Identifier
Values
[1,0] => [1] => [1] => [1] => 0
[1,0,1,0] => [1,2] => [2,1] => [2,1] => 1
[1,1,0,0] => [2,1] => [1,2] => [1,2] => 0
[1,0,1,0,1,0] => [1,2,3] => [3,2,1] => [3,2,1] => 1
[1,0,1,1,0,0] => [1,3,2] => [2,3,1] => [2,3,1] => 1
[1,1,0,0,1,0] => [2,1,3] => [3,1,2] => [2,3,1] => 1
[1,1,0,1,0,0] => [2,3,1] => [1,3,2] => [1,3,2] => 1
[1,1,1,0,0,0] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 2
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [3,4,2,1] => [3,4,2,1] => 2
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [4,2,3,1] => [3,4,2,1] => 2
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [2,4,3,1] => [2,4,3,1] => 1
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [2,3,4,1] => [2,3,4,1] => 1
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [4,3,1,2] => [3,4,2,1] => 2
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [3,4,1,2] => [4,3,2,1] => 2
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [4,1,3,2] => [2,4,3,1] => 1
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [1,4,3,2] => [1,4,3,2] => 1
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [1,3,4,2] => [1,3,4,2] => 1
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [4,1,2,3] => [2,3,4,1] => 1
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [1,4,2,3] => [1,3,4,2] => 1
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [1,2,4,3] => [1,2,4,3] => 1
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => 2
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [4,5,3,2,1] => [4,5,3,2,1] => 2
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [5,3,4,2,1] => [4,5,3,2,1] => 2
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [3,5,4,2,1] => [3,5,4,2,1] => 2
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [3,4,5,2,1] => [3,4,5,2,1] => 2
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [5,4,2,3,1] => [4,5,3,2,1] => 2
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [4,5,2,3,1] => [5,4,3,2,1] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [5,2,4,3,1] => [3,5,4,2,1] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [2,5,4,3,1] => [2,5,4,3,1] => 2
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [2,4,5,3,1] => [2,4,5,3,1] => 2
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [5,2,3,4,1] => [3,4,5,2,1] => 2
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [2,5,3,4,1] => [2,4,5,3,1] => 2
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [2,3,5,4,1] => [2,3,5,4,1] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [2,3,4,5,1] => [2,3,4,5,1] => 1
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [5,4,3,1,2] => [4,5,3,2,1] => 2
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [4,5,3,1,2] => [5,4,3,2,1] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [5,3,4,1,2] => [5,4,3,2,1] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [3,5,4,1,2] => [3,4,5,2,1] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [3,4,5,1,2] => [3,5,4,2,1] => 2
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [5,4,1,3,2] => [3,5,4,2,1] => 2
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [4,5,1,3,2] => [5,3,4,2,1] => 2
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [5,1,4,3,2] => [2,5,4,3,1] => 2
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [1,5,4,3,2] => [1,5,4,3,2] => 2
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [1,4,5,3,2] => [1,4,5,3,2] => 2
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [5,1,3,4,2] => [2,4,5,3,1] => 2
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [1,5,3,4,2] => [1,4,5,3,2] => 2
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [1,3,5,4,2] => [1,3,5,4,2] => 1
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [1,3,4,5,2] => [1,3,4,5,2] => 1
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [5,4,1,2,3] => [3,4,5,2,1] => 2
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [4,5,1,2,3] => [4,3,5,2,1] => 2
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [5,1,4,2,3] => [2,4,5,3,1] => 2
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [1,5,4,2,3] => [1,4,5,3,2] => 2
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [1,4,5,2,3] => [1,5,4,3,2] => 2
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [5,1,2,4,3] => [2,3,5,4,1] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [1,5,2,4,3] => [1,3,5,4,2] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [1,2,5,4,3] => [1,2,5,4,3] => 1
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [1,2,4,5,3] => [1,2,4,5,3] => 1
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [5,1,2,3,4] => [2,3,4,5,1] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [1,5,2,3,4] => [1,3,4,5,2] => 1
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [1,2,5,3,4] => [1,2,4,5,3] => 1
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [1,2,3,5,4] => [1,2,3,5,4] => 1
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 3
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => 3
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [6,4,5,3,2,1] => [5,6,4,3,2,1] => 3
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [4,6,5,3,2,1] => [4,6,5,3,2,1] => 3
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => [5,6,4,3,2,1] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [5,6,3,4,2,1] => [6,5,4,3,2,1] => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [6,3,5,4,2,1] => [4,6,5,3,2,1] => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [3,6,5,4,2,1] => [3,6,5,4,2,1] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [3,5,6,4,2,1] => [3,5,6,4,2,1] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [6,3,4,5,2,1] => [4,5,6,3,2,1] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [3,6,4,5,2,1] => [3,5,6,4,2,1] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [3,4,6,5,2,1] => [3,4,6,5,2,1] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => [5,6,4,3,2,1] => 3
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => [6,5,4,3,2,1] => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [4,6,5,2,3,1] => [4,5,6,3,2,1] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [4,5,6,2,3,1] => [4,6,5,3,2,1] => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [6,5,2,4,3,1] => [4,6,5,3,2,1] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [5,6,2,4,3,1] => [6,4,5,3,2,1] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [6,2,5,4,3,1] => [3,6,5,4,2,1] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [2,6,5,4,3,1] => [2,6,5,4,3,1] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [2,5,6,4,3,1] => [2,5,6,4,3,1] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [6,2,4,5,3,1] => [3,5,6,4,2,1] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [2,6,4,5,3,1] => [2,5,6,4,3,1] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [2,4,6,5,3,1] => [2,4,6,5,3,1] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [2,4,5,6,3,1] => [2,4,5,6,3,1] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [6,5,2,3,4,1] => [4,5,6,3,2,1] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [5,6,2,3,4,1] => [5,4,6,3,2,1] => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [6,2,5,3,4,1] => [3,5,6,4,2,1] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [2,6,5,3,4,1] => [2,5,6,4,3,1] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [2,5,6,3,4,1] => [2,6,5,4,3,1] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [6,2,3,5,4,1] => [3,4,6,5,2,1] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [2,6,3,5,4,1] => [2,4,6,5,3,1] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [2,3,6,5,4,1] => [2,3,6,5,4,1] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [2,3,5,6,4,1] => [2,3,5,6,4,1] => 2
>>> Load all 274 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [6,2,3,4,5,1] => [3,4,5,6,2,1] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [2,6,3,4,5,1] => [2,4,5,6,3,1] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [2,3,6,4,5,1] => [2,3,5,6,4,1] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [2,3,4,6,5,1] => [2,3,4,6,5,1] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [6,5,4,3,1,2] => [5,6,4,3,2,1] => 3
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [6,4,5,3,1,2] => [6,5,4,3,2,1] => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [4,6,5,3,1,2] => [4,5,6,3,2,1] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [4,5,6,3,1,2] => [4,6,5,3,2,1] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [6,5,3,4,1,2] => [6,5,4,3,2,1] => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => [5,6,4,3,2,1] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [6,3,5,4,1,2] => [4,5,6,3,2,1] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [3,6,5,4,1,2] => [3,5,6,4,2,1] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [3,5,6,4,1,2] => [3,6,5,4,2,1] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [6,3,4,5,1,2] => [4,6,5,3,2,1] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [3,6,4,5,1,2] => [3,6,5,4,2,1] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [3,4,6,5,1,2] => [3,4,5,6,2,1] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => [3,4,6,5,2,1] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [6,5,4,1,3,2] => [4,6,5,3,2,1] => 3
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [5,6,4,1,3,2] => [6,4,5,3,2,1] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [6,4,5,1,3,2] => [6,4,5,3,2,1] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [4,6,5,1,3,2] => [5,4,6,3,2,1] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [4,5,6,1,3,2] => [5,6,4,3,2,1] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [6,5,1,4,3,2] => [3,6,5,4,2,1] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [5,6,1,4,3,2] => [6,3,5,4,2,1] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [6,1,5,4,3,2] => [2,6,5,4,3,1] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [1,5,6,4,3,2] => [1,5,6,4,3,2] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [6,1,4,5,3,2] => [2,5,6,4,3,1] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [1,6,4,5,3,2] => [1,5,6,4,3,2] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [1,4,6,5,3,2] => [1,4,6,5,3,2] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [1,4,5,6,3,2] => [1,4,5,6,3,2] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [6,5,1,3,4,2] => [3,5,6,4,2,1] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [5,6,1,3,4,2] => [5,3,6,4,2,1] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [6,1,5,3,4,2] => [2,5,6,4,3,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [1,6,5,3,4,2] => [1,5,6,4,3,2] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [1,5,6,3,4,2] => [1,6,5,4,3,2] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [6,1,3,5,4,2] => [2,4,6,5,3,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [1,6,3,5,4,2] => [1,4,6,5,3,2] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [1,3,6,5,4,2] => [1,3,6,5,4,2] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [1,3,5,6,4,2] => [1,3,5,6,4,2] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [6,1,3,4,5,2] => [2,4,5,6,3,1] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [1,6,3,4,5,2] => [1,4,5,6,3,2] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [1,3,6,4,5,2] => [1,3,5,6,4,2] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [1,3,4,6,5,2] => [1,3,4,6,5,2] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [1,3,4,5,6,2] => [1,3,4,5,6,2] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [6,5,4,1,2,3] => [4,5,6,3,2,1] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [5,6,4,1,2,3] => [5,4,6,3,2,1] => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [6,4,5,1,2,3] => [5,4,6,3,2,1] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [4,6,5,1,2,3] => [6,4,5,3,2,1] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [4,5,6,1,2,3] => [6,5,4,3,2,1] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [6,5,1,4,2,3] => [3,5,6,4,2,1] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [5,6,1,4,2,3] => [5,3,6,4,2,1] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [6,1,5,4,2,3] => [2,5,6,4,3,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [1,6,5,4,2,3] => [1,5,6,4,3,2] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [1,5,6,4,2,3] => [1,6,5,4,3,2] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [6,1,4,5,2,3] => [2,6,5,4,3,1] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [1,6,4,5,2,3] => [1,6,5,4,3,2] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [1,4,6,5,2,3] => [1,4,5,6,3,2] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [1,4,5,6,2,3] => [1,4,6,5,3,2] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [6,5,1,2,4,3] => [3,4,6,5,2,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [5,6,1,2,4,3] => [4,3,6,5,2,1] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [6,1,5,2,4,3] => [2,4,6,5,3,1] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [1,6,5,2,4,3] => [1,4,6,5,3,2] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [1,5,6,2,4,3] => [1,6,4,5,3,2] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [6,1,2,5,4,3] => [2,3,6,5,4,1] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [1,6,2,5,4,3] => [1,3,6,5,4,2] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [1,2,5,6,4,3] => [1,2,5,6,4,3] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [6,1,2,4,5,3] => [2,3,5,6,4,1] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [1,6,2,4,5,3] => [1,3,5,6,4,2] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [1,2,6,4,5,3] => [1,2,5,6,4,3] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [1,2,4,6,5,3] => [1,2,4,6,5,3] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [1,2,4,5,6,3] => [1,2,4,5,6,3] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [6,5,1,2,3,4] => [3,4,5,6,2,1] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [5,6,1,2,3,4] => [4,3,5,6,2,1] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [6,1,5,2,3,4] => [2,4,5,6,3,1] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [1,6,5,2,3,4] => [1,4,5,6,3,2] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [1,5,6,2,3,4] => [1,5,4,6,3,2] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [6,1,2,5,3,4] => [2,3,5,6,4,1] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [1,6,2,5,3,4] => [1,3,5,6,4,2] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [1,2,6,5,3,4] => [1,2,5,6,4,3] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [1,2,5,6,3,4] => [1,2,6,5,4,3] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [6,1,2,3,5,4] => [2,3,4,6,5,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [1,6,2,3,5,4] => [1,3,4,6,5,2] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [1,2,6,3,5,4] => [1,2,4,6,5,3] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [1,2,3,5,6,4] => [1,2,3,5,6,4] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [1,4,5,7,6,3,2] => [1,4,5,7,6,3,2] => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [1,4,5,6,7,3,2] => [1,4,5,6,7,3,2] => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [1,3,7,6,5,4,2] => [1,3,7,6,5,4,2] => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [1,3,6,7,5,4,2] => [1,3,6,7,5,4,2] => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [1,3,7,5,6,4,2] => [1,3,6,7,5,4,2] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [1,3,5,7,6,4,2] => [1,3,5,7,6,4,2] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [1,3,5,6,7,4,2] => [1,3,5,6,7,4,2] => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [1,3,7,6,4,5,2] => [1,3,6,7,5,4,2] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [1,3,6,7,4,5,2] => [1,3,7,6,5,4,2] => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [1,7,3,4,6,5,2] => [1,4,5,7,6,3,2] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [1,3,7,4,6,5,2] => [1,3,5,7,6,4,2] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [1,3,4,7,6,5,2] => [1,3,4,7,6,5,2] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [1,3,4,6,7,5,2] => [1,3,4,6,7,5,2] => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [1,7,3,4,5,6,2] => [1,4,5,6,7,3,2] => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [1,3,7,4,5,6,2] => [1,3,5,6,7,4,2] => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [1,3,4,7,5,6,2] => [1,3,4,6,7,5,2] => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [1,3,4,5,7,6,2] => [1,3,4,5,7,6,2] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [1,3,4,5,6,7,2] => [1,3,4,5,6,7,2] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [1,4,5,7,6,2,3] => [1,4,5,6,7,3,2] => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [1,4,5,6,7,2,3] => [1,4,5,7,6,3,2] => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [1,7,2,6,5,4,3] => [1,3,7,6,5,4,2] => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [1,2,6,7,5,4,3] => [1,2,6,7,5,4,3] => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [1,7,2,5,6,4,3] => [1,3,6,7,5,4,2] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [1,2,7,5,6,4,3] => [1,2,6,7,5,4,3] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [1,2,5,7,6,4,3] => [1,2,5,7,6,4,3] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [1,2,5,6,7,4,3] => [1,2,5,6,7,4,3] => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [1,7,2,6,4,5,3] => [1,3,6,7,5,4,2] => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [1,2,7,6,4,5,3] => [1,2,6,7,5,4,3] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [1,2,6,7,4,5,3] => [1,2,7,6,5,4,3] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [1,7,2,4,6,5,3] => [1,3,5,7,6,4,2] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [1,2,7,4,6,5,3] => [1,2,5,7,6,4,3] => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [1,2,4,7,6,5,3] => [1,2,4,7,6,5,3] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [1,2,4,6,7,5,3] => [1,2,4,6,7,5,3] => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [1,7,2,4,5,6,3] => [1,3,5,6,7,4,2] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [1,2,7,4,5,6,3] => [1,2,5,6,7,4,3] => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [1,2,4,7,5,6,3] => [1,2,4,6,7,5,3] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [1,2,4,5,7,6,3] => [1,2,4,5,7,6,3] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [1,2,4,5,6,7,3] => [1,2,4,5,6,7,3] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [1,7,2,6,5,3,4] => [1,3,6,7,5,4,2] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [1,2,7,6,5,3,4] => [1,2,6,7,5,4,3] => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [1,2,6,7,5,3,4] => [1,2,7,6,5,4,3] => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [1,7,2,5,6,3,4] => [1,3,7,6,5,4,2] => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [1,2,7,5,6,3,4] => [1,2,7,6,5,4,3] => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [1,2,5,7,6,3,4] => [1,2,5,6,7,4,3] => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [1,2,5,6,7,3,4] => [1,2,5,7,6,4,3] => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [1,7,6,2,3,5,4] => [1,4,5,7,6,3,2] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [1,7,2,6,3,5,4] => [1,3,5,7,6,4,2] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [1,2,7,6,3,5,4] => [1,2,5,7,6,4,3] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [1,2,6,7,3,5,4] => [1,2,7,5,6,4,3] => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [1,7,2,3,6,5,4] => [1,3,4,7,6,5,2] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [1,2,7,3,6,5,4] => [1,2,4,7,6,5,3] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [1,2,3,6,7,5,4] => [1,2,3,6,7,5,4] => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [1,7,2,3,5,6,4] => [1,3,4,6,7,5,2] => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [1,2,7,3,5,6,4] => [1,2,4,6,7,5,3] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [1,2,3,7,5,6,4] => [1,2,3,6,7,5,4] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [1,2,3,5,7,6,4] => [1,2,3,5,7,6,4] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [1,2,3,5,6,7,4] => [1,2,3,5,6,7,4] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [1,7,6,2,3,4,5] => [1,4,5,6,7,3,2] => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [1,7,2,6,3,4,5] => [1,3,5,6,7,4,2] => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [1,2,7,6,3,4,5] => [1,2,5,6,7,4,3] => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [1,2,6,7,3,4,5] => [1,2,6,5,7,4,3] => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [1,7,2,3,6,4,5] => [1,3,4,6,7,5,2] => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [1,2,7,3,6,4,5] => [1,2,4,6,7,5,3] => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [1,2,3,7,6,4,5] => [1,2,3,6,7,5,4] => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [1,2,3,6,7,4,5] => [1,2,3,7,6,5,4] => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [1,7,2,3,4,6,5] => [1,3,4,5,7,6,2] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [1,2,7,3,4,6,5] => [1,2,4,5,7,6,3] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [1,2,3,7,4,6,5] => [1,2,3,5,7,6,4] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [1,2,3,4,6,7,5] => [1,2,3,4,6,7,5] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,5,4,3,2,7,1] => [1,7,2,3,4,5,6] => [1,3,4,5,6,7,2] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [1,2,7,3,4,5,6] => [1,2,4,5,6,7,3] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
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Description
The number of visible descents of a permutation.
A visible descent of a permutation $\pi$ is a position $i$ such that $\pi(i+1) \leq \min(i, \pi(i))$.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
catalanization
Description
The catalanization of a permutation.
For a permutation $\sigma$, this is the product of the reflections corresponding to the inversions of $\sigma$ in lex-order.
A permutation is $231$-avoiding if and only if it is a fixpoint of this map. Also, for every permutation there exists an index $k$ such that the $k$-fold application of this map is $231$-avoiding.