Identifier
Values
[1,0] => [2,1] => [2] => [1,1,0,0,1,0] => 0
[1,0,1,0] => [3,1,2] => [3] => [1,1,1,0,0,0,1,0] => 0
[1,1,0,0] => [2,3,1] => [3] => [1,1,1,0,0,0,1,0] => 0
[1,0,1,0,1,0] => [4,1,2,3] => [4] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,1,0,0] => [3,1,4,2] => [4] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,0] => [2,4,1,3] => [4] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,0,0] => [4,3,1,2] => [4] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,0] => [2,3,4,1] => [4] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [3,2] => [1,1,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => [6,4,1,2,3,7,5] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [5,4,1,2,6,7,3] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [2,6,5,1,3,7,4] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,7,6,1,4,5] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,1,2,8,3,4,5,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [8,1,2,6,3,7,4,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [8,1,2,5,7,3,4,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,1,8,2,3,4,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,1,7,2,3,4,5,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,1,7,2,3,4,8,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,1,8,2,3,7,4,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,1,5,2,6,3,4,7] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [7,1,8,2,6,3,4,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [7,1,5,2,6,3,8,4] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [8,1,5,2,6,7,3,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [3,1,7,8,2,4,5,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,8,6,2,7,4,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,1,4,6,2,3,5,7] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,1,4,8,2,3,5,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [7,1,4,6,2,3,8,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,1,8,5,2,3,4,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [8,1,4,6,2,7,3,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [8,1,6,5,2,7,3,4] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [3,1,8,5,7,2,4,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [8,1,4,5,7,2,3,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [8,1,4,7,6,2,3,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,7,1,8,3,4,5,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,8,1,5,7,3,4,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,8,1,2,3,4,6,7] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,7,1,2,3,4,8,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,6,1,2,3,4,8,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [5,6,1,2,3,8,4,7] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [5,8,1,2,3,7,4,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
>>> Load all 208 entries. <<<
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8,6,1,2,3,7,4,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,1,2,3,7,8,4] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8,4,1,2,7,3,5,6] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [5,8,1,2,6,3,4,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8,7,1,2,6,3,4,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,7,1,2,6,3,8,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,8,1,2,6,7,3,4] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,3,1,8,2,4,5,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [8,3,1,6,2,7,4,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,4,1,5,2,3,6,7] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,4,1,5,2,3,8,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,8,1,5,2,3,4,7] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8,7,1,5,2,3,4,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [6,7,1,5,2,3,8,4] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,4,1,5,2,8,3,7] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [8,4,1,5,2,7,3,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [6,8,1,5,2,7,3,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [6,4,1,5,2,7,8,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8,3,1,5,7,2,4,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,1,5,6,2,3,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7,8,1,5,6,2,3,4] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7,4,1,5,6,2,8,3] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8,4,1,5,6,7,2,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,6,8,1,3,4,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,8,7,1,3,4,5,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,6,7,1,3,4,8,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [2,6,8,1,3,7,4,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [2,8,5,1,6,3,4,7] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,7,8,1,6,3,4,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,7,5,1,6,3,8,4] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,8,5,1,6,7,3,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,3,5,1,2,4,6,7] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [7,3,5,1,2,4,8,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,3,8,1,2,4,5,7] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8,3,7,1,2,4,5,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,3,7,1,2,4,8,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,3,5,1,2,8,4,7] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [8,3,5,1,2,7,4,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,3,8,1,2,7,4,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [6,3,5,1,2,7,8,4] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,8,4,1,2,3,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,4,1,2,3,5,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,1,2,3,8,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [6,8,4,1,2,7,3,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,3,5,1,6,2,4,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7,3,8,1,6,2,4,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7,3,5,1,6,2,8,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,5,4,1,6,2,3,7] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7,8,4,1,6,2,3,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7,5,4,1,6,2,8,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8,3,5,1,6,7,2,4] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8,5,4,1,6,7,2,3] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,7,8,1,4,5,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,3,8,6,1,7,4,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,8,4,6,1,3,5,7] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [2,7,4,8,1,3,5,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,7,4,6,1,3,8,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,7,8,5,1,3,4,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,8,4,6,1,7,3,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,8,6,5,1,7,3,4] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,3,4,6,1,2,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,3,4,8,1,2,5,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7,3,4,6,1,2,8,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,3,6,5,1,2,4,7] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,3,8,5,1,2,4,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7,3,6,5,1,2,8,4] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,8,4,5,1,2,3,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [8,3,4,6,1,7,2,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8,3,6,5,1,7,2,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [8,6,4,5,1,7,2,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,3,8,5,7,1,4,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,8,4,5,7,1,3,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,8,4,7,6,1,3,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8,3,4,5,7,1,2,6] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8,3,4,7,6,1,2,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8,3,7,5,6,1,2,4] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [7,1,2,8,3,4,5,9,6] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [8,1,2,5,9,3,4,6,7] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,1,4,9,2,3,5,6,8] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [9,1,4,8,2,3,5,6,7] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [5,9,1,2,3,8,4,6,7] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [8,6,1,2,3,7,4,9,5] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [9,6,1,2,3,7,8,4,5] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8,4,1,2,9,3,5,6,7] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [9,7,1,2,6,3,8,4,5] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [9,4,1,6,2,8,3,5,7] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [2,6,9,1,3,4,5,7,8] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [2,9,5,1,6,7,8,3,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [9,3,7,1,2,4,5,6,8] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [6,9,4,1,2,3,5,7,8] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [6,8,4,1,2,3,5,9,7] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8,5,4,1,6,7,2,9,3] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [9,5,4,1,6,7,8,2,3] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [2,3,7,9,1,4,5,6,8] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [2,3,9,6,1,7,8,4,5] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [2,9,6,5,1,7,8,3,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [9,3,4,8,1,2,5,6,7] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,8,9,6,1,2,3,4,5] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8,3,6,5,1,7,2,9,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8,3,4,7,6,1,2,9,5] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [9,3,7,5,6,1,8,2,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [2,3,9,5,6,8,1,4,7] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [2,9,4,5,6,8,1,3,7] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [2,9,4,5,8,7,1,3,6] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 0
[] => [1] => [1] => [1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [10,6,1,2,3,4,9,5,7,8] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [5,11,1,2,3,10,4,6,7,8,9] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 0
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Description
The number of centered tunnels of a Dyck path.
A tunnel is a pair (a,b) where a is the position of an open parenthesis and b is the position of the matching close parenthesis. If a+b==n then the tunnel is called centered.
Map
cycle type
Description
The cycle type of a permutation as a partition.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.