Identifier
Values
[[1]] => [[1]] => [1] => [1,0] => 0
[[1],[1]] => [[1,1]] => [2] => [1,0,1,0] => 0
[[2]] => [[2]] => [2] => [1,0,1,0] => 0
[[1,1]] => [[1],[1]] => [1,1] => [1,1,0,0] => 1
[[1],[1],[1]] => [[1,1,1]] => [3] => [1,0,1,0,1,0] => 0
[[2],[1]] => [[2,1]] => [3] => [1,0,1,0,1,0] => 0
[[1,1],[1]] => [[1,1],[1]] => [2,1] => [1,0,1,1,0,0] => 1
[[3]] => [[3]] => [3] => [1,0,1,0,1,0] => 0
[[2,1]] => [[2],[1]] => [2,1] => [1,0,1,1,0,0] => 1
[[1,1,1]] => [[1],[1],[1]] => [1,1,1] => [1,1,0,1,0,0] => 2
[[1],[1],[1],[1]] => [[1,1,1,1]] => [4] => [1,0,1,0,1,0,1,0] => 0
[[2],[1],[1]] => [[2,1,1]] => [4] => [1,0,1,0,1,0,1,0] => 0
[[2],[2]] => [[2,2]] => [4] => [1,0,1,0,1,0,1,0] => 0
[[1,1],[1],[1]] => [[1,1,1],[1]] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[[1,1],[1,1]] => [[1,1],[1,1]] => [2,2] => [1,1,1,0,0,0] => 1
[[3],[1]] => [[3,1]] => [4] => [1,0,1,0,1,0,1,0] => 0
[[2,1],[1]] => [[2,1],[1]] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[[1,1,1],[1]] => [[1,1],[1],[1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[[4]] => [[4]] => [4] => [1,0,1,0,1,0,1,0] => 0
[[3,1]] => [[3],[1]] => [3,1] => [1,0,1,0,1,1,0,0] => 1
[[2,2]] => [[2],[2]] => [2,2] => [1,1,1,0,0,0] => 1
[[2,1,1]] => [[2],[1],[1]] => [2,1,1] => [1,0,1,1,0,1,0,0] => 2
[[1,1,1,1]] => [[1],[1],[1],[1]] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 3
[[1],[1],[1],[1],[1]] => [[1,1,1,1,1]] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[[2],[1],[1],[1]] => [[2,1,1,1]] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[[2],[2],[1]] => [[2,2,1]] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[[1,1],[1],[1],[1]] => [[1,1,1,1],[1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[1,1],[1,1],[1]] => [[1,1,1],[1,1]] => [3,2] => [1,0,1,1,1,0,0,0] => 1
[[3],[1],[1]] => [[3,1,1]] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[[3],[2]] => [[3,2]] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[[2,1],[1],[1]] => [[2,1,1],[1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[2,1],[2]] => [[2,2],[1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[2,1],[1,1]] => [[2,1],[1,1]] => [3,2] => [1,0,1,1,1,0,0,0] => 1
[[1,1,1],[1],[1]] => [[1,1,1],[1],[1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[[1,1,1],[1,1]] => [[1,1],[1,1],[1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[[4],[1]] => [[4,1]] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[[3,1],[1]] => [[3,1],[1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[2,2],[1]] => [[2,1],[2]] => [3,2] => [1,0,1,1,1,0,0,0] => 1
[[2,1,1],[1]] => [[2,1],[1],[1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[[1,1,1,1],[1]] => [[1,1],[1],[1],[1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 3
[[5]] => [[5]] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
[[4,1]] => [[4],[1]] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
[[3,2]] => [[3],[2]] => [3,2] => [1,0,1,1,1,0,0,0] => 1
[[3,1,1]] => [[3],[1],[1]] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 2
[[2,2,1]] => [[2],[2],[1]] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[[2,1,1,1]] => [[2],[1],[1],[1]] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 3
[[1,1,1,1,1]] => [[1],[1],[1],[1],[1]] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[[1],[1],[1],[1],[1],[1]] => [[1,1,1,1,1,1]] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[2],[1],[1],[1],[1]] => [[2,1,1,1,1]] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[2],[2],[1],[1]] => [[2,2,1,1]] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[2],[2],[2]] => [[2,2,2]] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[1,1],[1],[1],[1],[1]] => [[1,1,1,1,1],[1]] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[[1,1],[1,1],[1],[1]] => [[1,1,1,1],[1,1]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[1,1],[1,1],[1,1]] => [[1,1,1],[1,1,1]] => [3,3] => [1,1,1,0,1,0,0,0] => 1
[[3],[1],[1],[1]] => [[3,1,1,1]] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[3],[2],[1]] => [[3,2,1]] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[3],[3]] => [[3,3]] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[2,1],[1],[1],[1]] => [[2,1,1,1],[1]] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[[2,1],[2],[1]] => [[2,2,1],[1]] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[[2,1],[1,1],[1]] => [[2,1,1],[1,1]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[2,1],[2,1]] => [[2,2],[1,1]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[1,1,1],[1],[1],[1]] => [[1,1,1,1],[1],[1]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[1,1,1],[1,1],[1]] => [[1,1,1],[1,1],[1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[[1,1,1],[1,1,1]] => [[1,1],[1,1],[1,1]] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[[4],[1],[1]] => [[4,1,1]] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[4],[2]] => [[4,2]] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[3,1],[1],[1]] => [[3,1,1],[1]] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[[3,1],[2]] => [[3,2],[1]] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[[3,1],[1,1]] => [[3,1],[1,1]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[2,2],[1],[1]] => [[2,1,1],[2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[2,2],[2]] => [[2,2],[2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[2,2],[1,1]] => [[2,1],[2,1]] => [3,3] => [1,1,1,0,1,0,0,0] => 1
[[2,1,1],[1],[1]] => [[2,1,1],[1],[1]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[2,1,1],[2]] => [[2,2],[1],[1]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[2,1,1],[1,1]] => [[2,1],[1,1],[1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[[1,1,1,1],[1],[1]] => [[1,1,1],[1],[1],[1]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[[1,1,1,1],[1,1]] => [[1,1],[1,1],[1],[1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 3
[[5],[1]] => [[5,1]] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[4,1],[1]] => [[4,1],[1]] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[[3,2],[1]] => [[3,1],[2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[3,1,1],[1]] => [[3,1],[1],[1]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[2,2,1],[1]] => [[2,1],[2],[1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[[2,1,1,1],[1]] => [[2,1],[1],[1],[1]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[[1,1,1,1,1],[1]] => [[1,1],[1],[1],[1],[1]] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[6]] => [[6]] => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[[5,1]] => [[5],[1]] => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[[4,2]] => [[4],[2]] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
[[4,1,1]] => [[4],[1],[1]] => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 2
[[3,3]] => [[3],[3]] => [3,3] => [1,1,1,0,1,0,0,0] => 1
[[3,2,1]] => [[3],[2],[1]] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
[[3,1,1,1]] => [[3],[1],[1],[1]] => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 3
[[2,2,2]] => [[2],[2],[2]] => [2,2,2] => [1,1,1,1,0,0,0,0] => 2
[[2,2,1,1]] => [[2],[2],[1],[1]] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 3
[[2,1,1,1,1]] => [[2],[1],[1],[1],[1]] => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 4
[[1,1,1,1,1,1]] => [[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5
[[1,1],[1,1],[1],[1],[1]] => [[1,1,1,1,1],[1,1]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[[1,1],[1,1],[1,1],[1]] => [[1,1,1,1],[1,1,1]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[2,1],[1,1],[1],[1]] => [[2,1,1,1],[1,1]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[[2,1],[1,1],[1,1]] => [[2,1,1],[1,1,1]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[2,1],[2,1],[1]] => [[2,2,1],[1,1]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[[1,1,1],[1,1],[1],[1]] => [[1,1,1,1],[1,1],[1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
>>> Load all 256 entries. <<<
[[1,1,1],[1,1],[1,1]] => [[1,1,1],[1,1,1],[1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 2
[[1,1,1],[1,1,1],[1]] => [[1,1,1],[1,1],[1,1]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 2
[[3,1],[1,1],[1]] => [[3,1,1],[1,1]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[[3,1],[2,1]] => [[3,2],[1,1]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[[2,2],[1],[1],[1]] => [[2,1,1,1],[2]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[[2,2],[2],[1]] => [[2,2,1],[2]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[[2,2],[1,1],[1]] => [[2,1,1],[2,1]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[2,2],[2,1]] => [[2,2],[2,1]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[2,1,1],[1,1],[1]] => [[2,1,1],[1,1],[1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[[2,1,1],[2,1]] => [[2,2],[1,1],[1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[[2,1,1],[1,1,1]] => [[2,1],[1,1],[1,1]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 2
[[1,1,1,1],[1,1],[1]] => [[1,1,1],[1,1],[1],[1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,1,1,1],[1,1,1]] => [[1,1],[1,1],[1,1],[1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 3
[[4,1],[1,1]] => [[4,1],[1,1]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[[3,2],[1],[1]] => [[3,1,1],[2]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[[3,2],[2]] => [[3,2],[2]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[[3,2],[1,1]] => [[3,1],[2,1]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[3,1,1],[1,1]] => [[3,1],[1,1],[1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[[2,2,1],[1],[1]] => [[2,1,1],[2],[1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[[2,2,1],[2]] => [[2,2],[2],[1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[[2,2,1],[1,1]] => [[2,1],[2,1],[1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 2
[[2,1,1,1],[1,1]] => [[2,1],[1,1],[1],[1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[1,1,1,1,1],[1,1]] => [[1,1],[1,1],[1],[1],[1]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[4,2],[1]] => [[4,1],[2]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[[3,3],[1]] => [[3,1],[3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[3,2,1],[1]] => [[3,1],[2],[1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[[2,2,2],[1]] => [[2,1],[2],[2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 2
[[2,2,1,1],[1]] => [[2,1],[2],[1],[1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[5,2]] => [[5],[2]] => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[[4,3]] => [[4],[3]] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
[[4,2,1]] => [[4],[2],[1]] => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 2
[[3,3,1]] => [[3],[3],[1]] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 2
[[3,2,2]] => [[3],[2],[2]] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 2
[[3,2,1,1]] => [[3],[2],[1],[1]] => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 3
[[2,2,2,1]] => [[2],[2],[2],[1]] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 3
[[2,2,1,1,1]] => [[2],[2],[1],[1],[1]] => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[[1,1],[1,1],[1,1],[1],[1]] => [[1,1,1,1,1],[1,1,1]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[[1,1],[1,1],[1,1],[1,1]] => [[1,1,1,1],[1,1,1,1]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
[[2,1],[1,1],[1,1],[1]] => [[2,1,1,1],[1,1,1]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[[2,1],[2,1],[1,1]] => [[2,2,1],[1,1,1]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[[1,1,1],[1,1],[1,1],[1]] => [[1,1,1,1],[1,1,1],[1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[[1,1,1],[1,1,1],[1],[1]] => [[1,1,1,1],[1,1],[1,1]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[1,1,1],[1,1,1],[1,1]] => [[1,1,1],[1,1,1],[1,1]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
[[3,1],[1,1],[1,1]] => [[3,1,1],[1,1,1]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[[2,2],[1,1],[1],[1]] => [[2,1,1,1],[2,1]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[[2,2],[1,1],[1,1]] => [[2,1,1],[2,1,1]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
[[2,2],[2,1],[1]] => [[2,2,1],[2,1]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[[2,2],[2,2]] => [[2,2],[2,2]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
[[2,1,1],[1,1],[1,1]] => [[2,1,1],[1,1,1],[1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[[2,1,1],[1,1,1],[1]] => [[2,1,1],[1,1],[1,1]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[2,1,1],[2,1,1]] => [[2,2],[1,1],[1,1]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[1,1,1,1],[1,1],[1,1]] => [[1,1,1],[1,1,1],[1],[1]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[1,1,1,1],[1,1,1],[1]] => [[1,1,1],[1,1],[1,1],[1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[[1,1,1,1],[1,1,1,1]] => [[1,1],[1,1],[1,1],[1,1]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 3
[[3,2],[1,1],[1]] => [[3,1,1],[2,1]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[[3,2],[2,1]] => [[3,2],[2,1]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[[3,1,1],[1,1,1]] => [[3,1],[1,1],[1,1]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[2,2,1],[1,1],[1]] => [[2,1,1],[2,1],[1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[[2,2,1],[2,1]] => [[2,2],[2,1],[1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[[2,2,1],[1,1,1]] => [[2,1],[2,1],[1,1]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
[[2,1,1,1],[1,1,1]] => [[2,1],[1,1],[1,1],[1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[[1,1,1,1,1],[1,1,1]] => [[1,1],[1,1],[1,1],[1],[1]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[4,2],[1,1]] => [[4,1],[2,1]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[[3,3],[1],[1]] => [[3,1,1],[3]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[[3,3],[2]] => [[3,2],[3]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[[3,3],[1,1]] => [[3,1],[3,1]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
[[3,2,1],[1,1]] => [[3,1],[2,1],[1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[[2,2,2],[1],[1]] => [[2,1,1],[2],[2]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[2,2,2],[2]] => [[2,2],[2],[2]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[2,2,2],[1,1]] => [[2,1],[2,1],[2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
[[2,2,1,1],[1,1]] => [[2,1],[2,1],[1],[1]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[4,3],[1]] => [[4,1],[3]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[[3,3,1],[1]] => [[3,1],[3],[1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[[3,2,2],[1]] => [[3,1],[2],[2]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[2,2,2,1],[1]] => [[2,1],[2],[2],[1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[[5,3]] => [[5],[3]] => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[[4,4]] => [[4],[4]] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
[[4,3,1]] => [[4],[3],[1]] => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 2
[[4,2,2]] => [[4],[2],[2]] => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[[3,3,2]] => [[3],[3],[2]] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
[[3,3,1,1]] => [[3],[3],[1],[1]] => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 3
[[3,2,2,1]] => [[3],[2],[2],[1]] => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 3
[[2,2,2,2]] => [[2],[2],[2],[2]] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 3
[[2,2,2,1,1]] => [[2],[2],[2],[1],[1]] => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[[1,1],[1,1],[1,1],[1,1],[1]] => [[1,1,1,1,1],[1,1,1,1]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[[2,1],[1,1],[1,1],[1,1]] => [[2,1,1,1],[1,1,1,1]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[[1,1,1],[1,1],[1,1],[1,1]] => [[1,1,1,1],[1,1,1,1],[1]] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[[1,1,1],[1,1,1],[1,1],[1]] => [[1,1,1,1],[1,1,1],[1,1]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[1,1,1],[1,1,1],[1,1,1]] => [[1,1,1],[1,1,1],[1,1,1]] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 2
[[2,2],[1,1],[1,1],[1]] => [[2,1,1,1],[2,1,1]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[[2,2],[2,1],[1,1]] => [[2,2,1],[2,1,1]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[[2,2],[2,2],[1]] => [[2,2,1],[2,2]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[[2,1,1],[1,1,1],[1,1]] => [[2,1,1],[1,1,1],[1,1]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[1,1,1,1],[1,1,1],[1,1]] => [[1,1,1],[1,1,1],[1,1],[1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[[1,1,1,1],[1,1,1,1],[1]] => [[1,1,1],[1,1],[1,1],[1,1]] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[[3,2],[1,1],[1,1]] => [[3,1,1],[2,1,1]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[[3,2],[2,2]] => [[3,2],[2,2]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[[2,2,1],[1,1],[1,1]] => [[2,1,1],[2,1,1],[1]] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[[2,2,1],[1,1,1],[1]] => [[2,1,1],[2,1],[1,1]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[2,2,1],[2,2]] => [[2,2],[2,2],[1]] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[[2,2,1],[2,1,1]] => [[2,2],[2,1],[1,1]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[2,1,1,1],[1,1,1,1]] => [[2,1],[1,1],[1,1],[1,1]] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[[1,1,1,1,1],[1,1,1,1]] => [[1,1],[1,1],[1,1],[1,1],[1]] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 4
[[3,3],[1,1],[1]] => [[3,1,1],[3,1]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[[3,3],[2,1]] => [[3,2],[3,1]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[[3,2,1],[1,1,1]] => [[3,1],[2,1],[1,1]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[2,2,2],[1,1],[1]] => [[2,1,1],[2,1],[2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[2,2,2],[2,1]] => [[2,2],[2,1],[2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[2,2,2],[1,1,1]] => [[2,1],[2,1],[2,1]] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 2
[[2,2,1,1],[1,1,1]] => [[2,1],[2,1],[1,1],[1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[[4,3],[1,1]] => [[4,1],[3,1]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[[3,3,1],[1,1]] => [[3,1],[3,1],[1]] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[[3,2,2],[1,1]] => [[3,1],[2,1],[2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[2,2,2,1],[1,1]] => [[2,1],[2,1],[2],[1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[[4,4],[1]] => [[4,1],[4]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[[3,3,2],[1]] => [[3,1],[3],[2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[2,2,2,2],[1]] => [[2,1],[2],[2],[2]] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[[5,4]] => [[5],[4]] => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[[4,4,1]] => [[4],[4],[1]] => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[[4,3,2]] => [[4],[3],[2]] => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
[[3,3,3]] => [[3],[3],[3]] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 2
[[3,3,2,1]] => [[3],[3],[2],[1]] => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 3
[[3,2,2,2]] => [[3],[2],[2],[2]] => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
[[2,2,2,2,1]] => [[2],[2],[2],[2],[1]] => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 4
[[1,1],[1,1],[1,1],[1,1],[1,1]] => [[1,1,1,1,1],[1,1,1,1,1]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[[1,1,1],[1,1,1],[1,1],[1,1]] => [[1,1,1,1],[1,1,1,1],[1,1]] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[[1,1,1],[1,1,1],[1,1,1],[1]] => [[1,1,1,1],[1,1,1],[1,1,1]] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[2,2],[1,1],[1,1],[1,1]] => [[2,1,1,1],[2,1,1,1]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[[2,2],[2,2],[1,1]] => [[2,2,1],[2,2,1]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[[2,1,1],[1,1,1],[1,1,1]] => [[2,1,1],[1,1,1],[1,1,1]] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[1,1,1,1],[1,1,1],[1,1,1]] => [[1,1,1],[1,1,1],[1,1,1],[1]] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 3
[[1,1,1,1],[1,1,1,1],[1,1]] => [[1,1,1],[1,1,1],[1,1],[1,1]] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[2,2,1],[1,1,1],[1,1]] => [[2,1,1],[2,1,1],[1,1]] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[[2,2,1],[2,2,1]] => [[2,2],[2,2],[1,1]] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[[1,1,1,1,1],[1,1,1,1,1]] => [[1,1],[1,1],[1,1],[1,1],[1,1]] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 4
[[3,3],[1,1],[1,1]] => [[3,1,1],[3,1,1]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[[3,3],[2,2]] => [[3,2],[3,2]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[[2,2,2],[1,1],[1,1]] => [[2,1,1],[2,1,1],[2]] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[[2,2,2],[1,1,1],[1]] => [[2,1,1],[2,1],[2,1]] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[2,2,2],[2,2]] => [[2,2],[2,2],[2]] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[[2,2,2],[2,1,1]] => [[2,2],[2,1],[2,1]] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[2,2,1,1],[1,1,1,1]] => [[2,1],[2,1],[1,1],[1,1]] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[3,3,1],[1,1,1]] => [[3,1],[3,1],[1,1]] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[[3,2,2],[1,1,1]] => [[3,1],[2,1],[2,1]] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[2,2,2,1],[1,1,1]] => [[2,1],[2,1],[2,1],[1]] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 3
[[4,4],[1,1]] => [[4,1],[4,1]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[[3,3,2],[1,1]] => [[3,1],[3,1],[2]] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[[2,2,2,2],[1,1]] => [[2,1],[2,1],[2],[2]] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[3,3,3],[1]] => [[3,1],[3],[3]] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[5,5]] => [[5],[5]] => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[[4,4,2]] => [[4],[4],[2]] => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
[[4,3,3]] => [[4],[3],[3]] => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
[[3,3,3,1]] => [[3],[3],[3],[1]] => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 3
[[3,3,2,2]] => [[3],[3],[2],[2]] => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[2,2,2,2,2]] => [[2],[2],[2],[2],[2]] => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 4
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Description
The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1.
Map
to partition
Description
The underlying integer partition of a plane partition.
This is the partition whose parts are the sums of the individual rows of the plane partition.
Map
transpose
Description
The transpose of a plane partition.
This is the mirror symmetry along the vertical axis.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.