Identifier
Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00182: Skew partitions —outer shape⟶ Integer partitions
Images
[1] => [1] => [[1],[]] => [1]
[1,1] => [2] => [[2],[]] => [2]
[2] => [1,1] => [[1,1],[]] => [1,1]
[1,1,1] => [3] => [[3],[]] => [3]
[1,2] => [1,2] => [[2,1],[]] => [2,1]
[2,1] => [2,1] => [[2,2],[1]] => [2,2]
[3] => [1,1,1] => [[1,1,1],[]] => [1,1,1]
[1,1,1,1] => [4] => [[4],[]] => [4]
[1,1,2] => [1,3] => [[3,1],[]] => [3,1]
[1,2,1] => [2,2] => [[3,2],[1]] => [3,2]
[1,3] => [1,1,2] => [[2,1,1],[]] => [2,1,1]
[2,1,1] => [3,1] => [[3,3],[2]] => [3,3]
[2,2] => [1,2,1] => [[2,2,1],[1]] => [2,2,1]
[3,1] => [2,1,1] => [[2,2,2],[1,1]] => [2,2,2]
[4] => [1,1,1,1] => [[1,1,1,1],[]] => [1,1,1,1]
[1,1,1,1,1] => [5] => [[5],[]] => [5]
[1,1,1,2] => [1,4] => [[4,1],[]] => [4,1]
[1,1,2,1] => [2,3] => [[4,2],[1]] => [4,2]
[1,1,3] => [1,1,3] => [[3,1,1],[]] => [3,1,1]
[1,2,1,1] => [3,2] => [[4,3],[2]] => [4,3]
[1,2,2] => [1,2,2] => [[3,2,1],[1]] => [3,2,1]
[1,3,1] => [2,1,2] => [[3,2,2],[1,1]] => [3,2,2]
[1,4] => [1,1,1,2] => [[2,1,1,1],[]] => [2,1,1,1]
[2,1,1,1] => [4,1] => [[4,4],[3]] => [4,4]
[2,1,2] => [1,3,1] => [[3,3,1],[2]] => [3,3,1]
[2,2,1] => [2,2,1] => [[3,3,2],[2,1]] => [3,3,2]
[2,3] => [1,1,2,1] => [[2,2,1,1],[1]] => [2,2,1,1]
[3,1,1] => [3,1,1] => [[3,3,3],[2,2]] => [3,3,3]
[3,2] => [1,2,1,1] => [[2,2,2,1],[1,1]] => [2,2,2,1]
[4,1] => [2,1,1,1] => [[2,2,2,2],[1,1,1]] => [2,2,2,2]
[5] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => [1,1,1,1,1]
[1,1,1,1,1,1] => [6] => [[6],[]] => [6]
[1,1,1,1,2] => [1,5] => [[5,1],[]] => [5,1]
[1,1,1,2,1] => [2,4] => [[5,2],[1]] => [5,2]
[1,1,1,3] => [1,1,4] => [[4,1,1],[]] => [4,1,1]
[1,1,2,1,1] => [3,3] => [[5,3],[2]] => [5,3]
[1,1,2,2] => [1,2,3] => [[4,2,1],[1]] => [4,2,1]
[1,1,3,1] => [2,1,3] => [[4,2,2],[1,1]] => [4,2,2]
[1,1,4] => [1,1,1,3] => [[3,1,1,1],[]] => [3,1,1,1]
[1,2,1,1,1] => [4,2] => [[5,4],[3]] => [5,4]
[1,2,1,2] => [1,3,2] => [[4,3,1],[2]] => [4,3,1]
[1,2,2,1] => [2,2,2] => [[4,3,2],[2,1]] => [4,3,2]
[1,2,3] => [1,1,2,2] => [[3,2,1,1],[1]] => [3,2,1,1]
[1,3,1,1] => [3,1,2] => [[4,3,3],[2,2]] => [4,3,3]
[1,3,2] => [1,2,1,2] => [[3,2,2,1],[1,1]] => [3,2,2,1]
[1,4,1] => [2,1,1,2] => [[3,2,2,2],[1,1,1]] => [3,2,2,2]
[1,5] => [1,1,1,1,2] => [[2,1,1,1,1],[]] => [2,1,1,1,1]
[2,1,1,1,1] => [5,1] => [[5,5],[4]] => [5,5]
[2,1,1,2] => [1,4,1] => [[4,4,1],[3]] => [4,4,1]
[2,1,2,1] => [2,3,1] => [[4,4,2],[3,1]] => [4,4,2]
[2,1,3] => [1,1,3,1] => [[3,3,1,1],[2]] => [3,3,1,1]
[2,2,1,1] => [3,2,1] => [[4,4,3],[3,2]] => [4,4,3]
[2,2,2] => [1,2,2,1] => [[3,3,2,1],[2,1]] => [3,3,2,1]
[2,3,1] => [2,1,2,1] => [[3,3,2,2],[2,1,1]] => [3,3,2,2]
[2,4] => [1,1,1,2,1] => [[2,2,1,1,1],[1]] => [2,2,1,1,1]
[3,1,1,1] => [4,1,1] => [[4,4,4],[3,3]] => [4,4,4]
[3,1,2] => [1,3,1,1] => [[3,3,3,1],[2,2]] => [3,3,3,1]
[3,2,1] => [2,2,1,1] => [[3,3,3,2],[2,2,1]] => [3,3,3,2]
[3,3] => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => [2,2,2,1,1]
[4,1,1] => [3,1,1,1] => [[3,3,3,3],[2,2,2]] => [3,3,3,3]
[4,2] => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => [2,2,2,2,1]
[5,1] => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => [2,2,2,2,2]
[6] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => [1,1,1,1,1,1]
[1,1,1,1,1,1,1] => [7] => [[7],[]] => [7]
[1,1,1,1,1,2] => [1,6] => [[6,1],[]] => [6,1]
[1,1,1,1,2,1] => [2,5] => [[6,2],[1]] => [6,2]
[1,1,1,1,3] => [1,1,5] => [[5,1,1],[]] => [5,1,1]
[1,1,1,2,1,1] => [3,4] => [[6,3],[2]] => [6,3]
[1,1,1,2,2] => [1,2,4] => [[5,2,1],[1]] => [5,2,1]
[1,1,1,3,1] => [2,1,4] => [[5,2,2],[1,1]] => [5,2,2]
[1,1,1,4] => [1,1,1,4] => [[4,1,1,1],[]] => [4,1,1,1]
[1,1,2,1,1,1] => [4,3] => [[6,4],[3]] => [6,4]
[1,1,2,1,2] => [1,3,3] => [[5,3,1],[2]] => [5,3,1]
[1,1,2,2,1] => [2,2,3] => [[5,3,2],[2,1]] => [5,3,2]
[1,1,2,3] => [1,1,2,3] => [[4,2,1,1],[1]] => [4,2,1,1]
[1,1,3,1,1] => [3,1,3] => [[5,3,3],[2,2]] => [5,3,3]
[1,1,3,2] => [1,2,1,3] => [[4,2,2,1],[1,1]] => [4,2,2,1]
[1,1,4,1] => [2,1,1,3] => [[4,2,2,2],[1,1,1]] => [4,2,2,2]
[1,1,5] => [1,1,1,1,3] => [[3,1,1,1,1],[]] => [3,1,1,1,1]
[1,2,1,1,1,1] => [5,2] => [[6,5],[4]] => [6,5]
[1,2,1,1,2] => [1,4,2] => [[5,4,1],[3]] => [5,4,1]
[1,2,1,2,1] => [2,3,2] => [[5,4,2],[3,1]] => [5,4,2]
[1,2,1,3] => [1,1,3,2] => [[4,3,1,1],[2]] => [4,3,1,1]
[1,2,2,1,1] => [3,2,2] => [[5,4,3],[3,2]] => [5,4,3]
[1,2,2,2] => [1,2,2,2] => [[4,3,2,1],[2,1]] => [4,3,2,1]
[1,2,3,1] => [2,1,2,2] => [[4,3,2,2],[2,1,1]] => [4,3,2,2]
[1,2,4] => [1,1,1,2,2] => [[3,2,1,1,1],[1]] => [3,2,1,1,1]
[1,3,1,1,1] => [4,1,2] => [[5,4,4],[3,3]] => [5,4,4]
[1,3,1,2] => [1,3,1,2] => [[4,3,3,1],[2,2]] => [4,3,3,1]
[1,3,2,1] => [2,2,1,2] => [[4,3,3,2],[2,2,1]] => [4,3,3,2]
[1,3,3] => [1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => [3,2,2,1,1]
[1,4,1,1] => [3,1,1,2] => [[4,3,3,3],[2,2,2]] => [4,3,3,3]
[1,4,2] => [1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => [3,2,2,2,1]
[1,5,1] => [2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => [3,2,2,2,2]
[1,6] => [1,1,1,1,1,2] => [[2,1,1,1,1,1],[]] => [2,1,1,1,1,1]
[2,1,1,1,1,1] => [6,1] => [[6,6],[5]] => [6,6]
[2,1,1,1,2] => [1,5,1] => [[5,5,1],[4]] => [5,5,1]
[2,1,1,2,1] => [2,4,1] => [[5,5,2],[4,1]] => [5,5,2]
[2,1,1,3] => [1,1,4,1] => [[4,4,1,1],[3]] => [4,4,1,1]
[2,1,2,1,1] => [3,3,1] => [[5,5,3],[4,2]] => [5,5,3]
[2,1,2,2] => [1,2,3,1] => [[4,4,2,1],[3,1]] => [4,4,2,1]
>>> Load all 256 entries. <<<
[2,1,3,1] => [2,1,3,1] => [[4,4,2,2],[3,1,1]] => [4,4,2,2]
[2,1,4] => [1,1,1,3,1] => [[3,3,1,1,1],[2]] => [3,3,1,1,1]
[2,2,1,1,1] => [4,2,1] => [[5,5,4],[4,3]] => [5,5,4]
[2,2,1,2] => [1,3,2,1] => [[4,4,3,1],[3,2]] => [4,4,3,1]
[2,2,2,1] => [2,2,2,1] => [[4,4,3,2],[3,2,1]] => [4,4,3,2]
[2,2,3] => [1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => [3,3,2,1,1]
[2,3,1,1] => [3,1,2,1] => [[4,4,3,3],[3,2,2]] => [4,4,3,3]
[2,3,2] => [1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => [3,3,2,2,1]
[2,4,1] => [2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => [3,3,2,2,2]
[2,5] => [1,1,1,1,2,1] => [[2,2,1,1,1,1],[1]] => [2,2,1,1,1,1]
[3,1,1,1,1] => [5,1,1] => [[5,5,5],[4,4]] => [5,5,5]
[3,1,1,2] => [1,4,1,1] => [[4,4,4,1],[3,3]] => [4,4,4,1]
[3,1,2,1] => [2,3,1,1] => [[4,4,4,2],[3,3,1]] => [4,4,4,2]
[3,1,3] => [1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => [3,3,3,1,1]
[3,2,1,1] => [3,2,1,1] => [[4,4,4,3],[3,3,2]] => [4,4,4,3]
[3,2,2] => [1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => [3,3,3,2,1]
[3,3,1] => [2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => [3,3,3,2,2]
[3,4] => [1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => [2,2,2,1,1,1]
[4,1,1,1] => [4,1,1,1] => [[4,4,4,4],[3,3,3]] => [4,4,4,4]
[4,1,2] => [1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => [3,3,3,3,1]
[4,2,1] => [2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => [3,3,3,3,2]
[4,3] => [1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => [2,2,2,2,1,1]
[5,1,1] => [3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => [3,3,3,3,3]
[5,2] => [1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => [2,2,2,2,2,1]
[6,1] => [2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [2,2,2,2,2,2]
[7] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1] => [8] => [[8],[]] => [8]
[1,1,1,1,1,1,2] => [1,7] => [[7,1],[]] => [7,1]
[1,1,1,1,1,3] => [1,1,6] => [[6,1,1],[]] => [6,1,1]
[1,1,1,1,4] => [1,1,1,5] => [[5,1,1,1],[]] => [5,1,1,1]
[1,1,1,2,1,1,1] => [4,4] => [[7,4],[3]] => [7,4]
[1,1,1,5] => [1,1,1,1,4] => [[4,1,1,1,1],[]] => [4,1,1,1,1]
[1,1,2,1,1,2] => [1,4,3] => [[6,4,1],[3]] => [6,4,1]
[1,1,2,1,2,1] => [2,3,3] => [[6,4,2],[3,1]] => [6,4,2]
[1,1,2,1,3] => [1,1,3,3] => [[5,3,1,1],[2]] => [5,3,1,1]
[1,1,2,2,1,1] => [3,2,3] => [[6,4,3],[3,2]] => [6,4,3]
[1,1,2,2,2] => [1,2,2,3] => [[5,3,2,1],[2,1]] => [5,3,2,1]
[1,1,2,3,1] => [2,1,2,3] => [[5,3,2,2],[2,1,1]] => [5,3,2,2]
[1,1,3,1,1,1] => [4,1,3] => [[6,4,4],[3,3]] => [6,4,4]
[1,1,3,1,2] => [1,3,1,3] => [[5,3,3,1],[2,2]] => [5,3,3,1]
[1,1,3,2,1] => [2,2,1,3] => [[5,3,3,2],[2,2,1]] => [5,3,3,2]
[1,1,4,1,1] => [3,1,1,3] => [[5,3,3,3],[2,2,2]] => [5,3,3,3]
[1,1,6] => [1,1,1,1,1,3] => [[3,1,1,1,1,1],[]] => [3,1,1,1,1,1]
[1,2,1,1,2,1] => [2,4,2] => [[6,5,2],[4,1]] => [6,5,2]
[1,2,1,2,1,1] => [3,3,2] => [[6,5,3],[4,2]] => [6,5,3]
[1,2,1,2,2] => [1,2,3,2] => [[5,4,2,1],[3,1]] => [5,4,2,1]
[1,2,1,3,1] => [2,1,3,2] => [[5,4,2,2],[3,1,1]] => [5,4,2,2]
[1,2,1,4] => [1,1,1,3,2] => [[4,3,1,1,1],[2]] => [4,3,1,1,1]
[1,2,2,1,1,1] => [4,2,2] => [[6,5,4],[4,3]] => [6,5,4]
[1,2,2,1,2] => [1,3,2,2] => [[5,4,3,1],[3,2]] => [5,4,3,1]
[1,2,2,2,1] => [2,2,2,2] => [[5,4,3,2],[3,2,1]] => [5,4,3,2]
[1,2,2,3] => [1,1,2,2,2] => [[4,3,2,1,1],[2,1]] => [4,3,2,1,1]
[1,2,3,1,1] => [3,1,2,2] => [[5,4,3,3],[3,2,2]] => [5,4,3,3]
[1,2,3,2] => [1,2,1,2,2] => [[4,3,2,2,1],[2,1,1]] => [4,3,2,2,1]
[1,2,4,1] => [2,1,1,2,2] => [[4,3,2,2,2],[2,1,1,1]] => [4,3,2,2,2]
[1,2,5] => [1,1,1,1,2,2] => [[3,2,1,1,1,1],[1]] => [3,2,1,1,1,1]
[1,3,1,1,2] => [1,4,1,2] => [[5,4,4,1],[3,3]] => [5,4,4,1]
[1,3,1,2,1] => [2,3,1,2] => [[5,4,4,2],[3,3,1]] => [5,4,4,2]
[1,3,1,3] => [1,1,3,1,2] => [[4,3,3,1,1],[2,2]] => [4,3,3,1,1]
[1,3,2,1,1] => [3,2,1,2] => [[5,4,4,3],[3,3,2]] => [5,4,4,3]
[1,3,2,2] => [1,2,2,1,2] => [[4,3,3,2,1],[2,2,1]] => [4,3,3,2,1]
[1,3,3,1] => [2,1,2,1,2] => [[4,3,3,2,2],[2,2,1,1]] => [4,3,3,2,2]
[1,3,4] => [1,1,1,2,1,2] => [[3,2,2,1,1,1],[1,1]] => [3,2,2,1,1,1]
[1,4,1,1,1] => [4,1,1,2] => [[5,4,4,4],[3,3,3]] => [5,4,4,4]
[1,4,1,2] => [1,3,1,1,2] => [[4,3,3,3,1],[2,2,2]] => [4,3,3,3,1]
[1,4,2,1] => [2,2,1,1,2] => [[4,3,3,3,2],[2,2,2,1]] => [4,3,3,3,2]
[1,4,3] => [1,1,2,1,1,2] => [[3,2,2,2,1,1],[1,1,1]] => [3,2,2,2,1,1]
[1,5,2] => [1,2,1,1,1,2] => [[3,2,2,2,2,1],[1,1,1,1]] => [3,2,2,2,2,1]
[1,6,1] => [2,1,1,1,1,2] => [[3,2,2,2,2,2],[1,1,1,1,1]] => [3,2,2,2,2,2]
[1,7] => [1,1,1,1,1,1,2] => [[2,1,1,1,1,1,1],[]] => [2,1,1,1,1,1,1]
[2,1,1,1,1,1,1] => [7,1] => [[7,7],[6]] => [7,7]
[2,1,1,2,1,1] => [3,4,1] => [[6,6,3],[5,2]] => [6,6,3]
[2,1,2,1,1,1] => [4,3,1] => [[6,6,4],[5,3]] => [6,6,4]
[2,1,2,1,2] => [1,3,3,1] => [[5,5,3,1],[4,2]] => [5,5,3,1]
[2,1,2,2,1] => [2,2,3,1] => [[5,5,3,2],[4,2,1]] => [5,5,3,2]
[2,1,2,3] => [1,1,2,3,1] => [[4,4,2,1,1],[3,1]] => [4,4,2,1,1]
[2,1,3,1,1] => [3,1,3,1] => [[5,5,3,3],[4,2,2]] => [5,5,3,3]
[2,1,3,2] => [1,2,1,3,1] => [[4,4,2,2,1],[3,1,1]] => [4,4,2,2,1]
[2,1,4,1] => [2,1,1,3,1] => [[4,4,2,2,2],[3,1,1,1]] => [4,4,2,2,2]
[2,2,1,1,2] => [1,4,2,1] => [[5,5,4,1],[4,3]] => [5,5,4,1]
[2,2,1,2,1] => [2,3,2,1] => [[5,5,4,2],[4,3,1]] => [5,5,4,2]
[2,2,1,3] => [1,1,3,2,1] => [[4,4,3,1,1],[3,2]] => [4,4,3,1,1]
[2,2,2,1,1] => [3,2,2,1] => [[5,5,4,3],[4,3,2]] => [5,5,4,3]
[2,2,2,2] => [1,2,2,2,1] => [[4,4,3,2,1],[3,2,1]] => [4,4,3,2,1]
[2,2,3,1] => [2,1,2,2,1] => [[4,4,3,2,2],[3,2,1,1]] => [4,4,3,2,2]
[2,2,4] => [1,1,1,2,2,1] => [[3,3,2,1,1,1],[2,1]] => [3,3,2,1,1,1]
[2,3,1,1,1] => [4,1,2,1] => [[5,5,4,4],[4,3,3]] => [5,5,4,4]
[2,3,1,2] => [1,3,1,2,1] => [[4,4,3,3,1],[3,2,2]] => [4,4,3,3,1]
[2,3,2,1] => [2,2,1,2,1] => [[4,4,3,3,2],[3,2,2,1]] => [4,4,3,3,2]
[2,3,3] => [1,1,2,1,2,1] => [[3,3,2,2,1,1],[2,1,1]] => [3,3,2,2,1,1]
[2,4,1,1] => [3,1,1,2,1] => [[4,4,3,3,3],[3,2,2,2]] => [4,4,3,3,3]
[2,4,2] => [1,2,1,1,2,1] => [[3,3,2,2,2,1],[2,1,1,1]] => [3,3,2,2,2,1]
[2,5,1] => [2,1,1,1,2,1] => [[3,3,2,2,2,2],[2,1,1,1,1]] => [3,3,2,2,2,2]
[2,6] => [1,1,1,1,1,2,1] => [[2,2,1,1,1,1,1],[1]] => [2,2,1,1,1,1,1]
[3,1,1,1,1,1] => [6,1,1] => [[6,6,6],[5,5]] => [6,6,6]
[3,1,1,2,1] => [2,4,1,1] => [[5,5,5,2],[4,4,1]] => [5,5,5,2]
[3,1,2,1,1] => [3,3,1,1] => [[5,5,5,3],[4,4,2]] => [5,5,5,3]
[3,1,2,2] => [1,2,3,1,1] => [[4,4,4,2,1],[3,3,1]] => [4,4,4,2,1]
[3,1,3,1] => [2,1,3,1,1] => [[4,4,4,2,2],[3,3,1,1]] => [4,4,4,2,2]
[3,2,1,1,1] => [4,2,1,1] => [[5,5,5,4],[4,4,3]] => [5,5,5,4]
[3,2,1,2] => [1,3,2,1,1] => [[4,4,4,3,1],[3,3,2]] => [4,4,4,3,1]
[3,2,2,1] => [2,2,2,1,1] => [[4,4,4,3,2],[3,3,2,1]] => [4,4,4,3,2]
[3,2,3] => [1,1,2,2,1,1] => [[3,3,3,2,1,1],[2,2,1]] => [3,3,3,2,1,1]
[3,3,1,1] => [3,1,2,1,1] => [[4,4,4,3,3],[3,3,2,2]] => [4,4,4,3,3]
[3,3,2] => [1,2,1,2,1,1] => [[3,3,3,2,2,1],[2,2,1,1]] => [3,3,3,2,2,1]
[3,4,1] => [2,1,1,2,1,1] => [[3,3,3,2,2,2],[2,2,1,1,1]] => [3,3,3,2,2,2]
[3,5] => [1,1,1,1,2,1,1] => [[2,2,2,1,1,1,1],[1,1]] => [2,2,2,1,1,1,1]
[4,1,1,1,1] => [5,1,1,1] => [[5,5,5,5],[4,4,4]] => [5,5,5,5]
[4,1,1,2] => [1,4,1,1,1] => [[4,4,4,4,1],[3,3,3]] => [4,4,4,4,1]
[4,1,2,1] => [2,3,1,1,1] => [[4,4,4,4,2],[3,3,3,1]] => [4,4,4,4,2]
[4,2,1,1] => [3,2,1,1,1] => [[4,4,4,4,3],[3,3,3,2]] => [4,4,4,4,3]
[4,2,2] => [1,2,2,1,1,1] => [[3,3,3,3,2,1],[2,2,2,1]] => [3,3,3,3,2,1]
[4,3,1] => [2,1,2,1,1,1] => [[3,3,3,3,2,2],[2,2,2,1,1]] => [3,3,3,3,2,2]
[4,4] => [1,1,1,2,1,1,1] => [[2,2,2,2,1,1,1],[1,1,1]] => [2,2,2,2,1,1,1]
[5,1,1,1] => [4,1,1,1,1] => [[4,4,4,4,4],[3,3,3,3]] => [4,4,4,4,4]
[5,2,1] => [2,2,1,1,1,1] => [[3,3,3,3,3,2],[2,2,2,2,1]] => [3,3,3,3,3,2]
[5,3] => [1,1,2,1,1,1,1] => [[2,2,2,2,2,1,1],[1,1,1,1]] => [2,2,2,2,2,1,1]
[6,1,1] => [3,1,1,1,1,1] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [3,3,3,3,3,3]
[6,2] => [1,2,1,1,1,1,1] => [[2,2,2,2,2,2,1],[1,1,1,1,1]] => [2,2,2,2,2,2,1]
[7,1] => [2,1,1,1,1,1,1] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [2,2,2,2,2,2,2]
[8] => [1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1] => [9] => [[9],[]] => [9]
[1,1,1,1,1,1,1,2] => [1,8] => [[8,1],[]] => [8,1]
[1,1,1,1,1,1,3] => [1,1,7] => [[7,1,1],[]] => [7,1,1]
[1,1,1,1,1,4] => [1,1,1,6] => [[6,1,1,1],[]] => [6,1,1,1]
[1,1,1,1,5] => [1,1,1,1,5] => [[5,1,1,1,1],[]] => [5,1,1,1,1]
[1,1,1,6] => [1,1,1,1,1,4] => [[4,1,1,1,1,1],[]] => [4,1,1,1,1,1]
[1,1,7] => [1,1,1,1,1,1,3] => [[3,1,1,1,1,1,1],[]] => [3,1,1,1,1,1,1]
[1,8] => [1,1,1,1,1,1,1,2] => [[2,1,1,1,1,1,1,1],[]] => [2,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1] => [8,1] => [[8,8],[7]] => [8,8]
[3,1,1,1,1,1,1] => [7,1,1] => [[7,7,7],[6,6]] => [7,7,7]
[4,1,1,1,1,1] => [6,1,1,1] => [[6,6,6,6],[5,5,5]] => [6,6,6,6]
[5,1,1,1,1] => [5,1,1,1,1] => [[5,5,5,5,5],[4,4,4,4]] => [5,5,5,5,5]
[6,1,1,1] => [4,1,1,1,1,1] => [[4,4,4,4,4,4],[3,3,3,3,3]] => [4,4,4,4,4,4]
[7,1,1] => [3,1,1,1,1,1,1] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [3,3,3,3,3,3,3]
[8,1] => [2,1,1,1,1,1,1,1] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [2,2,2,2,2,2,2,2]
[9] => [1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1] => [10] => [[10],[]] => [10]
[1,1,1,1,1,1,1,1,2] => [1,9] => [[9,1],[]] => [9,1]
[1,1,1,1,1,1,1,3] => [1,1,8] => [[8,1,1],[]] => [8,1,1]
[1,1,1,1,1,1,4] => [1,1,1,7] => [[7,1,1,1],[]] => [7,1,1,1]
[1,1,1,1,1,5] => [1,1,1,1,6] => [[6,1,1,1,1],[]] => [6,1,1,1,1]
[1,1,1,1,6] => [1,1,1,1,1,5] => [[5,1,1,1,1,1],[]] => [5,1,1,1,1,1]
[1,1,1,7] => [1,1,1,1,1,1,4] => [[4,1,1,1,1,1,1],[]] => [4,1,1,1,1,1,1]
[1,1,8] => [1,1,1,1,1,1,1,3] => [[3,1,1,1,1,1,1,1],[]] => [3,1,1,1,1,1,1,1]
[1,9] => [1,1,1,1,1,1,1,1,2] => [[2,1,1,1,1,1,1,1,1],[]] => [2,1,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1] => [9,1] => [[9,9],[8]] => [9,9]
[3,1,1,1,1,1,1,1] => [8,1,1] => [[8,8,8],[7,7]] => [8,8,8]
[4,1,1,1,1,1,1] => [7,1,1,1] => [[7,7,7,7],[6,6,6]] => [7,7,7,7]
[5,1,1,1,1,1] => [6,1,1,1,1] => [[6,6,6,6,6],[5,5,5,5]] => [6,6,6,6,6]
[6,1,1,1,1] => [5,1,1,1,1,1] => [[5,5,5,5,5,5],[4,4,4,4,4]] => [5,5,5,5,5,5]
[7,1,1,1] => [4,1,1,1,1,1,1] => [[4,4,4,4,4,4,4],[3,3,3,3,3,3]] => [4,4,4,4,4,4,4]
[8,1,1] => [3,1,1,1,1,1,1,1] => [[3,3,3,3,3,3,3,3],[2,2,2,2,2,2,2]] => [3,3,3,3,3,3,3,3]
[9,1] => [2,1,1,1,1,1,1,1,1] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]] => [2,2,2,2,2,2,2,2,2]
[10] => [1,1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1,1,1]
Map
conjugate
Description
The conjugate of a composition.
The conjugate of a composition $C$ is defined as the complement (Mp00039complement) of the reversal (Mp00038reverse) of $C$.
Equivalently, the ribbon shape corresponding to the conjugate of $C$ is the conjugate of the ribbon shape of $C$.
Map
to ribbon
Description
The ribbon shape corresponding to an integer composition.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.
Map
outer shape
Description
The outer shape of the skew partition.