Identifier
Values
[1,0] => [1] => [1] => [1,0,1,0] => 1
[1,0,1,0] => [2,1] => [1,1] => [1,0,1,1,0,0] => 2
[1,1,0,0] => [1,2] => [2] => [1,1,0,0,1,0] => 1
[1,1,1,0,0,0] => [1,2,3] => [3] => [1,1,1,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0] => [2,1,4,3] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0] => [2,4,1,3] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0] => [3,1,4,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,6,1,3,4] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,4] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,8,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,8,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,8,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,6,1,3,8,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,6,8,3,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,8,3,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,4,3,7,5,8,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,3,7,5,8,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,4,7,3,5,8,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,4,1,7,3,5,8,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,7,8,5,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,3,7,8,5,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,4,1,7,3,8,5,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,4,7,8,3,5,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,8,3,5,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,4,7,1,8,3,5,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,5,6,1,3,4,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,6,8,4,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,6,8,4,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,5,6,1,3,8,4,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,5,6,8,3,4,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,5,1,6,8,3,4,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,7,4,8,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,7,3,4,8,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,5,7,1,3,4,8,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,1,5,3,7,8,4,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,5,1,3,7,8,4,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,1,5,7,3,8,4,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,7,8,3,4,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,5,1,7,8,3,4,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,5,7,1,8,3,4,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,5,7,8,1,3,4,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,6,3,7,4,8,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,7,4,8,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [2,1,6,7,3,4,8,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,6,1,7,3,4,8,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,6,7,1,3,4,8,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,1,6,3,7,8,4,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,6,1,3,7,8,4,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,6,7,1,3,8,4,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,1,6,7,8,3,4,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,6,1,7,8,3,4,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,6,7,1,8,3,4,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,6,7,8,1,3,4,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,8,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,8,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,8,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
>>> Load all 212 entries. <<<
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [3,4,1,6,2,8,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,8,2,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [3,4,1,6,8,2,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,6,8,1,2,5,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,7,5,8,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,7,5,8,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,7,2,5,8,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,7,1,2,5,8,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,7,8,5,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,7,8,5,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,7,1,8,2,5,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,7,8,1,2,5,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,5,1,2,6,4,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,5,6,1,2,4,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,5,2,6,8,4,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,5,1,2,6,8,4,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,5,6,8,2,4,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,5,1,6,8,2,4,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,5,6,1,8,2,4,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,8,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,5,1,2,7,4,8,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,5,7,2,4,8,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,7,1,2,4,8,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,7,8,4,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,5,1,2,7,8,4,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,5,7,2,8,4,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,5,1,7,2,8,4,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,7,8,2,4,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,5,1,7,8,2,4,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,6,2,7,4,8,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,6,1,2,7,4,8,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,6,1,7,2,4,8,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,6,7,1,2,4,8,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,6,1,2,7,8,4,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,1,6,7,2,8,4,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,6,1,7,2,8,4,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,6,7,1,2,8,4,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,6,1,7,8,2,4,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,6,7,8,1,2,4,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [4,5,1,2,6,3,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [4,1,5,6,2,3,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,1,2,3,8,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [4,1,5,2,6,8,3,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [4,5,1,2,6,8,3,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [4,1,5,6,2,8,3,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [4,5,6,1,2,8,3,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [4,1,5,6,8,2,3,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [4,5,1,6,8,2,3,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [4,5,6,1,8,2,3,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,8,1,2,3,7] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,7,3,8,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [4,5,1,7,2,3,8,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [4,1,5,2,7,8,3,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,5,1,2,7,8,3,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [4,1,5,7,2,8,3,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,5,1,7,2,8,3,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [4,5,7,1,2,8,3,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,6,2,7,3,8,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,6,7,2,3,8,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,6,7,1,2,3,8,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,6,1,2,7,8,3,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,6,1,7,2,8,3,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,6,7,1,2,8,3,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,6,7,8,2,3,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,6,1,7,8,2,3,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,6,7,1,8,2,3,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,6,7,8,1,2,3,5] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [5,6,1,2,7,3,8,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [5,1,6,7,2,3,8,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [5,6,1,7,2,3,8,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,1,2,3,8,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [5,6,1,2,7,8,3,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [5,1,6,7,2,8,3,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [5,6,7,1,2,8,3,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [5,1,6,7,8,2,3,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [5,6,1,7,8,2,3,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7,10,9] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7,10,9] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7,10,9] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,10,7,9] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,6,8,10,1,3,5,7,9] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,6,5,9,10,7,8] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,8,7,10,9] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4,9,10,7,8] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [2,7,8,9,10,1,3,4,5,6] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7,10,9] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,8,7,10,9] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,7,8,5,6,10,9] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,4,1,2,8,9,10,5,6,7] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,8,7,10,9] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3,9,10,7,8] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4,10,9] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4,10,9] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [6,1,7,2,8,3,9,4,10,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [6,1,7,8,9,10,2,3,4,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,8,7,10,9] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,6,1,8,9,2,10,4,5,7] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [4,6,7,1,9,2,3,10,5,8] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4,9,10,7,8] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Map
Robinson-Schensted tableau shape
Description
Sends a permutation to its Robinson-Schensted tableau shape.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
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
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.