Identifier
Values
[1,0] => [1,0] => [[1],[]] => 0
[1,0,1,0] => [1,1,0,0] => [[2],[]] => 0
[1,1,0,0] => [1,0,1,0] => [[1,1],[]] => 0
[1,0,1,0,1,0] => [1,1,0,1,0,0] => [[3],[]] => 0
[1,0,1,1,0,0] => [1,1,0,0,1,0] => [[2,2],[1]] => 0
[1,1,0,0,1,0] => [1,1,1,0,0,0] => [[2,2],[]] => 1
[1,1,0,1,0,0] => [1,0,1,0,1,0] => [[1,1,1],[]] => 0
[1,1,1,0,0,0] => [1,0,1,1,0,0] => [[2,1],[]] => 0
[1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [[4],[]] => 0
[1,0,1,0,1,1,0,0] => [1,1,0,1,0,0,1,0] => [[3,3],[2]] => 0
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,0] => [[3,3],[1]] => 1
[1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => [[2,2,2],[1,1]] => 0
[1,0,1,1,1,0,0,0] => [1,1,0,0,1,1,0,0] => [[3,2],[1]] => 0
[1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0] => [[3,2],[]] => 1
[1,1,0,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => [[2,2,2],[1]] => 1
[1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,0] => [[2,2,2],[]] => 2
[1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => [[1,1,1,1],[]] => 0
[1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0] => [[2,1,1],[]] => 0
[1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,0] => [[3,3],[]] => 2
[1,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0] => [[2,2,1],[1]] => 0
[1,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0] => [[3,1],[]] => 0
[1,1,1,1,0,0,0,0] => [1,0,1,1,1,0,0,0] => [[2,2,1],[]] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => [[5],[]] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => [[4,4],[3]] => 0
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => [[4,4],[2]] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => [[3,3,3],[2,2]] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0] => [[4,3],[2]] => 0
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [[4,3],[1]] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [[3,3,3],[2,1]] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0] => [[3,3,3],[1,1]] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2],[1,1,1]] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0] => [[3,2,2],[1,1]] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,0] => [[4,4],[1]] => 2
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => [[3,3,2],[2,1]] => 0
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0] => [[4,2],[1]] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => [[3,3,2],[1,1]] => 1
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [[4,2],[]] => 1
[1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => [[3,3,2],[2]] => 1
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => [[3,3,2],[1]] => 2
[1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2],[1,1]] => 1
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => [[3,2,2],[1]] => 1
[1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [[3,2,2],[]] => 2
[1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2],[1]] => 2
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1],[]] => 0
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1],[]] => 0
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1],[1]] => 0
[1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => [[3,1,1],[]] => 0
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1],[]] => 1
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [[4,3],[]] => 2
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => [[3,3,3],[2]] => 2
[1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1],[1,1]] => 0
[1,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0] => [[3,2,1],[1]] => 0
[1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => [[3,3,1],[2]] => 0
[1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => [[4,1],[]] => 0
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,1,0,0,0] => [[3,3,1],[1]] => 1
[1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1],[1]] => 1
[1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => [[3,2,1],[]] => 1
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1],[]] => 2
[1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => [[3,3,1],[]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [[6],[]] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5],[4]] => 0
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [[5,5],[3]] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4],[3,3]] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4],[3]] => 0
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [[5,4],[2]] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[4,4,4],[3,2]] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3],[2,2,2]] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3],[2,2]] => 0
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3],[3,2]] => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3],[2]] => 0
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[4,4,3],[2,2]] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [[5,3],[1]] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[4,4,3],[3,1]] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2,1]] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[4,3,3],[2,1]] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1,1]] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1,1]] => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1,1]] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2],[1,1]] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1,1]] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2,1]] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2],[2,1]] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2],[3,1]] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2],[1]] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[4,4,2],[2,1]] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1,1]] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[4,3,2],[1,1]] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2],[]] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[4,4,2],[3]] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2]] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[4,3,2],[2]] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1]] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1]] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1]] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[4,2,2],[1]] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1],[]] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1],[]] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1],[1]] => 0
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1],[]] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1],[]] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1],[1,1]] => 0
>>> Load all 187 entries. <<<
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1],[1]] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1],[2]] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1],[]] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,1,0,0,0] => [[3,3,1,1],[1]] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1,1],[1]] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1],[]] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1],[1,1,1]] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1],[1,1]] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1],[2,1]] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1],[1]] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[3,3,2,1],[1,1]] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1],[2,2]] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1],[2]] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1],[3]] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1],[]] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[4,4,1],[2]] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[3,3,3,1],[2,1]] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[4,3,1],[1]] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2,1],[1,1]] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[3,2,2,1],[1]] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => [[3,3,2,1],[2]] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1],[]] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7],[]] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[6,6],[5]] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[5,5,5],[4,4]] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[6,5],[4]] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4],[3,3,3]] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4],[3,3]] => 0
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4],[4,3]] => 0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[6,4],[3]] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2,2]] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3],[2,2,2]] => 0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3],[3,2,2]] => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3],[2,2]] => 0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3],[3,3,2]] => 0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3],[3,2]] => 0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3],[4,2]] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[6,3],[2]] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1,1,1]] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2],[1,1,1,1]] => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2],[2,1,1,1]] => 0
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2],[1,1,1]] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2],[2,2,1,1]] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2],[2,1,1]] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2],[3,1,1]] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[5,2,2],[1,1]] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2],[2,2,2,1]] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2],[2,2,1]] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2],[3,2,1]] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2],[2,1]] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2],[3,3,1]] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2],[3,1]] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[5,5,2],[4,1]] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[6,2],[1]] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1],[]] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1],[]] => 0
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1,1],[1]] => 0
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1],[]] => 0
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1,1],[1,1]] => 0
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1,1],[1]] => 0
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1,1],[2]] => 0
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1],[]] => 0
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1,1],[1,1,1]] => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1,1],[1,1]] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1,1],[2,1]] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1,1],[1]] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1,1],[2,2]] => 0
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1,1],[2]] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1,1],[3]] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1],[]] => 0
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,1],[1,1,1,1]] => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,1],[1,1,1]] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,1],[2,1,1]] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,1],[1,1]] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,1],[2,2,1]] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,1],[2,1]] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,1],[3,1]] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2,1],[1]] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,1],[2,2,2]] => 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,1],[2,2]] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,1],[3,2]] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3,1],[2]] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4,1],[3,3]] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4,1],[3]] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5,1],[4]] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1],[]] => 0
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Description
The number of two-by-two squares inside a skew partition.
This is, the number of cells $(i,j)$ in a skew partition for which the box $(i+1,j+1)$ is also a cell inside the skew partition.
Map
skew partition
Description
The parallelogram polyomino corresponding to a Dyck path, interpreted as a skew partition.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
This map returns the skew partition definded by the diagram of $\gamma(D)$.
Map
promotion
Description
The promotion of the two-row standard Young tableau of a Dyck path.
Dyck paths of semilength $n$ are in bijection with standard Young tableaux of shape $(n^2)$, see Mp00033to two-row standard tableau.
This map is the bijection on such standard Young tableaux given by Schützenberger's promotion. For definitions and details, see [1] and the references therein.