,4,6] => [5,4,2,3,1,6] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,1,2,6,4] => [5,3,1,2,6,4] => [6,4,2,3,1,5] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,1,6,2,4] => [5,3,1,6,2,4] => [5,2,3,1,6,4] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,1,2,4] => [5,3,6,1,2,4] => [6,4,1,5,2,3] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,1,2,4,5] => [6,3,1,2,4,5] => [6,5,4,2,3,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,2,3,5,6] => [1,4,2,3,5,6] => [1,4,3,2,5,6] => 0
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,1,2,3,6,5] => [1,4,2,3,6,5] => [1,4,3,2,6,5] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,1,2,5,3,6] => [1,4,2,5,3,6] => [1,5,3,2,4,6] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,1,2,5,6,3] => [1,4,2,5,6,3] => [1,6,3,2,4,5] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,1,2,6,3,5] => [1,4,2,6,3,5] => [1,6,5,3,2,4] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,1,5,2,3,6] => [1,4,5,2,3,6] => [1,4,2,5,3,6] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,1,5,2,6,3] => [1,4,5,2,6,3] => [1,4,2,6,3,5] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,1,5,6,2,3] => [1,4,5,6,2,3] => [1,6,3,5,2,4] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,1,6,2,3,5] => [1,4,6,2,3,5] => [1,4,2,6,5,3] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,1,2,3,6] => [5,4,1,2,3,6] => [4,2,5,3,1,6] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,1,2,6,3] => [5,4,1,2,6,3] => [4,2,6,3,1,5] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,1,6,2,3] => [5,4,1,6,2,3] => [6,3,1,5,2,4] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,1,2,3] => [5,4,6,1,2,3] => [5,2,4,1,6,3] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,1,2,3,5] => [6,4,1,2,3,5] => [4,2,6,5,3,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6] => [1,5,2,3,4,6] => [1,5,4,3,2,6] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,6,4] => [1,5,2,3,6,4] => [1,6,4,3,2,5] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,1,2,6,3,4] => [1,5,2,6,3,4] => [1,5,3,2,6,4] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,1,6,2,3,4] => [1,5,6,2,3,4] => [1,6,4,2,5,3] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,1,2,3,4] => [6,5,1,2,3,4] => [6,4,2,5,3,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,1,2,3,4,5] => [1,6,2,3,4,5] => [1,6,5,4,3,2] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,5,6] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,3,7,4,5] => [1,2,3,6,7,4,5] => [1,2,3,6,4,7,5] => 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => [3,2,1,4,5,6,7] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,2] => [3,1,4,5,6,7,2] => [7,2,1,3,4,5,6] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,2,6,7,4] => [3,1,5,2,6,7,4] => [7,4,2,1,3,5,6] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,2,3,5,6,7] => [4,1,2,3,5,6,7] => [4,3,2,1,5,6,7] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,6,7,3] => [4,1,2,5,6,7,3] => [7,3,2,1,4,5,6] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,2,3,4,6,7] => [5,1,2,3,4,6,7] => [5,4,3,2,1,6,7] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2,3,4,7,6] => [5,1,2,3,4,7,6] => [5,4,3,2,1,7,6] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,2,3,4,5,7] => [6,1,2,3,4,5,7] => [6,5,4,3,2,1,7] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,2,3,4,5,6] => [7,1,2,3,4,5,6] => [7,6,5,4,3,2,1] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,4,5,6] => [2,1,7,3,4,5,6] => [2,1,7,6,5,4,3] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,3,6,7,4] => [2,1,3,5,6,7,4] => [2,1,3,7,4,5,6] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [3,2,4,1,5,6,7] => [2,4,1,3,5,6,7] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [3,2,4,5,1,6,7] => [2,5,1,3,4,6,7] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [3,2,4,5,6,1,7] => [2,6,1,3,4,5,7] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,1] => [3,2,4,5,6,7,1] => [2,7,1,3,4,5,6] => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,1,3,4,5,7] => [6,2,1,3,4,5,7] => [2,6,5,4,3,1,7] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,1,4,5,2,7,6] => [1,3,4,5,2,7,6] => [1,5,2,3,4,7,6] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,1,4,5,6,7,2] => [1,3,4,5,6,7,2] => [1,7,2,3,4,5,6] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,1,4,6,7,2,5] => [1,3,4,6,7,2,5] => [1,6,2,3,4,7,5] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,6,7,2] => [4,3,1,5,6,7,2] => [7,2,3,1,4,5,6] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [3,4,5,1,6,2,7] => [4,3,5,1,6,2,7] => [4,1,6,2,3,5,7] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,1,2,4] => [5,3,6,7,1,2,4] => [5,1,6,2,3,7,4] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,1,2,3,4,5,6] => [1,7,2,3,4,5,6] => [1,7,6,5,4,3,2] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,1] => [3,2,4,5,6,7,8,1] => [2,8,1,3,4,5,6,7] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,1,2,6,7,4,8,5] => [1,3,2,6,7,4,8,5] => [1,3,2,6,4,8,5,7] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,1,6,2,7,3,8,5] => [1,4,6,2,7,3,8,5] => [1,4,2,6,3,8,5,7] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,1,2,3,4,5,6,7] => [1,8,2,3,4,5,6,7] => [1,8,7,6,5,4,3,2] => 0
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Description
The number of occurrences of the pattern 23-1.
See Permutations/#Pattern-avoiding_permutations for the definition of the pattern $23\!\!-\!\!1$.
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
Alexandersson Kebede
Description
Sends a permutation to a permutation and it preserves the set of right-to-left minima.
Take a permutation $\pi$ of length $n$. The mapping looks for a smallest odd integer $i\in[n-1]$ such that swapping the entries $\pi(i)$ and $\pi(i+1)$ preserves the set of right-to-left minima. Otherwise, $\pi$ will be a fixed element of the mapping. Note that the map changes the sign of all non-fixed elements.
There are exactly $\binom{\lfloor n/2 \rfloor}{k-\lceil n/2 \rceil}$ elements in $S_n$ fixed under this map, with exactly $k$ right-to-left minima, see Lemma 35 in [1].