Identifier
Values
[1,0] => [1] => [1] => [1] => 0
[1,0,1,0] => [2,1] => [2,1] => [2,1] => 1
[1,1,0,0] => [1,2] => [1,2] => [1,2] => 0
[1,0,1,0,1,0] => [3,2,1] => [3,2,1] => [2,3,1] => 1
[1,0,1,1,0,0] => [2,3,1] => [2,3,1] => [3,1,2] => 1
[1,1,0,0,1,0] => [3,1,2] => [2,3,1] => [3,1,2] => 1
[1,1,0,1,0,0] => [2,1,3] => [2,1,3] => [2,1,3] => 1
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [4,3,2,1] => [3,2,4,1] => 2
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [3,4,2,1] => [4,1,3,2] => 2
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [3,4,2,1] => [4,1,3,2] => 2
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [3,2,4,1] => [2,4,1,3] => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [2,3,4,1] => [4,1,2,3] => 1
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [3,4,2,1] => [4,1,3,2] => 2
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [4,3,2,1] => [3,2,4,1] => 2
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [3,2,4,1] => [2,4,1,3] => 1
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [3,2,1,4] => [2,3,1,4] => 1
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [2,3,1,4] => [3,1,2,4] => 1
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [2,3,4,1] => [4,1,2,3] => 1
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [2,3,1,4] => [3,1,2,4] => 1
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [5,4,3,2,1] => [3,4,2,5,1] => 2
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [4,5,3,2,1] => [3,5,1,4,2] => 2
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [4,5,3,2,1] => [3,5,1,4,2] => 2
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [4,3,5,2,1] => [5,1,4,2,3] => 2
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [3,4,5,2,1] => [4,2,5,1,3] => 2
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [4,5,3,2,1] => [3,5,1,4,2] => 2
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [5,4,3,2,1] => [3,4,2,5,1] => 2
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [4,3,5,2,1] => [5,1,4,2,3] => 2
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [4,3,2,5,1] => [3,2,5,1,4] => 2
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [3,4,2,5,1] => [5,1,3,2,4] => 2
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [3,4,5,2,1] => [4,2,5,1,3] => 2
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [3,4,2,5,1] => [5,1,3,2,4] => 2
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [3,2,4,5,1] => [2,5,1,3,4] => 1
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [2,3,4,5,1] => [5,1,2,3,4] => 1
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [4,5,3,2,1] => [3,5,1,4,2] => 2
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [5,4,3,2,1] => [3,4,2,5,1] => 2
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [5,4,3,2,1] => [3,4,2,5,1] => 2
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [5,3,4,2,1] => [4,2,3,5,1] => 2
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [3,5,4,2,1] => [5,1,3,4,2] => 2
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [4,3,5,2,1] => [5,1,4,2,3] => 2
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [3,4,5,2,1] => [4,2,5,1,3] => 2
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [4,3,2,5,1] => [3,2,5,1,4] => 2
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [4,3,2,1,5] => [3,2,4,1,5] => 2
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [3,4,2,1,5] => [4,1,3,2,5] => 2
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [3,4,2,5,1] => [5,1,3,2,4] => 2
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [3,4,2,1,5] => [4,1,3,2,5] => 2
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [3,2,4,1,5] => [2,4,1,3,5] => 1
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [2,3,4,1,5] => [4,1,2,3,5] => 1
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [3,4,5,2,1] => [4,2,5,1,3] => 2
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [4,3,5,2,1] => [5,1,4,2,3] => 2
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [3,4,2,5,1] => [5,1,3,2,4] => 2
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [3,4,2,1,5] => [4,1,3,2,5] => 2
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [4,3,2,1,5] => [3,2,4,1,5] => 2
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [3,2,4,5,1] => [2,5,1,3,4] => 1
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [3,2,4,1,5] => [2,4,1,3,5] => 1
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [3,2,1,4,5] => [2,3,1,4,5] => 1
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => 1
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [2,3,4,5,1] => [5,1,2,3,4] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [2,3,4,1,5] => [4,1,2,3,5] => 1
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => 1
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => [4,3,5,2,6,1] => 3
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => [4,3,6,1,5,2] => 3
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [5,6,4,3,2,1] => [4,3,6,1,5,2] => 3
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => [6,1,5,2,4,3] => 3
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => [5,2,6,1,4,3] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [5,6,4,3,2,1] => [4,3,6,1,5,2] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [6,5,4,3,2,1] => [4,3,5,2,6,1] => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [5,4,6,3,2,1] => [6,1,5,2,4,3] => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => [3,6,1,5,2,4] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => [3,5,2,6,1,4] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [4,5,6,3,2,1] => [5,2,6,1,4,3] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [4,5,3,6,2,1] => [3,5,2,6,1,4] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [4,3,5,6,2,1] => [5,2,3,6,1,4] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => [6,1,3,5,2,4] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [5,6,4,3,2,1] => [4,3,6,1,5,2] => 3
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [6,5,4,3,2,1] => [4,3,5,2,6,1] => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [6,5,4,3,2,1] => [4,3,5,2,6,1] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [6,4,5,3,2,1] => [5,2,4,3,6,1] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [4,6,5,3,2,1] => [6,1,4,3,5,2] => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [5,4,6,3,2,1] => [6,1,5,2,4,3] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [4,5,6,3,2,1] => [5,2,6,1,4,3] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [5,4,3,6,2,1] => [3,6,1,5,2,4] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => [3,4,2,6,1,5] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [4,5,3,2,6,1] => [3,6,1,4,2,5] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [4,5,3,6,2,1] => [3,5,2,6,1,4] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [4,5,3,2,6,1] => [3,6,1,4,2,5] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [4,3,5,2,6,1] => [6,1,4,2,3,5] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => [4,2,6,1,3,5] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [4,5,6,3,2,1] => [5,2,6,1,4,3] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [5,4,6,3,2,1] => [6,1,5,2,4,3] => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [4,5,3,6,2,1] => [3,5,2,6,1,4] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [4,5,3,2,6,1] => [3,6,1,4,2,5] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [5,4,3,2,6,1] => [3,4,2,6,1,5] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [4,3,5,6,2,1] => [5,2,3,6,1,4] => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [4,3,5,2,6,1] => [6,1,4,2,3,5] => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => [3,2,6,1,4,5] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => [6,1,3,2,4,5] => 2
>>> Load all 235 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [3,4,5,6,2,1] => [6,1,3,5,2,4] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [3,4,5,2,6,1] => [4,2,6,1,3,5] => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [3,4,2,5,6,1] => [6,1,3,2,4,5] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => [2,6,1,3,4,5] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [5,6,4,3,2,1] => [4,3,6,1,5,2] => 3
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [6,5,4,3,2,1] => [4,3,5,2,6,1] => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [6,5,4,3,2,1] => [4,3,5,2,6,1] => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [6,4,5,3,2,1] => [5,2,4,3,6,1] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [4,6,5,3,2,1] => [6,1,4,3,5,2] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [6,5,4,3,2,1] => [4,3,5,2,6,1] => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [5,6,4,3,2,1] => [4,3,6,1,5,2] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [6,4,5,3,2,1] => [5,2,4,3,6,1] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [6,4,3,5,2,1] => [3,5,2,4,6,1] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [4,6,3,5,2,1] => [3,6,1,4,5,2] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [4,6,5,3,2,1] => [6,1,4,3,5,2] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [4,6,3,5,2,1] => [3,6,1,4,5,2] => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [4,3,6,5,2,1] => [6,1,4,5,2,3] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [3,4,6,5,2,1] => [5,2,4,6,1,3] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [5,4,6,3,2,1] => [6,1,5,2,4,3] => 3
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [4,5,6,3,2,1] => [5,2,6,1,4,3] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [4,5,6,3,2,1] => [5,2,6,1,4,3] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [4,6,5,3,2,1] => [6,1,4,3,5,2] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [6,4,5,3,2,1] => [5,2,4,3,6,1] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [5,4,3,6,2,1] => [3,6,1,5,2,4] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [4,5,3,6,2,1] => [3,5,2,6,1,4] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [5,4,3,2,6,1] => [3,4,2,6,1,5] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [3,4,2,5,1,6] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => [3,5,1,4,2,6] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [4,5,3,2,6,1] => [3,6,1,4,2,5] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [4,5,3,2,1,6] => [3,5,1,4,2,6] => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [4,3,5,2,1,6] => [5,1,4,2,3,6] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => [4,2,5,1,3,6] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [4,5,3,6,2,1] => [3,5,2,6,1,4] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [5,4,3,6,2,1] => [3,6,1,5,2,4] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [4,5,3,2,6,1] => [3,6,1,4,2,5] => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [4,5,3,2,1,6] => [3,5,1,4,2,6] => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [5,4,3,2,1,6] => [3,4,2,5,1,6] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [4,3,5,2,6,1] => [6,1,4,2,3,5] => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [4,3,5,2,1,6] => [5,1,4,2,3,6] => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [4,3,2,5,1,6] => [3,2,5,1,4,6] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => [5,1,3,2,4,6] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [3,4,5,2,6,1] => [4,2,6,1,3,5] => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [3,4,5,2,1,6] => [4,2,5,1,3,6] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [3,4,2,5,1,6] => [5,1,3,2,4,6] => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => [2,5,1,3,4,6] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [4,5,6,3,2,1] => [5,2,6,1,4,3] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [5,4,6,3,2,1] => [6,1,5,2,4,3] => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [5,4,6,3,2,1] => [6,1,5,2,4,3] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [5,6,4,3,2,1] => [4,3,6,1,5,2] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [6,5,4,3,2,1] => [4,3,5,2,6,1] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [4,5,3,6,2,1] => [3,5,2,6,1,4] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [5,4,3,6,2,1] => [3,6,1,5,2,4] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [4,5,3,2,6,1] => [3,6,1,4,2,5] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [4,5,3,2,1,6] => [3,5,1,4,2,6] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [5,4,3,2,1,6] => [3,4,2,5,1,6] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [5,4,3,2,6,1] => [3,4,2,6,1,5] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [5,4,3,2,1,6] => [3,4,2,5,1,6] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [5,3,4,2,1,6] => [4,2,3,5,1,6] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [3,5,4,2,1,6] => [5,1,3,4,2,6] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [4,3,5,6,2,1] => [5,2,3,6,1,4] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [3,4,5,6,2,1] => [6,1,3,5,2,4] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [4,3,5,2,6,1] => [6,1,4,2,3,5] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [4,3,5,2,1,6] => [5,1,4,2,3,6] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [3,4,5,2,1,6] => [4,2,5,1,3,6] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [4,3,2,5,6,1] => [3,2,6,1,4,5] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [4,3,2,5,1,6] => [3,2,5,1,4,6] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => [3,2,4,1,5,6] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => [4,1,3,2,5,6] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [3,4,2,5,6,1] => [6,1,3,2,4,5] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [3,4,2,5,1,6] => [5,1,3,2,4,6] => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [3,4,2,1,5,6] => [4,1,3,2,5,6] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => [2,4,1,3,5,6] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [3,4,5,6,2,1] => [6,1,3,5,2,4] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [4,3,5,6,2,1] => [5,2,3,6,1,4] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [3,4,5,2,6,1] => [4,2,6,1,3,5] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [3,4,5,2,1,6] => [4,2,5,1,3,6] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [4,3,5,2,1,6] => [5,1,4,2,3,6] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [3,4,2,5,6,1] => [6,1,3,2,4,5] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [3,4,2,5,1,6] => [5,1,3,2,4,6] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [3,4,2,1,5,6] => [4,1,3,2,5,6] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [4,3,2,1,5,6] => [3,2,4,1,5,6] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [3,2,4,5,6,1] => [2,6,1,3,4,5] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [3,2,4,5,1,6] => [2,5,1,3,4,6] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [3,2,4,1,5,6] => [2,4,1,3,5,6] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [3,2,4,5,6,7,1] => [2,7,1,3,4,5,6] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1,7] => [2,6,1,3,4,5,7] => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6,7] => [4,2,5,1,3,6,7] => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [3,4,5,2,1,6,7] => [4,2,5,1,3,6,7] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6,7] => [2,5,1,3,4,6,7] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => 1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [3,4,5,2,1,6,7] => [4,2,5,1,3,6,7] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6,7] => [2,4,1,3,5,6,7] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => 1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [3,4,5,2,1,6,7] => [4,2,5,1,3,6,7] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [3,2,4,5,6,7,1] => [2,7,1,3,4,5,6] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [3,2,4,5,6,1,7] => [2,6,1,3,4,5,7] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [3,2,4,5,1,6,7] => [2,5,1,3,4,6,7] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [3,2,4,1,5,6,7] => [2,4,1,3,5,6,7] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [5,4,6,3,7,2,8,1] => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [8,7,6,5,4,3,2,1] => [5,4,6,3,7,2,8,1] => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [8,7,6,5,4,3,2,1] => [5,4,6,3,7,2,8,1] => 4
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [8,7,6,5,4,3,2,1] => [5,4,6,3,7,2,8,1] => 4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [8,7,6,5,4,3,2,1] => [5,4,6,3,7,2,8,1] => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [8,7,6,5,4,3,2,1] => [5,4,6,3,7,2,8,1] => 4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => [7,6,8,5,4,3,2,1] => [5,4,8,1,7,2,6,3] => 4
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [8,7,6,5,4,3,2,1] => [5,4,6,3,7,2,8,1] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => [7,6,8,5,4,3,2,1] => [5,4,8,1,7,2,6,3] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => [7,6,8,5,4,3,2,1] => [5,4,8,1,7,2,6,3] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [8,7,6,5,4,3,2,1] => [5,4,6,3,7,2,8,1] => 4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1] => [8,1,2,3,4,5,6,7] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [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
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Description
The number of isolated descents of a permutation.
A descent $i$ is isolated if neither $i+1$ nor $i-1$ are descents. If a permutation has only isolated descents, then it is called primitive in [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 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
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.