Identifier
Values
[1,0] => [[1],[]] => [[1],[]] => [1] => 1
[1,0,1,0] => [[1,1],[]] => [[2],[]] => [2] => 2
[1,1,0,0] => [[2],[]] => [[1,1],[]] => [1,1] => 1
[1,0,1,0,1,0] => [[1,1,1],[]] => [[3],[]] => [3] => 3
[1,0,1,1,0,0] => [[2,1],[]] => [[2,1],[]] => [2,1] => 1
[1,1,0,0,1,0] => [[2,2],[1]] => [[2,2],[1]] => [1,2] => 1
[1,1,0,1,0,0] => [[3],[]] => [[1,1,1],[]] => [1,1,1] => 1
[1,1,1,0,0,0] => [[2,2],[]] => [[2,2],[]] => [2,2] => 2
[1,0,1,0,1,0,1,0] => [[1,1,1,1],[]] => [[4],[]] => [4] => 4
[1,0,1,0,1,1,0,0] => [[2,1,1],[]] => [[3,1],[]] => [3,1] => 1
[1,0,1,1,0,0,1,0] => [[2,2,1],[1]] => [[3,2],[1]] => [2,2] => 2
[1,0,1,1,0,1,0,0] => [[3,1],[]] => [[2,1,1],[]] => [2,1,1] => 1
[1,0,1,1,1,0,0,0] => [[2,2,1],[]] => [[3,2],[]] => [3,2] => 2
[1,1,0,0,1,0,1,0] => [[2,2,2],[1,1]] => [[3,3],[2]] => [1,3] => 1
[1,1,0,0,1,1,0,0] => [[3,2],[1]] => [[2,2,1],[1]] => [1,2,1] => 1
[1,1,0,1,0,0,1,0] => [[3,3],[2]] => [[2,2,2],[1,1]] => [1,1,2] => 1
[1,1,0,1,0,1,0,0] => [[4],[]] => [[1,1,1,1],[]] => [1,1,1,1] => 1
[1,1,0,1,1,0,0,0] => [[3,3],[1]] => [[2,2,2],[1]] => [1,2,2] => 1
[1,1,1,0,0,0,1,0] => [[2,2,2],[1]] => [[3,3],[1]] => [2,3] => 2
[1,1,1,0,0,1,0,0] => [[3,2],[]] => [[2,2,1],[]] => [2,2,1] => 1
[1,1,1,0,1,0,0,0] => [[2,2,2],[]] => [[3,3],[]] => [3,3] => 3
[1,1,1,1,0,0,0,0] => [[3,3],[]] => [[2,2,2],[]] => [2,2,2] => 2
[1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1],[]] => [[5],[]] => [5] => 5
[1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1],[]] => [[4,1],[]] => [4,1] => 1
[1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1],[1]] => [[4,2],[1]] => [3,2] => 2
[1,0,1,0,1,1,0,1,0,0] => [[3,1,1],[]] => [[3,1,1],[]] => [3,1,1] => 1
[1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1],[]] => [[4,2],[]] => [4,2] => 2
[1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1],[1,1]] => [[4,3],[2]] => [2,3] => 2
[1,0,1,1,0,0,1,1,0,0] => [[3,2,1],[1]] => [[3,2,1],[1]] => [2,2,1] => 1
[1,0,1,1,0,1,0,0,1,0] => [[3,3,1],[2]] => [[3,2,2],[1,1]] => [2,1,2] => 1
[1,0,1,1,0,1,0,1,0,0] => [[4,1],[]] => [[2,1,1,1],[]] => [2,1,1,1] => 1
[1,0,1,1,0,1,1,0,0,0] => [[3,3,1],[1]] => [[3,2,2],[1]] => [2,2,2] => 2
[1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1],[1]] => [[4,3],[1]] => [3,3] => 3
[1,0,1,1,1,0,0,1,0,0] => [[3,2,1],[]] => [[3,2,1],[]] => [3,2,1] => 1
[1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1],[]] => [[4,3],[]] => [4,3] => 3
[1,0,1,1,1,1,0,0,0,0] => [[3,3,1],[]] => [[3,2,2],[]] => [3,2,2] => 2
[1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2],[1,1,1]] => [[4,4],[3]] => [1,4] => 1
[1,1,0,0,1,0,1,1,0,0] => [[3,2,2],[1,1]] => [[3,3,1],[2]] => [1,3,1] => 1
[1,1,0,0,1,1,0,0,1,0] => [[3,3,2],[2,1]] => [[3,3,2],[2,1]] => [1,2,2] => 1
[1,1,0,0,1,1,0,1,0,0] => [[4,2],[1]] => [[2,2,1,1],[1]] => [1,2,1,1] => 1
[1,1,0,0,1,1,1,0,0,0] => [[3,3,2],[1,1]] => [[3,3,2],[2]] => [1,3,2] => 1
[1,1,0,1,0,0,1,0,1,0] => [[3,3,3],[2,2]] => [[3,3,3],[2,2]] => [1,1,3] => 1
[1,1,0,1,0,0,1,1,0,0] => [[4,3],[2]] => [[2,2,2,1],[1,1]] => [1,1,2,1] => 1
[1,1,0,1,0,1,0,0,1,0] => [[4,4],[3]] => [[2,2,2,2],[1,1,1]] => [1,1,1,2] => 1
[1,1,0,1,0,1,0,1,0,0] => [[5],[]] => [[1,1,1,1,1],[]] => [1,1,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0] => [[4,4],[2]] => [[2,2,2,2],[1,1]] => [1,1,2,2] => 1
[1,1,0,1,1,0,0,0,1,0] => [[3,3,3],[2,1]] => [[3,3,3],[2,1]] => [1,2,3] => 1
[1,1,0,1,1,0,0,1,0,0] => [[4,3],[1]] => [[2,2,2,1],[1]] => [1,2,2,1] => 1
[1,1,0,1,1,0,1,0,0,0] => [[3,3,3],[1,1]] => [[3,3,3],[2]] => [1,3,3] => 1
[1,1,0,1,1,1,0,0,0,0] => [[4,4],[1]] => [[2,2,2,2],[1]] => [1,2,2,2] => 1
[1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2],[1,1]] => [[4,4],[2]] => [2,4] => 2
[1,1,1,0,0,0,1,1,0,0] => [[3,2,2],[1]] => [[3,3,1],[1]] => [2,3,1] => 1
[1,1,1,0,0,1,0,0,1,0] => [[3,3,2],[2]] => [[3,3,2],[1,1]] => [2,2,2] => 2
[1,1,1,0,0,1,0,1,0,0] => [[4,2],[]] => [[2,2,1,1],[]] => [2,2,1,1] => 1
[1,1,1,0,0,1,1,0,0,0] => [[3,3,2],[1]] => [[3,3,2],[1]] => [2,3,2] => 2
[1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2],[1]] => [[4,4],[1]] => [3,4] => 3
[1,1,1,0,1,0,0,1,0,0] => [[3,2,2],[]] => [[3,3,1],[]] => [3,3,1] => 1
[1,1,1,0,1,0,1,0,0,0] => [[2,2,2,2],[]] => [[4,4],[]] => [4,4] => 4
[1,1,1,0,1,1,0,0,0,0] => [[3,3,2],[]] => [[3,3,2],[]] => [3,3,2] => 2
[1,1,1,1,0,0,0,0,1,0] => [[3,3,3],[2]] => [[3,3,3],[1,1]] => [2,2,3] => 2
[1,1,1,1,0,0,0,1,0,0] => [[4,3],[]] => [[2,2,2,1],[]] => [2,2,2,1] => 1
[1,1,1,1,0,0,1,0,0,0] => [[3,3,3],[1]] => [[3,3,3],[1]] => [2,3,3] => 2
[1,1,1,1,0,1,0,0,0,0] => [[4,4],[]] => [[2,2,2,2],[]] => [2,2,2,2] => 2
[1,1,1,1,1,0,0,0,0,0] => [[3,3,3],[]] => [[3,3,3],[]] => [3,3,3] => 3
[1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1],[]] => [[6],[]] => [6] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1],[]] => [[5,1],[]] => [5,1] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1],[1]] => [[5,2],[1]] => [4,2] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1],[]] => [[4,1,1],[]] => [4,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1],[]] => [[5,2],[]] => [5,2] => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1],[1,1]] => [[5,3],[2]] => [3,3] => 3
[1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1],[1]] => [[4,2,1],[1]] => [3,2,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1],[2]] => [[4,2,2],[1,1]] => [3,1,2] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1],[]] => [[3,1,1,1],[]] => [3,1,1,1] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [[3,3,1,1],[1]] => [[4,2,2],[1]] => [3,2,2] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1,1],[1]] => [[5,3],[1]] => [4,3] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1],[]] => [[4,2,1],[]] => [4,2,1] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1,1],[]] => [[5,3],[]] => [5,3] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [[3,3,1,1],[]] => [[4,2,2],[]] => [4,2,2] => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1],[1,1,1]] => [[5,4],[3]] => [2,4] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1],[1,1]] => [[4,3,1],[2]] => [2,3,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1],[2,1]] => [[4,3,2],[2,1]] => [2,2,2] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1],[1]] => [[3,2,1,1],[1]] => [2,2,1,1] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [[3,3,2,1],[1,1]] => [[4,3,2],[2]] => [2,3,2] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1],[2,2]] => [[4,3,3],[2,2]] => [2,1,3] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1],[2]] => [[3,2,2,1],[1,1]] => [2,1,2,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1],[3]] => [[3,2,2,2],[1,1,1]] => [2,1,1,2] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1],[]] => [[2,1,1,1,1],[]] => [2,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [[4,4,1],[2]] => [[3,2,2,2],[1,1]] => [2,1,2,2] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [[3,3,3,1],[2,1]] => [[4,3,3],[2,1]] => [2,2,3] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [[4,3,1],[1]] => [[3,2,2,1],[1]] => [2,2,2,1] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [[3,3,3,1],[1,1]] => [[4,3,3],[2]] => [2,3,3] => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [[4,4,1],[1]] => [[3,2,2,2],[1]] => [2,2,2,2] => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2,1],[1,1]] => [[5,4],[2]] => [3,4] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [[3,2,2,1],[1]] => [[4,3,1],[1]] => [3,3,1] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [[3,3,2,1],[2]] => [[4,3,2],[1,1]] => [3,2,2] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1],[]] => [[3,2,1,1],[]] => [3,2,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [[3,3,2,1],[1]] => [[4,3,2],[1]] => [3,3,2] => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2,1],[1]] => [[5,4],[1]] => [4,4] => 4
[1,0,1,1,1,0,1,0,0,1,0,0] => [[3,2,2,1],[]] => [[4,3,1],[]] => [4,3,1] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [[2,2,2,2,1],[]] => [[5,4],[]] => [5,4] => 4
[1,0,1,1,1,0,1,1,0,0,0,0] => [[3,3,2,1],[]] => [[4,3,2],[]] => [4,3,2] => 2
>>> Load all 294 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [[3,3,3,1],[2]] => [[4,3,3],[1,1]] => [3,2,3] => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [[4,3,1],[]] => [[3,2,2,1],[]] => [3,2,2,1] => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [[3,3,3,1],[1]] => [[4,3,3],[1]] => [3,3,3] => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [[4,4,1],[]] => [[3,2,2,2],[]] => [3,2,2,2] => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1,1]] => [[5,5],[4]] => [1,5] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1,1]] => [[4,4,1],[3]] => [1,4,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1,1]] => [[4,4,2],[3,1]] => [1,3,2] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2],[1,1]] => [[3,3,1,1],[2]] => [1,3,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1,1]] => [[4,4,2],[3]] => [1,4,2] => 1
[1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2,1]] => [[4,4,3],[3,2]] => [1,2,3] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2],[2,1]] => [[3,3,2,1],[2,1]] => [1,2,2,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2],[3,1]] => [[3,3,2,2],[2,1,1]] => [1,2,1,2] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2],[1]] => [[2,2,1,1,1],[1]] => [1,2,1,1,1] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [[4,4,2],[2,1]] => [[3,3,2,2],[2,1]] => [1,2,2,2] => 1
[1,1,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1,1]] => [[4,4,3],[3,1]] => [1,3,3] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [[4,3,2],[1,1]] => [[3,3,2,1],[2]] => [1,3,2,1] => 1
[1,1,0,0,1,1,1,0,1,0,0,0] => [[3,3,3,2],[1,1,1]] => [[4,4,3],[3]] => [1,4,3] => 1
[1,1,0,0,1,1,1,1,0,0,0,0] => [[4,4,2],[1,1]] => [[3,3,2,2],[2]] => [1,3,2,2] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3],[2,2,2]] => [[4,4,4],[3,3]] => [1,1,4] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3],[2,2]] => [[3,3,3,1],[2,2]] => [1,1,3,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3],[3,2]] => [[3,3,3,2],[2,2,1]] => [1,1,2,2] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3],[2]] => [[2,2,2,1,1],[1,1]] => [1,1,2,1,1] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [[4,4,3],[2,2]] => [[3,3,3,2],[2,2]] => [1,1,3,2] => 1
[1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4],[3,3]] => [[3,3,3,3],[2,2,2]] => [1,1,1,3] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4],[3]] => [[2,2,2,2,1],[1,1,1]] => [1,1,1,2,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5],[4]] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1,2] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [[6],[]] => [[1,1,1,1,1,1],[]] => [1,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [[5,5],[3]] => [[2,2,2,2,2],[1,1,1]] => [1,1,1,2,2] => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [[4,4,4],[3,2]] => [[3,3,3,3],[2,2,1]] => [1,1,2,3] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [[5,4],[2]] => [[2,2,2,2,1],[1,1]] => [1,1,2,2,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [[4,4,4],[2,2]] => [[3,3,3,3],[2,2]] => [1,1,3,3] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => [[5,5],[2]] => [[2,2,2,2,2],[1,1]] => [1,1,2,2,2] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2,1]] => [[4,4,4],[3,2]] => [1,2,4] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [[4,3,3],[2,1]] => [[3,3,3,1],[2,1]] => [1,2,3,1] => 1
[1,1,0,1,1,0,0,1,0,0,1,0] => [[4,4,3],[3,1]] => [[3,3,3,2],[2,1,1]] => [1,2,2,2] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [[5,3],[1]] => [[2,2,2,1,1],[1]] => [1,2,2,1,1] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [[4,4,3],[2,1]] => [[3,3,3,2],[2,1]] => [1,2,3,2] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => [[3,3,3,3],[2,1,1]] => [[4,4,4],[3,1]] => [1,3,4] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [[4,3,3],[1,1]] => [[3,3,3,1],[2]] => [1,3,3,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [[3,3,3,3],[1,1,1]] => [[4,4,4],[3]] => [1,4,4] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => [[4,4,3],[1,1]] => [[3,3,3,2],[2]] => [1,3,3,2] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [[4,4,4],[3,1]] => [[3,3,3,3],[2,1,1]] => [1,2,2,3] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [[5,4],[1]] => [[2,2,2,2,1],[1]] => [1,2,2,2,1] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [[4,4,4],[2,1]] => [[3,3,3,3],[2,1]] => [1,2,3,3] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [[5,5],[1]] => [[2,2,2,2,2],[1]] => [1,2,2,2,2] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1]] => [[5,5],[3]] => [2,5] => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1]] => [[4,4,1],[2]] => [2,4,1] => 1
[1,1,1,0,0,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1]] => [[4,4,2],[2,1]] => [2,3,2] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [[4,2,2],[1]] => [[3,3,1,1],[1]] => [2,3,1,1] => 1
[1,1,1,0,0,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1]] => [[4,4,2],[2]] => [2,4,2] => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2]] => [[4,4,3],[2,2]] => [2,2,3] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [[4,3,2],[2]] => [[3,3,2,1],[1,1]] => [2,2,2,1] => 1
[1,1,1,0,0,1,0,1,0,0,1,0] => [[4,4,2],[3]] => [[3,3,2,2],[1,1,1]] => [2,2,1,2] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2],[]] => [[2,2,1,1,1],[]] => [2,2,1,1,1] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => [[4,4,2],[2]] => [[3,3,2,2],[1,1]] => [2,2,2,2] => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1]] => [[4,4,3],[2,1]] => [2,3,3] => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [[4,3,2],[1]] => [[3,3,2,1],[1]] => [2,3,2,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [[3,3,3,2],[1,1]] => [[4,4,3],[2]] => [2,4,3] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [[4,4,2],[1]] => [[3,3,2,2],[1]] => [2,3,2,2] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2],[1,1]] => [[5,5],[2]] => [3,5] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [[3,2,2,2],[1]] => [[4,4,1],[1]] => [3,4,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [[3,3,2,2],[2]] => [[4,4,2],[1,1]] => [3,3,2] => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [[4,2,2],[]] => [[3,3,1,1],[]] => [3,3,1,1] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => [[3,3,2,2],[1]] => [[4,4,2],[1]] => [3,4,2] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [[2,2,2,2,2],[1]] => [[5,5],[1]] => [4,5] => 4
[1,1,1,0,1,0,1,0,0,1,0,0] => [[3,2,2,2],[]] => [[4,4,1],[]] => [4,4,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [[3,3,3,2],[2]] => [[4,4,3],[1,1]] => [3,3,3] => 3
[1,1,1,0,1,1,0,0,0,1,0,0] => [[4,3,2],[]] => [[3,3,2,1],[]] => [3,3,2,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2]] => [[4,4,4],[2,2]] => [2,2,4] => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [[4,3,3],[2]] => [[3,3,3,1],[1,1]] => [2,2,3,1] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [[4,4,3],[3]] => [[3,3,3,2],[1,1,1]] => [2,2,2,2] => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [[5,3],[]] => [[2,2,2,1,1],[]] => [2,2,2,1,1] => 1
[1,1,1,1,0,0,0,1,1,0,0,0] => [[4,4,3],[2]] => [[3,3,3,2],[1,1]] => [2,2,3,2] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [[3,3,3,3],[2,1]] => [[4,4,4],[2,1]] => [2,3,4] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [[4,3,3],[1]] => [[3,3,3,1],[1]] => [2,3,3,1] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [[4,4,4],[3]] => [[3,3,3,3],[1,1,1]] => [2,2,2,3] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [[5,4],[]] => [[2,2,2,2,1],[]] => [2,2,2,2,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1],[]] => [[7],[]] => [7] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1],[]] => [[6,1],[]] => [6,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1,1],[1]] => [[6,2],[1]] => [5,2] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1],[]] => [[5,1,1],[]] => [5,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1,1],[]] => [[6,2],[]] => [6,2] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1,1],[1,1]] => [[6,3],[2]] => [4,3] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1,1],[1]] => [[5,2,1],[1]] => [4,2,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1,1],[2]] => [[5,2,2],[1,1]] => [4,1,2] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1],[]] => [[4,1,1,1],[]] => [4,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1,1,1],[1]] => [[6,3],[1]] => [5,3] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1,1],[]] => [[5,2,1],[]] => [5,2,1] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1,1,1],[]] => [[6,3],[]] => [6,3] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[3,3,1,1,1],[]] => [[5,2,2],[]] => [5,2,2] => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1,1],[1,1,1]] => [[6,4],[3]] => [3,4] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1,1],[1,1]] => [[5,3,1],[2]] => [3,3,1] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1,1],[2,1]] => [[5,3,2],[2,1]] => [3,2,2] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1,1],[1]] => [[4,2,1,1],[1]] => [3,2,1,1] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1,1],[2,2]] => [[5,3,3],[2,2]] => [3,1,3] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1,1],[2]] => [[4,2,2,1],[1,1]] => [3,1,2,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1,1],[3]] => [[4,2,2,2],[1,1,1]] => [3,1,1,2] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1],[]] => [[3,1,1,1,1],[]] => [3,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2,1,1],[1,1]] => [[6,4],[2]] => [4,4] => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1,1],[]] => [[4,2,1,1],[]] => [4,2,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[3,3,2,1,1],[1]] => [[5,3,2],[1]] => [4,3,2] => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2,1,1],[1]] => [[6,4],[1]] => [5,4] => 4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[3,2,2,1,1],[]] => [[5,3,1],[]] => [5,3,1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[3,3,3,1,1],[2]] => [[5,3,3],[1,1]] => [4,2,3] => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[4,3,1,1],[]] => [[4,2,2,1],[]] => [4,2,2,1] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,1],[1,1,1,1]] => [[6,5],[4]] => [2,5] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,1],[1,1,1]] => [[5,4,1],[3]] => [2,4,1] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,1],[2,1,1]] => [[5,4,2],[3,1]] => [2,3,2] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,1],[1,1]] => [[4,3,1,1],[2]] => [2,3,1,1] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,1],[2,2,1]] => [[5,4,3],[3,2]] => [2,2,3] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,1],[2,1]] => [[4,3,2,1],[2,1]] => [2,2,2,1] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,1],[3,1]] => [[4,3,2,2],[2,1,1]] => [2,2,1,2] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2,1],[1]] => [[3,2,1,1,1],[1]] => [2,2,1,1,1] => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,1],[2,2,2]] => [[5,4,4],[3,3]] => [2,1,4] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,1],[2,2]] => [[4,3,3,1],[2,2]] => [2,1,3,1] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,1],[3,2]] => [[4,3,3,2],[2,2,1]] => [2,1,2,2] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3,1],[2]] => [[3,2,2,1,1],[1,1]] => [2,1,2,1,1] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4,1],[3,3]] => [[4,3,3,3],[2,2,2]] => [2,1,1,3] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4,1],[3]] => [[3,2,2,2,1],[1,1,1]] => [2,1,1,2,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5,1],[4]] => [[3,2,2,2,2],[1,1,1,1]] => [2,1,1,1,2] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1],[]] => [[2,1,1,1,1,1],[]] => [2,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2,1],[1,1,1]] => [[6,5],[3]] => [3,5] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[3,3,2,2,1],[1,1]] => [[5,4,2],[2]] => [3,4,2] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2,1],[]] => [[3,2,1,1,1],[]] => [3,2,1,1,1] => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[3,3,3,2,1],[2,1]] => [[5,4,3],[2,1]] => [3,3,3] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[2,2,2,2,2,1],[1,1]] => [[6,5],[2]] => [4,5] => 4
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[4,2,2,1],[]] => [[4,3,1,1],[]] => [4,3,1,1] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[3,3,3,3,1],[2,2]] => [[5,4,4],[2,2]] => [3,2,4] => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[5,3,1],[]] => [[3,2,2,1,1],[]] => [3,2,2,1,1] => 1
[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]] => [[6,6],[5]] => [1,6] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2],[1,1,1,1]] => [[5,5,1],[4]] => [1,5,1] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2],[2,1,1,1]] => [[5,5,2],[4,1]] => [1,4,2] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2],[1,1,1]] => [[4,4,1,1],[3]] => [1,4,1,1] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2],[2,2,1,1]] => [[5,5,3],[4,2]] => [1,3,3] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2],[2,1,1]] => [[4,4,2,1],[3,1]] => [1,3,2,1] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2],[3,1,1]] => [[4,4,2,2],[3,1,1]] => [1,3,1,2] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[5,2,2],[1,1]] => [[3,3,1,1,1],[2]] => [1,3,1,1,1] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2],[2,2,2,1]] => [[5,5,4],[4,3]] => [1,2,4] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2],[2,2,1]] => [[4,4,3,1],[3,2]] => [1,2,3,1] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2],[3,2,1]] => [[4,4,3,2],[3,2,1]] => [1,2,2,2] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2],[2,1]] => [[3,3,2,1,1],[2,1]] => [1,2,2,1,1] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2],[3,3,1]] => [[4,4,3,3],[3,2,2]] => [1,2,1,3] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2],[3,1]] => [[3,3,2,2,1],[2,1,1]] => [1,2,1,2,1] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[5,5,2],[4,1]] => [[3,3,2,2,2],[2,1,1,1]] => [1,2,1,1,2] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[6,2],[1]] => [[2,2,1,1,1,1],[1]] => [1,2,1,1,1,1] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2,2]] => [[5,5,5],[4,4]] => [1,1,5] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3],[2,2,2]] => [[4,4,4,1],[3,3]] => [1,1,4,1] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3],[3,2,2]] => [[4,4,4,2],[3,3,1]] => [1,1,3,2] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3],[2,2]] => [[3,3,3,1,1],[2,2]] => [1,1,3,1,1] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3],[3,3,2]] => [[4,4,4,3],[3,3,2]] => [1,1,2,3] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3],[3,2]] => [[3,3,3,2,1],[2,2,1]] => [1,1,2,2,1] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3],[4,2]] => [[3,3,3,2,2],[2,2,1,1]] => [1,1,2,1,2] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[6,3],[2]] => [[2,2,2,1,1,1],[1,1]] => [1,1,2,1,1,1] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4],[3,3,3]] => [[4,4,4,4],[3,3,3]] => [1,1,1,4] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4],[3,3]] => [[3,3,3,3,1],[2,2,2]] => [1,1,1,3,1] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4],[4,3]] => [[3,3,3,3,2],[2,2,2,1]] => [1,1,1,2,2] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[6,4],[3]] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1,2,1,1] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[5,5,5],[4,4]] => [[3,3,3,3,3],[2,2,2,2]] => [1,1,1,1,3] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[6,5],[4]] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1,2,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[6,6],[5]] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1,2] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7],[]] => [[1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1,1]] => [[6,6],[4]] => [2,6] => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2,2],[1,1,1]] => [[5,5,2],[3]] => [2,5,2] => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2,2],[2,1,1]] => [[5,5,3],[3,1]] => [2,4,3] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2],[]] => [[2,2,1,1,1,1],[]] => [2,2,1,1,1,1] => 1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3,2],[2,2,1]] => [[5,5,4],[3,2]] => [2,3,4] => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1]] => [[6,6],[3]] => [3,6] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[5,2,2],[]] => [[3,3,1,1,1],[]] => [3,3,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2]] => [[5,5,5],[3,3]] => [2,2,5] => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[6,3],[]] => [[2,2,2,1,1,1],[]] => [2,2,2,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1,1],[]] => [[8],[]] => [8] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1,1],[]] => [[7,1],[]] => [7,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1,1],[]] => [[6,1,1],[]] => [6,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1,1,1],[]] => [[7,2],[]] => [7,2] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1,1],[]] => [[5,1,1,1],[]] => [5,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1,1,1],[]] => [[6,2,1],[]] => [6,2,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1,1],[]] => [[4,1,1,1,1],[]] => [4,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1,1,1],[]] => [[5,2,1,1],[]] => [5,2,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1,1],[]] => [[3,1,1,1,1,1],[]] => [3,1,1,1,1,1] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2,1,1],[]] => [[4,2,1,1,1],[]] => [4,2,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,1],[]] => [[2,1,1,1,1,1,1],[]] => [2,1,1,1,1,1,1] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[6,2,1],[]] => [[3,2,1,1,1,1],[]] => [3,2,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8],[]] => [[1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,2],[]] => [[2,2,1,1,1,1,1],[]] => [2,2,1,1,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[9],[]] => [[1,1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1,1,1],[]] => [[9],[]] => [9] => 9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1,1,1],[]] => [[8,1],[]] => [8,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1,1,1],[]] => [[7,1,1],[]] => [7,1,1] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1,1,1],[]] => [[6,1,1,1],[]] => [6,1,1,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1,1,1],[]] => [[5,1,1,1,1],[]] => [5,1,1,1,1] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1,1,1],[]] => [[4,1,1,1,1,1],[]] => [4,1,1,1,1,1] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7,1,1],[]] => [[3,1,1,1,1,1,1],[]] => [3,1,1,1,1,1,1] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[8,1],[]] => [[2,1,1,1,1,1,1,1],[]] => [2,1,1,1,1,1,1,1] => 1
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Description
The smallest part of an integer composition.
Map
row lengths
Description
The sequence of row lengths from top to bottom.
Map
conjugate
Description
The conjugate of the skew partition.
The conjugate of a skew partition $\lambda$ is the skew partition $\lambda^*$ whose Ferrers diagram is obtained from the Ferrers diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
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 $\gamma(D)$.