Identifier
Values
[1,0] => [1] => [1] => 0
[1,0,1,0] => [2,1] => [1,2] => 0
[1,1,0,0] => [1,2] => [2,1] => 0
[1,0,1,0,1,0] => [2,1,3] => [3,1,2] => 0
[1,0,1,1,0,0] => [2,3,1] => [2,1,3] => 1
[1,1,0,0,1,0] => [3,1,2] => [1,3,2] => 0
[1,1,0,1,0,0] => [1,3,2] => [2,3,1] => 0
[1,1,1,0,0,0] => [1,2,3] => [3,2,1] => 0
[1,0,1,0,1,0,1,0] => [2,1,4,3] => [3,4,1,2] => 0
[1,0,1,0,1,1,0,0] => [2,4,1,3] => [2,1,4,3] => 1
[1,0,1,1,0,0,1,0] => [2,1,3,4] => [4,3,1,2] => 0
[1,0,1,1,0,1,0,0] => [2,3,1,4] => [4,2,1,3] => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [3,2,1,4] => 2
[1,1,0,0,1,0,1,0] => [3,1,4,2] => [1,3,2,4] => 1
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [3,1,4,2] => 1
[1,1,0,1,0,0,1,0] => [3,1,2,4] => [4,1,3,2] => 0
[1,1,0,1,0,1,0,0] => [1,3,2,4] => [4,2,3,1] => 0
[1,1,0,1,1,0,0,0] => [1,3,4,2] => [3,2,4,1] => 1
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [1,4,3,2] => 0
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [2,4,3,1] => 0
[1,1,1,0,1,0,0,0] => [1,2,4,3] => [3,4,2,1] => 0
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [4,3,2,1] => 0
[1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [5,3,4,1,2] => 0
[1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,5] => [5,2,1,4,3] => 1
[1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => [4,3,5,1,2] => 1
[1,0,1,0,1,1,0,1,0,0] => [2,4,1,5,3] => [2,1,4,3,5] => 2
[1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => [4,2,1,5,3] => 2
[1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => [3,5,4,1,2] => 0
[1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,4] => [2,1,5,4,3] => 1
[1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,4] => [4,5,3,1,2] => 0
[1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,4] => [4,5,2,1,3] => 1
[1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4] => [3,2,1,5,4] => 2
[1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5] => [5,4,3,1,2] => 0
[1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,5] => [5,4,2,1,3] => 1
[1,0,1,1,1,0,1,0,0,0] => [2,3,4,1,5] => [5,3,2,1,4] => 2
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [4,3,2,1,5] => 3
[1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5] => [5,1,3,2,4] => 1
[1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => [5,3,1,4,2] => 1
[1,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2] => [4,1,3,2,5] => 2
[1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => [3,1,4,2,5] => 2
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [4,3,1,5,2] => 2
[1,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4] => [1,3,2,5,4] => 1
[1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => [3,1,5,4,2] => 1
[1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4] => [4,5,1,3,2] => 0
[1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4] => [4,5,2,3,1] => 0
[1,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4] => [3,2,5,4,1] => 1
[1,1,0,1,1,0,0,0,1,0] => [3,1,2,4,5] => [5,4,1,3,2] => 0
[1,1,0,1,1,0,0,1,0,0] => [1,3,2,4,5] => [5,4,2,3,1] => 0
[1,1,0,1,1,0,1,0,0,0] => [1,3,4,2,5] => [5,3,2,4,1] => 1
[1,1,0,1,1,1,0,0,0,0] => [1,3,4,5,2] => [4,3,2,5,1] => 2
[1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => [1,4,2,5,3] => 1
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [4,1,5,3,2] => 1
[1,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3] => [1,4,3,5,2] => 1
[1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3] => [2,4,3,5,1] => 1
[1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => [4,2,5,3,1] => 1
[1,1,1,0,1,0,0,0,1,0] => [4,1,2,3,5] => [5,1,4,3,2] => 0
[1,1,1,0,1,0,0,1,0,0] => [1,4,2,3,5] => [5,2,4,3,1] => 0
[1,1,1,0,1,0,1,0,0,0] => [1,2,4,3,5] => [5,3,4,2,1] => 0
[1,1,1,0,1,1,0,0,0,0] => [1,2,4,5,3] => [4,3,5,2,1] => 1
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [1,5,4,3,2] => 0
[1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,4] => [2,5,4,3,1] => 0
[1,1,1,1,0,0,1,0,0,0] => [1,2,5,3,4] => [3,5,4,2,1] => 0
[1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,4] => [4,5,3,2,1] => 0
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [5,4,3,2,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5] => [5,6,2,1,4,3] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [4,3,6,5,1,2] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5] => [2,1,4,3,6,5] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5] => [4,2,1,6,5,3] => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [6,5,3,4,1,2] => 0
[1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,5,6] => [6,5,2,1,4,3] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [6,4,3,5,1,2] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,5,3,6] => [6,2,1,4,3,5] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [6,4,2,1,5,3] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => [5,4,3,6,1,2] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,5,6,3] => [5,2,1,4,3,6] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,5,1,6,3] => [4,2,1,5,3,6] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,5,6,1,3] => [5,4,2,1,6,3] => 3
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [3,5,4,6,1,2] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [2,1,5,4,6,3] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => [5,3,6,4,1,2] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4] => [2,1,5,3,6,4] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,6,1,3,4] => [5,2,1,6,4,3] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => [6,3,5,4,1,2] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,6] => [6,2,1,5,4,3] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,6] => [6,4,5,3,1,2] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,6] => [6,4,5,2,1,3] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [6,3,2,1,5,4] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,3,5,6,4] => [5,4,6,3,1,2] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,6,4] => [5,4,6,2,1,3] => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,1,6,4] => [3,2,1,5,4,6] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4] => [5,3,2,1,6,4] => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => [3,6,5,4,1,2] => 0
[1,0,1,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5] => [2,1,6,5,4,3] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5] => [4,6,5,3,1,2] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5] => [4,6,5,2,1,3] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5] => [3,2,1,6,5,4] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5] => [5,6,4,3,1,2] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5] => [5,6,4,2,1,3] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5] => [5,6,3,2,1,4] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5] => [4,3,2,1,6,5] => 3
>>> Load all 206 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,5,6] => [6,5,4,3,1,2] => 0
[1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,5,6] => [6,5,4,2,1,3] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,5,6] => [6,5,3,2,1,4] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,1,6] => [6,4,3,2,1,5] => 3
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [5,4,3,2,1,6] => 4
[1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5] => [5,6,1,3,2,4] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5] => [5,6,3,1,4,2] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5] => [4,1,3,2,6,5] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5] => [3,1,4,2,6,5] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5] => [4,3,1,6,5,2] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [6,5,1,3,2,4] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,5,6] => [6,5,3,1,4,2] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [6,4,1,3,2,5] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,2,6] => [6,3,1,4,2,5] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [6,4,3,1,5,2] => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,5,6,2] => [5,4,1,3,2,6] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,6,2] => [5,3,1,4,2,6] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,5,1,6,2] => [4,3,1,5,2,6] => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [5,4,3,1,6,2] => 3
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,4] => [1,3,2,5,4,6] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4] => [3,1,5,4,6,2] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4] => [5,1,3,2,6,4] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4] => [3,1,5,2,6,4] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4] => [5,3,1,6,4,2] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,6] => [6,1,3,2,5,4] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,6] => [6,3,1,5,4,2] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,6] => [6,4,5,1,3,2] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4,6] => [6,4,5,2,3,1] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4,6] => [6,3,2,5,4,1] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,6,4] => [5,4,6,1,3,2] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,2,5,6,4] => [5,4,6,2,3,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,5,2,6,4] => [3,2,5,4,6,1] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => [5,3,2,6,4,1] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5] => [1,3,2,6,5,4] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5] => [3,1,6,5,4,2] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5] => [4,6,5,1,3,2] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,2,6,4,5] => [4,6,5,2,3,1] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,6,2,4,5] => [3,2,6,5,4,1] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5] => [5,6,4,1,3,2] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,2,6,5] => [5,6,3,2,4,1] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,4,6,2,5] => [4,3,2,6,5,1] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,5,6] => [6,5,4,1,3,2] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,2,5,6] => [6,5,3,2,4,1] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,4,5,2,6] => [6,4,3,2,5,1] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,5,6,2] => [5,4,3,2,6,1] => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3] => [1,4,2,5,3,6] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,3] => [4,1,5,3,6,2] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3] => [5,1,4,2,6,3] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3] => [4,1,5,2,6,3] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [5,4,1,6,3,2] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,6] => [6,1,4,2,5,3] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,6] => [6,4,1,5,3,2] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,6] => [6,1,4,3,5,2] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,2,5,3,6] => [6,2,4,3,5,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => [6,4,2,5,3,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,5,6,3] => [5,1,4,3,6,2] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,2,5,6,3] => [5,2,4,3,6,1] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => [4,2,5,3,6,1] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => [5,4,2,6,3,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5] => [1,4,2,6,5,3] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5] => [4,1,6,5,3,2] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5] => [1,4,3,6,5,2] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,2,6,3,5] => [2,4,3,6,5,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => [4,2,6,5,3,1] => 1
[1,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5] => [5,6,1,4,3,2] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,2,3,6,5] => [5,6,2,4,3,1] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,4,3,6,5] => [5,6,3,4,2,1] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,4,6,3,5] => [4,3,6,5,2,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,5,6] => [6,5,1,4,3,2] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,2,3,5,6] => [6,5,2,4,3,1] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,4,5,3,6] => [6,4,3,5,2,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,4,5,6,3] => [5,4,3,6,2,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4] => [1,5,2,6,4,3] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [5,1,6,4,3,2] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4] => [1,5,3,6,4,2] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => [2,5,3,6,4,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => [5,2,6,4,3,1] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4] => [1,5,4,6,3,2] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,2,3,6,4] => [2,5,4,6,3,1] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,5,3,6,4] => [3,5,4,6,2,1] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => [5,3,6,4,2,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,6] => [6,1,5,4,3,2] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,2,3,4,6] => [6,2,5,4,3,1] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,2,5,3,4,6] => [6,3,5,4,2,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,3,5,4,6] => [6,4,5,3,2,1] => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,2,3,5,6,4] => [5,4,6,3,2,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [1,6,5,4,3,2] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,6,2,3,4,5] => [2,6,5,4,3,1] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,6,3,4,5] => [3,6,5,4,2,1] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,3,6,4,5] => [4,6,5,3,2,1] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6] => [1,3,2,5,4,7,6] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,6,2,7,4,5] => [1,3,2,6,4,7,5] => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,7,5] => [1,3,2,6,5,7,4] => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,7,2,4,5,6] => [1,3,2,7,6,5,4] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,7,3,6] => [1,4,2,5,3,7,6] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5] => [1,4,2,6,3,7,5] => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5] => [1,4,2,6,5,7,3] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [1,4,3,6,5,7,2] => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,7,2,3,5,6] => [1,4,2,7,6,5,3] => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,7,3,5,6] => [1,4,3,7,6,5,2] => 1
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Description
The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation.
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
weak order rowmotion
Description
Return the reversal of the permutation obtained by inverting the corresponding Laguerre heap.
This map is the composite of Mp00241invert Laguerre heap and Mp00064reverse.
Conjecturally, it is also the rowmotion on the weak order:
Any semidistributive lattice $L$ has a canonical labeling of the edges of its Hasse diagram by its join irreducible elements (see [1] and [2]). Rowmotion on this lattice is the bijection which takes an element $x \in L$ with a given set of down-labels to the unique element $y \in L$ which has that set as its up-labels (see [2] and [3]). For example, if the lattice is the distributive lattice $J(P)$ of order ideals of a finite poset $P$, then this reduces to ordinary rowmotion on the order ideals of $P$.
The weak order (a.k.a. permutohedral order) on the permutations in $S_n$ is a semidistributive lattice. In this way, we obtain an action of rowmotion on the set of permutations in $S_n$.
Note that the dynamics of weak order rowmotion is poorly understood. A collection of nontrivial homomesies is described in Corollary 6.14 of [4].