Identifier
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00189: Skew partitions —rotate⟶ Skew partitions
Images
[1] => [1] => [[1],[]] => [[1],[]]
[2] => [1,1] => [[1,1],[]] => [[1,1],[]]
[1,1] => [2] => [[2],[]] => [[2],[]]
[3] => [1,1,1] => [[1,1,1],[]] => [[1,1,1],[]]
[2,1] => [2,1] => [[2,1],[]] => [[2,2],[1]]
[1,1,1] => [3] => [[3],[]] => [[3],[]]
[4] => [1,1,1,1] => [[1,1,1,1],[]] => [[1,1,1,1],[]]
[3,1] => [2,1,1] => [[2,1,1],[]] => [[2,2,2],[1,1]]
[2,2] => [2,2] => [[2,2],[]] => [[2,2],[]]
[2,1,1] => [3,1] => [[3,1],[]] => [[3,3],[2]]
[1,1,1,1] => [4] => [[4],[]] => [[4],[]]
[5] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => [[1,1,1,1,1],[]]
[4,1] => [2,1,1,1] => [[2,1,1,1],[]] => [[2,2,2,2],[1,1,1]]
[3,2] => [2,2,1] => [[2,2,1],[]] => [[2,2,2],[1]]
[3,1,1] => [3,1,1] => [[3,1,1],[]] => [[3,3,3],[2,2]]
[2,2,1] => [3,2] => [[3,2],[]] => [[3,3],[1]]
[2,1,1,1] => [4,1] => [[4,1],[]] => [[4,4],[3]]
[1,1,1,1,1] => [5] => [[5],[]] => [[5],[]]
[6] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => [[1,1,1,1,1,1],[]]
[5,1] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => [[2,2,2,2,2],[1,1,1,1]]
[4,2] => [2,2,1,1] => [[2,2,1,1],[]] => [[2,2,2,2],[1,1]]
[4,1,1] => [3,1,1,1] => [[3,1,1,1],[]] => [[3,3,3,3],[2,2,2]]
[3,3] => [2,2,2] => [[2,2,2],[]] => [[2,2,2],[]]
[3,2,1] => [3,2,1] => [[3,2,1],[]] => [[3,3,3],[2,1]]
[3,1,1,1] => [4,1,1] => [[4,1,1],[]] => [[4,4,4],[3,3]]
[2,2,2] => [3,3] => [[3,3],[]] => [[3,3],[]]
[2,2,1,1] => [4,2] => [[4,2],[]] => [[4,4],[2]]
[2,1,1,1,1] => [5,1] => [[5,1],[]] => [[5,5],[4]]
[1,1,1,1,1,1] => [6] => [[6],[]] => [[6],[]]
[7] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1],[]]
[6,1] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1,1,1]]
[5,2] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => [[2,2,2,2,2],[1,1,1]]
[5,1,1] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => [[3,3,3,3,3],[2,2,2,2]]
[4,3] => [2,2,2,1] => [[2,2,2,1],[]] => [[2,2,2,2],[1]]
[4,2,1] => [3,2,1,1] => [[3,2,1,1],[]] => [[3,3,3,3],[2,2,1]]
[4,1,1,1] => [4,1,1,1] => [[4,1,1,1],[]] => [[4,4,4,4],[3,3,3]]
[3,3,1] => [3,2,2] => [[3,2,2],[]] => [[3,3,3],[1,1]]
[3,2,2] => [3,3,1] => [[3,3,1],[]] => [[3,3,3],[2]]
[3,2,1,1] => [4,2,1] => [[4,2,1],[]] => [[4,4,4],[3,2]]
[3,1,1,1,1] => [5,1,1] => [[5,1,1],[]] => [[5,5,5],[4,4]]
[2,2,2,1] => [4,3] => [[4,3],[]] => [[4,4],[1]]
[2,2,1,1,1] => [5,2] => [[5,2],[]] => [[5,5],[3]]
[2,1,1,1,1,1] => [6,1] => [[6,1],[]] => [[6,6],[5]]
[1,1,1,1,1,1,1] => [7] => [[7],[]] => [[7],[]]
[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],[]]
[7,1] => [2,1,1,1,1,1,1] => [[2,1,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]]
[6,2] => [2,2,1,1,1,1] => [[2,2,1,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1,1]]
[6,1,1] => [3,1,1,1,1,1] => [[3,1,1,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,2,2]]
[5,3] => [2,2,2,1,1] => [[2,2,2,1,1],[]] => [[2,2,2,2,2],[1,1]]
[5,2,1] => [3,2,1,1,1] => [[3,2,1,1,1],[]] => [[3,3,3,3,3],[2,2,2,1]]
[5,1,1,1] => [4,1,1,1,1] => [[4,1,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,3]]
[4,4] => [2,2,2,2] => [[2,2,2,2],[]] => [[2,2,2,2],[]]
[4,3,1] => [3,2,2,1] => [[3,2,2,1],[]] => [[3,3,3,3],[2,1,1]]
[4,2,2] => [3,3,1,1] => [[3,3,1,1],[]] => [[3,3,3,3],[2,2]]
[4,2,1,1] => [4,2,1,1] => [[4,2,1,1],[]] => [[4,4,4,4],[3,3,2]]
[4,1,1,1,1] => [5,1,1,1] => [[5,1,1,1],[]] => [[5,5,5,5],[4,4,4]]
[3,3,2] => [3,3,2] => [[3,3,2],[]] => [[3,3,3],[1]]
[3,3,1,1] => [4,2,2] => [[4,2,2],[]] => [[4,4,4],[2,2]]
[3,2,2,1] => [4,3,1] => [[4,3,1],[]] => [[4,4,4],[3,1]]
[3,2,1,1,1] => [5,2,1] => [[5,2,1],[]] => [[5,5,5],[4,3]]
[3,1,1,1,1,1] => [6,1,1] => [[6,1,1],[]] => [[6,6,6],[5,5]]
[2,2,2,2] => [4,4] => [[4,4],[]] => [[4,4],[]]
[2,2,2,1,1] => [5,3] => [[5,3],[]] => [[5,5],[2]]
[2,2,1,1,1,1] => [6,2] => [[6,2],[]] => [[6,6],[4]]
[2,1,1,1,1,1,1] => [7,1] => [[7,1],[]] => [[7,7],[6]]
[1,1,1,1,1,1,1,1] => [8] => [[8],[]] => [[8],[]]
[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],[]]
[8,1] => [2,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]]
[7,2] => [2,2,1,1,1,1,1] => [[2,2,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2],[1,1,1,1,1]]
[7,1,1] => [3,1,1,1,1,1,1] => [[3,1,1,1,1,1,1],[]] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]]
[6,3] => [2,2,2,1,1,1] => [[2,2,2,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1]]
[6,2,1] => [3,2,1,1,1,1] => [[3,2,1,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,2,1]]
[6,1,1,1] => [4,1,1,1,1,1] => [[4,1,1,1,1,1],[]] => [[4,4,4,4,4,4],[3,3,3,3,3]]
[5,4] => [2,2,2,2,1] => [[2,2,2,2,1],[]] => [[2,2,2,2,2],[1]]
[5,3,1] => [3,2,2,1,1] => [[3,2,2,1,1],[]] => [[3,3,3,3,3],[2,2,1,1]]
[5,2,2] => [3,3,1,1,1] => [[3,3,1,1,1],[]] => [[3,3,3,3,3],[2,2,2]]
[5,2,1,1] => [4,2,1,1,1] => [[4,2,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,2]]
[5,1,1,1,1] => [5,1,1,1,1] => [[5,1,1,1,1],[]] => [[5,5,5,5,5],[4,4,4,4]]
[4,4,1] => [3,2,2,2] => [[3,2,2,2],[]] => [[3,3,3,3],[1,1,1]]
[4,3,2] => [3,3,2,1] => [[3,3,2,1],[]] => [[3,3,3,3],[2,1]]
[4,3,1,1] => [4,2,2,1] => [[4,2,2,1],[]] => [[4,4,4,4],[3,2,2]]
[4,2,2,1] => [4,3,1,1] => [[4,3,1,1],[]] => [[4,4,4,4],[3,3,1]]
[4,2,1,1,1] => [5,2,1,1] => [[5,2,1,1],[]] => [[5,5,5,5],[4,4,3]]
[4,1,1,1,1,1] => [6,1,1,1] => [[6,1,1,1],[]] => [[6,6,6,6],[5,5,5]]
[3,3,3] => [3,3,3] => [[3,3,3],[]] => [[3,3,3],[]]
[3,3,2,1] => [4,3,2] => [[4,3,2],[]] => [[4,4,4],[2,1]]
[3,3,1,1,1] => [5,2,2] => [[5,2,2],[]] => [[5,5,5],[3,3]]
[3,2,2,2] => [4,4,1] => [[4,4,1],[]] => [[4,4,4],[3]]
[3,2,2,1,1] => [5,3,1] => [[5,3,1],[]] => [[5,5,5],[4,2]]
[3,2,1,1,1,1] => [6,2,1] => [[6,2,1],[]] => [[6,6,6],[5,4]]
[3,1,1,1,1,1,1] => [7,1,1] => [[7,1,1],[]] => [[7,7,7],[6,6]]
[2,2,2,2,1] => [5,4] => [[5,4],[]] => [[5,5],[1]]
[2,2,2,1,1,1] => [6,3] => [[6,3],[]] => [[6,6],[3]]
[2,2,1,1,1,1,1] => [7,2] => [[7,2],[]] => [[7,7],[5]]
[2,1,1,1,1,1,1,1] => [8,1] => [[8,1],[]] => [[8,8],[7]]
[1,1,1,1,1,1,1,1,1] => [9] => [[9],[]] => [[9],[]]
[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],[]]
[9,1] => [2,1,1,1,1,1,1,1,1] => [[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]]
[8,2] => [2,2,1,1,1,1,1,1] => [[2,2,1,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1]]
[8,1,1] => [3,1,1,1,1,1,1,1] => [[3,1,1,1,1,1,1,1],[]] => [[3,3,3,3,3,3,3,3],[2,2,2,2,2,2,2]]
[7,3] => [2,2,2,1,1,1,1] => [[2,2,2,1,1,1,1],[]] => [[2,2,2,2,2,2,2],[1,1,1,1]]
>>> Load all 407 entries. <<<
[7,2,1] => [3,2,1,1,1,1,1] => [[3,2,1,1,1,1,1],[]] => [[3,3,3,3,3,3,3],[2,2,2,2,2,1]]
[7,1,1,1] => [4,1,1,1,1,1,1] => [[4,1,1,1,1,1,1],[]] => [[4,4,4,4,4,4,4],[3,3,3,3,3,3]]
[6,4] => [2,2,2,2,1,1] => [[2,2,2,2,1,1],[]] => [[2,2,2,2,2,2],[1,1]]
[6,3,1] => [3,2,2,1,1,1] => [[3,2,2,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,1,1]]
[6,2,2] => [3,3,1,1,1,1] => [[3,3,1,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,2]]
[6,2,1,1] => [4,2,1,1,1,1] => [[4,2,1,1,1,1],[]] => [[4,4,4,4,4,4],[3,3,3,3,2]]
[6,1,1,1,1] => [5,1,1,1,1,1] => [[5,1,1,1,1,1],[]] => [[5,5,5,5,5,5],[4,4,4,4,4]]
[5,5] => [2,2,2,2,2] => [[2,2,2,2,2],[]] => [[2,2,2,2,2],[]]
[5,4,1] => [3,2,2,2,1] => [[3,2,2,2,1],[]] => [[3,3,3,3,3],[2,1,1,1]]
[5,3,2] => [3,3,2,1,1] => [[3,3,2,1,1],[]] => [[3,3,3,3,3],[2,2,1]]
[5,3,1,1] => [4,2,2,1,1] => [[4,2,2,1,1],[]] => [[4,4,4,4,4],[3,3,2,2]]
[5,2,2,1] => [4,3,1,1,1] => [[4,3,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,1]]
[5,2,1,1,1] => [5,2,1,1,1] => [[5,2,1,1,1],[]] => [[5,5,5,5,5],[4,4,4,3]]
[5,1,1,1,1,1] => [6,1,1,1,1] => [[6,1,1,1,1],[]] => [[6,6,6,6,6],[5,5,5,5]]
[4,4,2] => [3,3,2,2] => [[3,3,2,2],[]] => [[3,3,3,3],[1,1]]
[4,4,1,1] => [4,2,2,2] => [[4,2,2,2],[]] => [[4,4,4,4],[2,2,2]]
[4,3,3] => [3,3,3,1] => [[3,3,3,1],[]] => [[3,3,3,3],[2]]
[4,3,2,1] => [4,3,2,1] => [[4,3,2,1],[]] => [[4,4,4,4],[3,2,1]]
[4,3,1,1,1] => [5,2,2,1] => [[5,2,2,1],[]] => [[5,5,5,5],[4,3,3]]
[4,2,2,2] => [4,4,1,1] => [[4,4,1,1],[]] => [[4,4,4,4],[3,3]]
[4,2,2,1,1] => [5,3,1,1] => [[5,3,1,1],[]] => [[5,5,5,5],[4,4,2]]
[4,2,1,1,1,1] => [6,2,1,1] => [[6,2,1,1],[]] => [[6,6,6,6],[5,5,4]]
[4,1,1,1,1,1,1] => [7,1,1,1] => [[7,1,1,1],[]] => [[7,7,7,7],[6,6,6]]
[3,3,3,1] => [4,3,3] => [[4,3,3],[]] => [[4,4,4],[1,1]]
[3,3,2,2] => [4,4,2] => [[4,4,2],[]] => [[4,4,4],[2]]
[3,3,2,1,1] => [5,3,2] => [[5,3,2],[]] => [[5,5,5],[3,2]]
[3,3,1,1,1,1] => [6,2,2] => [[6,2,2],[]] => [[6,6,6],[4,4]]
[3,2,2,2,1] => [5,4,1] => [[5,4,1],[]] => [[5,5,5],[4,1]]
[3,2,2,1,1,1] => [6,3,1] => [[6,3,1],[]] => [[6,6,6],[5,3]]
[3,2,1,1,1,1,1] => [7,2,1] => [[7,2,1],[]] => [[7,7,7],[6,5]]
[3,1,1,1,1,1,1,1] => [8,1,1] => [[8,1,1],[]] => [[8,8,8],[7,7]]
[2,2,2,2,2] => [5,5] => [[5,5],[]] => [[5,5],[]]
[2,2,2,2,1,1] => [6,4] => [[6,4],[]] => [[6,6],[2]]
[2,2,2,1,1,1,1] => [7,3] => [[7,3],[]] => [[7,7],[4]]
[2,2,1,1,1,1,1,1] => [8,2] => [[8,2],[]] => [[8,8],[6]]
[2,1,1,1,1,1,1,1,1] => [9,1] => [[9,1],[]] => [[9,9],[8]]
[1,1,1,1,1,1,1,1,1,1] => [10] => [[10],[]] => [[10],[]]
[11] => [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],[]]
[10,1] => [2,1,1,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1,1]]
[8,3] => [2,2,2,1,1,1,1,1] => [[2,2,2,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1]]
[7,2,2] => [3,3,1,1,1,1,1] => [[3,3,1,1,1,1,1],[]] => [[3,3,3,3,3,3,3],[2,2,2,2,2]]
[6,5] => [2,2,2,2,2,1] => [[2,2,2,2,2,1],[]] => [[2,2,2,2,2,2],[1]]
[6,2,1,1,1] => [5,2,1,1,1,1] => [[5,2,1,1,1,1],[]] => [[5,5,5,5,5,5],[4,4,4,4,3]]
[5,5,1] => [3,2,2,2,2] => [[3,2,2,2,2],[]] => [[3,3,3,3,3],[1,1,1,1]]
[5,4,2] => [3,3,2,2,1] => [[3,3,2,2,1],[]] => [[3,3,3,3,3],[2,1,1]]
[5,4,1,1] => [4,2,2,2,1] => [[4,2,2,2,1],[]] => [[4,4,4,4,4],[3,2,2,2]]
[5,3,3] => [3,3,3,1,1] => [[3,3,3,1,1],[]] => [[3,3,3,3,3],[2,2]]
[5,3,2,1] => [4,3,2,1,1] => [[4,3,2,1,1],[]] => [[4,4,4,4,4],[3,3,2,1]]
[5,3,1,1,1] => [5,2,2,1,1] => [[5,2,2,1,1],[]] => [[5,5,5,5,5],[4,4,3,3]]
[5,2,2,2] => [4,4,1,1,1] => [[4,4,1,1,1],[]] => [[4,4,4,4,4],[3,3,3]]
[5,2,2,1,1] => [5,3,1,1,1] => [[5,3,1,1,1],[]] => [[5,5,5,5,5],[4,4,4,2]]
[5,2,1,1,1,1] => [6,2,1,1,1] => [[6,2,1,1,1],[]] => [[6,6,6,6,6],[5,5,5,4]]
[4,4,3] => [3,3,3,2] => [[3,3,3,2],[]] => [[3,3,3,3],[1]]
[4,4,2,1] => [4,3,2,2] => [[4,3,2,2],[]] => [[4,4,4,4],[2,2,1]]
[4,4,1,1,1] => [5,2,2,2] => [[5,2,2,2],[]] => [[5,5,5,5],[3,3,3]]
[4,3,3,1] => [4,3,3,1] => [[4,3,3,1],[]] => [[4,4,4,4],[3,1,1]]
[4,3,2,2] => [4,4,2,1] => [[4,4,2,1],[]] => [[4,4,4,4],[3,2]]
[4,3,2,1,1] => [5,3,2,1] => [[5,3,2,1],[]] => [[5,5,5,5],[4,3,2]]
[4,2,2,2,1] => [5,4,1,1] => [[5,4,1,1],[]] => [[5,5,5,5],[4,4,1]]
[3,3,3,2] => [4,4,3] => [[4,4,3],[]] => [[4,4,4],[1]]
[3,3,3,1,1] => [5,3,3] => [[5,3,3],[]] => [[5,5,5],[2,2]]
[3,3,2,2,1] => [5,4,2] => [[5,4,2],[]] => [[5,5,5],[3,1]]
[3,3,1,1,1,1,1] => [7,2,2] => [[7,2,2],[]] => [[7,7,7],[5,5]]
[3,2,2,2,2] => [5,5,1] => [[5,5,1],[]] => [[5,5,5],[4]]
[2,2,2,2,2,1] => [6,5] => [[6,5],[]] => [[6,6],[1]]
[2,2,2,1,1,1,1,1] => [8,3] => [[8,3],[]] => [[8,8],[5]]
[2,1,1,1,1,1,1,1,1,1] => [10,1] => [[10,1],[]] => [[10,10],[9]]
[1,1,1,1,1,1,1,1,1,1,1] => [11] => [[11],[]] => [[11],[]]
[12] => [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],[]]
[10,2] => [2,2,1,1,1,1,1,1,1,1] => [[2,2,1,1,1,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]]
[6,6] => [2,2,2,2,2,2] => [[2,2,2,2,2,2],[]] => [[2,2,2,2,2,2],[]]
[6,5,1] => [3,2,2,2,2,1] => [[3,2,2,2,2,1],[]] => [[3,3,3,3,3,3],[2,1,1,1,1]]
[6,4,2] => [3,3,2,2,1,1] => [[3,3,2,2,1,1],[]] => [[3,3,3,3,3,3],[2,2,1,1]]
[6,3,1,1,1] => [5,2,2,1,1,1] => [[5,2,2,1,1,1],[]] => [[5,5,5,5,5,5],[4,4,4,3,3]]
[5,5,2] => [3,3,2,2,2] => [[3,3,2,2,2],[]] => [[3,3,3,3,3],[1,1,1]]
[5,4,3] => [3,3,3,2,1] => [[3,3,3,2,1],[]] => [[3,3,3,3,3],[2,1]]
[5,4,2,1] => [4,3,2,2,1] => [[4,3,2,2,1],[]] => [[4,4,4,4,4],[3,2,2,1]]
[5,4,1,1,1] => [5,2,2,2,1] => [[5,2,2,2,1],[]] => [[5,5,5,5,5],[4,3,3,3]]
[5,3,3,1] => [4,3,3,1,1] => [[4,3,3,1,1],[]] => [[4,4,4,4,4],[3,3,1,1]]
[5,3,2,2] => [4,4,2,1,1] => [[4,4,2,1,1],[]] => [[4,4,4,4,4],[3,3,2]]
[5,3,2,1,1] => [5,3,2,1,1] => [[5,3,2,1,1],[]] => [[5,5,5,5,5],[4,4,3,2]]
[5,2,2,2,1] => [5,4,1,1,1] => [[5,4,1,1,1],[]] => [[5,5,5,5,5],[4,4,4,1]]
[5,2,2,1,1,1] => [6,3,1,1,1] => [[6,3,1,1,1],[]] => [[6,6,6,6,6],[5,5,5,3]]
[4,4,4] => [3,3,3,3] => [[3,3,3,3],[]] => [[3,3,3,3],[]]
[4,4,3,1] => [4,3,3,2] => [[4,3,3,2],[]] => [[4,4,4,4],[2,1,1]]
[4,4,2,2] => [4,4,2,2] => [[4,4,2,2],[]] => [[4,4,4,4],[2,2]]
[4,4,2,1,1] => [5,3,2,2] => [[5,3,2,2],[]] => [[5,5,5,5],[3,3,2]]
[4,3,3,2] => [4,4,3,1] => [[4,4,3,1],[]] => [[4,4,4,4],[3,1]]
[4,3,3,1,1] => [5,3,3,1] => [[5,3,3,1],[]] => [[5,5,5,5],[4,2,2]]
[4,3,2,2,1] => [5,4,2,1] => [[5,4,2,1],[]] => [[5,5,5,5],[4,3,1]]
[3,3,3,3] => [4,4,4] => [[4,4,4],[]] => [[4,4,4],[]]
[3,3,3,2,1] => [5,4,3] => [[5,4,3],[]] => [[5,5,5],[2,1]]
[3,3,2,2,2] => [5,5,2] => [[5,5,2],[]] => [[5,5,5],[3]]
[3,3,2,2,1,1] => [6,4,2] => [[6,4,2],[]] => [[6,6,6],[4,2]]
[3,2,2,2,2,1] => [6,5,1] => [[6,5,1],[]] => [[6,6,6],[5,1]]
[2,2,2,2,2,2] => [6,6] => [[6,6],[]] => [[6,6],[]]
[2,2,1,1,1,1,1,1,1,1] => [10,2] => [[10,2],[]] => [[10,10],[8]]
[1,1,1,1,1,1,1,1,1,1,1,1] => [12] => [[12],[]] => [[12],[]]
[13] => [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],[]] => [[1,1,1,1,1,1,1,1,1,1,1,1,1],[]]
[8,3,2] => [3,3,2,1,1,1,1,1] => [[3,3,2,1,1,1,1,1],[]] => [[3,3,3,3,3,3,3,3],[2,2,2,2,2,1]]
[7,6] => [2,2,2,2,2,2,1] => [[2,2,2,2,2,2,1],[]] => [[2,2,2,2,2,2,2],[1]]
[6,6,1] => [3,2,2,2,2,2] => [[3,2,2,2,2,2],[]] => [[3,3,3,3,3,3],[1,1,1,1,1]]
[6,5,2] => [3,3,2,2,2,1] => [[3,3,2,2,2,1],[]] => [[3,3,3,3,3,3],[2,1,1,1]]
[6,3,2,1,1] => [5,3,2,1,1,1] => [[5,3,2,1,1,1],[]] => [[5,5,5,5,5,5],[4,4,4,3,2]]
[6,2,2,2,1] => [5,4,1,1,1,1] => [[5,4,1,1,1,1],[]] => [[5,5,5,5,5,5],[4,4,4,4,1]]
[5,5,3] => [3,3,3,2,2] => [[3,3,3,2,2],[]] => [[3,3,3,3,3],[1,1]]
[5,4,4] => [3,3,3,3,1] => [[3,3,3,3,1],[]] => [[3,3,3,3,3],[2]]
[5,4,3,1] => [4,3,3,2,1] => [[4,3,3,2,1],[]] => [[4,4,4,4,4],[3,2,1,1]]
[5,4,2,2] => [4,4,2,2,1] => [[4,4,2,2,1],[]] => [[4,4,4,4,4],[3,2,2]]
[5,4,2,1,1] => [5,3,2,2,1] => [[5,3,2,2,1],[]] => [[5,5,5,5,5],[4,3,3,2]]
[5,4,1,1,1,1] => [6,2,2,2,1] => [[6,2,2,2,1],[]] => [[6,6,6,6,6],[5,4,4,4]]
[5,3,3,2] => [4,4,3,1,1] => [[4,4,3,1,1],[]] => [[4,4,4,4,4],[3,3,1]]
[5,3,3,1,1] => [5,3,3,1,1] => [[5,3,3,1,1],[]] => [[5,5,5,5,5],[4,4,2,2]]
[5,3,2,2,1] => [5,4,2,1,1] => [[5,4,2,1,1],[]] => [[5,5,5,5,5],[4,4,3,1]]
[5,3,2,1,1,1] => [6,3,2,1,1] => [[6,3,2,1,1],[]] => [[6,6,6,6,6],[5,5,4,3]]
[4,4,4,1] => [4,3,3,3] => [[4,3,3,3],[]] => [[4,4,4,4],[1,1,1]]
[4,4,3,2] => [4,4,3,2] => [[4,4,3,2],[]] => [[4,4,4,4],[2,1]]
[4,4,3,1,1] => [5,3,3,2] => [[5,3,3,2],[]] => [[5,5,5,5],[3,2,2]]
[4,4,2,2,1] => [5,4,2,2] => [[5,4,2,2],[]] => [[5,5,5,5],[3,3,1]]
[4,3,3,3] => [4,4,4,1] => [[4,4,4,1],[]] => [[4,4,4,4],[3]]
[4,3,3,2,1] => [5,4,3,1] => [[5,4,3,1],[]] => [[5,5,5,5],[4,2,1]]
[3,3,3,3,1] => [5,4,4] => [[5,4,4],[]] => [[5,5,5],[1,1]]
[3,3,3,2,2] => [5,5,3] => [[5,5,3],[]] => [[5,5,5],[2]]
[3,3,2,2,2,1] => [6,5,2] => [[6,5,2],[]] => [[6,6,6],[4,1]]
[3,3,2,1,1,1,1,1] => [8,3,2] => [[8,3,2],[]] => [[8,8,8],[6,5]]
[3,2,2,2,2,2] => [6,6,1] => [[6,6,1],[]] => [[6,6,6],[5]]
[2,2,2,2,2,2,1] => [7,6] => [[7,6],[]] => [[7,7],[1]]
[1,1,1,1,1,1,1,1,1,1,1,1,1] => [13] => [[13],[]] => [[13],[]]
[14] => [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],[]] => [[1,1,1,1,1,1,1,1,1,1,1,1,1,1],[]]
[7,7] => [2,2,2,2,2,2,2] => [[2,2,2,2,2,2,2],[]] => [[2,2,2,2,2,2,2],[]]
[6,6,2] => [3,3,2,2,2,2] => [[3,3,2,2,2,2],[]] => [[3,3,3,3,3,3],[1,1,1,1]]
[6,5,3] => [3,3,3,2,2,1] => [[3,3,3,2,2,1],[]] => [[3,3,3,3,3,3],[2,1,1]]
[6,5,2,1] => [4,3,2,2,2,1] => [[4,3,2,2,2,1],[]] => [[4,4,4,4,4,4],[3,2,2,2,1]]
[6,5,1,1,1] => [5,2,2,2,2,1] => [[5,2,2,2,2,1],[]] => [[5,5,5,5,5,5],[4,3,3,3,3]]
[6,3,2,2,1] => [5,4,2,1,1,1] => [[5,4,2,1,1,1],[]] => [[5,5,5,5,5,5],[4,4,4,3,1]]
[6,2,2,2,2] => [5,5,1,1,1,1] => [[5,5,1,1,1,1],[]] => [[5,5,5,5,5,5],[4,4,4,4]]
[5,5,4] => [3,3,3,3,2] => [[3,3,3,3,2],[]] => [[3,3,3,3,3],[1]]
[5,5,1,1,1,1] => [6,2,2,2,2] => [[6,2,2,2,2],[]] => [[6,6,6,6,6],[4,4,4,4]]
[5,4,3,2] => [4,4,3,2,1] => [[4,4,3,2,1],[]] => [[4,4,4,4,4],[3,2,1]]
[5,4,3,1,1] => [5,3,3,2,1] => [[5,3,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,2]]
[5,4,2,2,1] => [5,4,2,2,1] => [[5,4,2,2,1],[]] => [[5,5,5,5,5],[4,3,3,1]]
[5,4,2,1,1,1] => [6,3,2,2,1] => [[6,3,2,2,1],[]] => [[6,6,6,6,6],[5,4,4,3]]
[5,3,3,2,1] => [5,4,3,1,1] => [[5,4,3,1,1],[]] => [[5,5,5,5,5],[4,4,2,1]]
[5,2,2,2,2,1] => [6,5,1,1,1] => [[6,5,1,1,1],[]] => [[6,6,6,6,6],[5,5,5,1]]
[4,4,4,2] => [4,4,3,3] => [[4,4,3,3],[]] => [[4,4,4,4],[1,1]]
[4,4,3,3] => [4,4,4,2] => [[4,4,4,2],[]] => [[4,4,4,4],[2]]
[4,4,3,2,1] => [5,4,3,2] => [[5,4,3,2],[]] => [[5,5,5,5],[3,2,1]]
[4,3,2,2,2,1] => [6,5,2,1] => [[6,5,2,1],[]] => [[6,6,6,6],[5,4,1]]
[3,3,3,3,2] => [5,5,4] => [[5,5,4],[]] => [[5,5,5],[1]]
[3,3,3,2,2,1] => [6,5,3] => [[6,5,3],[]] => [[6,6,6],[3,1]]
[3,3,2,2,2,2] => [6,6,2] => [[6,6,2],[]] => [[6,6,6],[4]]
[2,2,2,2,2,2,2] => [7,7] => [[7,7],[]] => [[7,7],[]]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14] => [[14],[]] => [[14],[]]
[15] => [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],[]] => [[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],[]]
[6,6,3] => [3,3,3,2,2,2] => [[3,3,3,2,2,2],[]] => [[3,3,3,3,3,3],[1,1,1]]
[6,5,4] => [3,3,3,3,2,1] => [[3,3,3,3,2,1],[]] => [[3,3,3,3,3,3],[2,1]]
[6,5,2,1,1] => [5,3,2,2,2,1] => [[5,3,2,2,2,1],[]] => [[5,5,5,5,5,5],[4,3,3,3,2]]
[6,3,3,3] => [4,4,4,1,1,1] => [[4,4,4,1,1,1],[]] => [[4,4,4,4,4,4],[3,3,3]]
[6,3,3,2,1] => [5,4,3,1,1,1] => [[5,4,3,1,1,1],[]] => [[5,5,5,5,5,5],[4,4,4,2,1]]
[5,5,5] => [3,3,3,3,3] => [[3,3,3,3,3],[]] => [[3,3,3,3,3],[]]
[5,4,3,2,1] => [5,4,3,2,1] => [[5,4,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,1]]
[5,4,3,1,1,1] => [6,3,3,2,1] => [[6,3,3,2,1],[]] => [[6,6,6,6,6],[5,4,3,3]]
[5,3,2,2,2,1] => [6,5,2,1,1] => [[6,5,2,1,1],[]] => [[6,6,6,6,6],[5,5,4,1]]
[4,4,4,3] => [4,4,4,3] => [[4,4,4,3],[]] => [[4,4,4,4],[1]]
[4,4,4,1,1,1] => [6,3,3,3] => [[6,3,3,3],[]] => [[6,6,6,6],[3,3,3]]
[3,3,3,3,3] => [5,5,5] => [[5,5,5],[]] => [[5,5,5],[]]
[3,3,3,3,2,1] => [6,5,4] => [[6,5,4],[]] => [[6,6,6],[2,1]]
[3,3,3,2,2,2] => [6,6,3] => [[6,6,3],[]] => [[6,6,6],[3]]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15] => [[15],[]] => [[15],[]]
[12,4] => [2,2,2,2,1,1,1,1,1,1,1,1] => [[2,2,2,2,1,1,1,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]]
[10,6] => [2,2,2,2,2,2,1,1,1,1] => [[2,2,2,2,2,2,1,1,1,1],[]] => [[2,2,2,2,2,2,2,2,2,2],[1,1,1,1]]
[8,8] => [2,2,2,2,2,2,2,2] => [[2,2,2,2,2,2,2,2],[]] => [[2,2,2,2,2,2,2,2],[]]
[7,5,3,1] => [4,3,3,2,2,1,1] => [[4,3,3,2,2,1,1],[]] => [[4,4,4,4,4,4,4],[3,3,2,2,1,1]]
[6,6,4] => [3,3,3,3,2,2] => [[3,3,3,3,2,2],[]] => [[3,3,3,3,3,3],[1,1]]
[6,5,4,1] => [4,3,3,3,2,1] => [[4,3,3,3,2,1],[]] => [[4,4,4,4,4,4],[3,2,1,1,1]]
[6,5,2,2,1] => [5,4,2,2,2,1] => [[5,4,2,2,2,1],[]] => [[5,5,5,5,5,5],[4,3,3,3,1]]
[6,4,3,2,1] => [5,4,3,2,1,1] => [[5,4,3,2,1,1],[]] => [[5,5,5,5,5,5],[4,4,3,2,1]]
[5,4,3,2,1,1] => [6,4,3,2,1] => [[6,4,3,2,1],[]] => [[6,6,6,6,6],[5,4,3,2]]
[5,4,2,2,2,1] => [6,5,2,2,1] => [[6,5,2,2,1],[]] => [[6,6,6,6,6],[5,4,4,1]]
[4,4,4,4] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]]
[4,3,3,3,2,1] => [6,5,4,1] => [[6,5,4,1],[]] => [[6,6,6,6],[5,2,1]]
[4,3,3,2,2,1,1] => [7,5,3,1] => [[7,5,3,1],[]] => [[7,7,7,7],[6,4,2]]
[3,3,3,3,2,2] => [6,6,4] => [[6,6,4],[]] => [[6,6,6],[2]]
[2,2,2,2,2,2,2,2] => [8,8] => [[8,8],[]] => [[8,8],[]]
[2,2,2,2,2,2,1,1,1,1] => [10,6] => [[10,6],[]] => [[10,10],[4]]
[2,2,2,2,1,1,1,1,1,1,1,1] => [12,4] => [[12,4],[]] => [[12,12],[8]]
[8,8,1] => [3,2,2,2,2,2,2,2] => [[3,2,2,2,2,2,2,2],[]] => [[3,3,3,3,3,3,3,3],[1,1,1,1,1,1,1]]
[6,5,4,1,1] => [5,3,3,3,2,1] => [[5,3,3,3,2,1],[]] => [[5,5,5,5,5,5],[4,3,2,2,2]]
[6,5,3,2,1] => [5,4,3,2,2,1] => [[5,4,3,2,2,1],[]] => [[5,5,5,5,5,5],[4,3,3,2,1]]
[5,4,3,2,2,1] => [6,5,3,2,1] => [[6,5,3,2,1],[]] => [[6,6,6,6,6],[5,4,3,1]]
[5,3,3,3,2,1] => [6,5,4,1,1] => [[6,5,4,1,1],[]] => [[6,6,6,6,6],[5,5,2,1]]
[3,2,2,2,2,2,2,2] => [8,8,1] => [[8,8,1],[]] => [[8,8,8],[7]]
[6,5,4,3,2,1] => [6,5,4,3,2,1] => [[6,5,4,3,2,1],[]] => [[6,6,6,6,6,6],[5,4,3,2,1]]
[5,5,4,3,2,1] => [6,5,4,3,2] => [[6,5,4,3,2],[]] => [[6,6,6,6,6],[4,3,2,1]]
[5,4,4,3,2,1] => [6,5,4,3,1] => [[6,5,4,3,1],[]] => [[6,6,6,6,6],[5,3,2,1]]
[4,4,4,3,2,1] => [6,5,4,3] => [[6,5,4,3],[]] => [[6,6,6,6],[3,2,1]]
[5,4,3,3,2,1] => [6,5,4,2,1] => [[6,5,4,2,1],[]] => [[6,6,6,6,6],[5,4,2,1]]
[6,5,4,3,2] => [5,5,4,3,2,1] => [[5,5,4,3,2,1],[]] => [[5,5,5,5,5,5],[4,3,2,1]]
[6,5,4,3,1] => [5,4,4,3,2,1] => [[5,4,4,3,2,1],[]] => [[5,5,5,5,5,5],[4,3,2,1,1]]
[6,5,4,2,1] => [5,4,3,3,2,1] => [[5,4,3,3,2,1],[]] => [[5,5,5,5,5,5],[4,3,2,2,1]]
[6,5,4,3] => [4,4,4,3,2,1] => [[4,4,4,3,2,1],[]] => [[4,4,4,4,4,4],[3,2,1]]
[7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [[7,6,5,4,3,2,1],[]] => [[7,7,7,7,7,7,7],[6,5,4,3,2,1]]
[6,6,5,4,3,2,1] => [7,6,5,4,3,2] => [[7,6,5,4,3,2],[]] => [[7,7,7,7,7,7],[5,4,3,2,1]]
[6,5,5,4,3,2,1] => [7,6,5,4,3,1] => [[7,6,5,4,3,1],[]] => [[7,7,7,7,7,7],[6,4,3,2,1]]
[5,5,5,4,3,2,1] => [7,6,5,4,3] => [[7,6,5,4,3],[]] => [[7,7,7,7,7],[4,3,2,1]]
[6,5,4,4,3,2,1] => [7,6,5,4,2,1] => [[7,6,5,4,2,1],[]] => [[7,7,7,7,7,7],[6,5,3,2,1]]
[6,4,4,4,3,2,1] => [7,6,5,4,1,1] => [[7,6,5,4,1,1],[]] => [[7,7,7,7,7,7],[6,6,3,2,1]]
[5,4,4,4,3,2,1] => [7,6,5,4,1] => [[7,6,5,4,1],[]] => [[7,7,7,7,7],[6,3,2,1]]
[4,4,4,4,3,2,1] => [7,6,5,4] => [[7,6,5,4],[]] => [[7,7,7,7],[3,2,1]]
[6,5,4,3,3,2,1] => [7,6,5,3,2,1] => [[7,6,5,3,2,1],[]] => [[7,7,7,7,7,7],[6,5,4,2,1]]
[6,5,3,3,3,2,1] => [7,6,5,2,2,1] => [[7,6,5,2,2,1],[]] => [[7,7,7,7,7,7],[6,5,5,2,1]]
[6,4,3,3,3,2,1] => [7,6,5,2,1,1] => [[7,6,5,2,1,1],[]] => [[7,7,7,7,7,7],[6,6,5,2,1]]
[6,3,3,3,3,2,1] => [7,6,5,1,1,1] => [[7,6,5,1,1,1],[]] => [[7,7,7,7,7,7],[6,6,6,2,1]]
[6,5,4,3,2,2,1] => [7,6,4,3,2,1] => [[7,6,4,3,2,1],[]] => [[7,7,7,7,7,7],[6,5,4,3,1]]
[6,5,4,2,2,2,1] => [7,6,3,3,2,1] => [[7,6,3,3,2,1],[]] => [[7,7,7,7,7,7],[6,5,4,4,1]]
[6,5,3,2,2,2,1] => [7,6,3,2,2,1] => [[7,6,3,2,2,1],[]] => [[7,7,7,7,7,7],[6,5,5,4,1]]
[6,5,2,2,2,2,1] => [7,6,2,2,2,1] => [[7,6,2,2,2,1],[]] => [[7,7,7,7,7,7],[6,5,5,5,1]]
[6,5,4,3,2,1,1] => [7,5,4,3,2,1] => [[7,5,4,3,2,1],[]] => [[7,7,7,7,7,7],[6,5,4,3,2]]
[6,5,4,3,1,1,1] => [7,4,4,3,2,1] => [[7,4,4,3,2,1],[]] => [[7,7,7,7,7,7],[6,5,4,3,3]]
[6,5,4,2,1,1,1] => [7,4,3,3,2,1] => [[7,4,3,3,2,1],[]] => [[7,7,7,7,7,7],[6,5,4,4,3]]
[6,5,4,1,1,1,1] => [7,3,3,3,2,1] => [[7,3,3,3,2,1],[]] => [[7,7,7,7,7,7],[6,5,4,4,4]]
[7,6,5,4,3,2] => [6,6,5,4,3,2,1] => [[6,6,5,4,3,2,1],[]] => [[6,6,6,6,6,6,6],[5,4,3,2,1]]
[6,6,2,2,2,2] => [6,6,2,2,2,2] => [[6,6,2,2,2,2],[]] => [[6,6,6,6,6,6],[4,4,4,4]]
[7,6,5,4,3,1] => [6,5,5,4,3,2,1] => [[6,5,5,4,3,2,1],[]] => [[6,6,6,6,6,6,6],[5,4,3,2,1,1]]
[7,6,5,4,2,1] => [6,5,4,4,3,2,1] => [[6,5,4,4,3,2,1],[]] => [[6,6,6,6,6,6,6],[5,4,3,2,2,1]]
[7,6,5,3,2,1] => [6,5,4,3,3,2,1] => [[6,5,4,3,3,2,1],[]] => [[6,6,6,6,6,6,6],[5,4,3,3,2,1]]
[7,6,4,3,2,1] => [6,5,4,3,2,2,1] => [[6,5,4,3,2,2,1],[]] => [[6,6,6,6,6,6,6],[5,4,4,3,2,1]]
[7,5,4,3,2,1] => [6,5,4,3,2,1,1] => [[6,5,4,3,2,1,1],[]] => [[6,6,6,6,6,6,6],[5,5,4,3,2,1]]
[7,4,4,3,2,1] => [6,5,4,3,1,1,1] => [[6,5,4,3,1,1,1],[]] => [[6,6,6,6,6,6,6],[5,5,5,3,2,1]]
[7,6,3,3,2,1] => [6,5,4,2,2,2,1] => [[6,5,4,2,2,2,1],[]] => [[6,6,6,6,6,6,6],[5,4,4,4,2,1]]
[7,3,3,3,2,1] => [6,5,4,1,1,1,1] => [[6,5,4,1,1,1,1],[]] => [[6,6,6,6,6,6,6],[5,5,5,5,2,1]]
[7,6,5,2,2,1] => [6,5,3,3,3,2,1] => [[6,5,3,3,3,2,1],[]] => [[6,6,6,6,6,6,6],[5,4,3,3,3,1]]
[7,6,2,2,2,1] => [6,5,2,2,2,2,1] => [[6,5,2,2,2,2,1],[]] => [[6,6,6,6,6,6,6],[5,4,4,4,4,1]]
[7,6,5,4,1,1] => [6,4,4,4,3,2,1] => [[6,4,4,4,3,2,1],[]] => [[6,6,6,6,6,6,6],[5,4,3,2,2,2]]
[7,6,5,1,1,1] => [6,3,3,3,3,2,1] => [[6,3,3,3,3,2,1],[]] => [[6,6,6,6,6,6,6],[5,4,3,3,3,3]]
[7,6,5,4,3] => [5,5,5,4,3,2,1] => [[5,5,5,4,3,2,1],[]] => [[5,5,5,5,5,5,5],[4,3,2,1]]
[7,6,5,4,1] => [5,4,4,4,3,2,1] => [[5,4,4,4,3,2,1],[]] => [[5,5,5,5,5,5,5],[4,3,2,1,1,1]]
[7,5,4,3,1] => [5,4,4,3,2,1,1] => [[5,4,4,3,2,1,1],[]] => [[5,5,5,5,5,5,5],[4,4,3,2,1,1]]
[7,6,5,4] => [4,4,4,4,3,2,1] => [[4,4,4,4,3,2,1],[]] => [[4,4,4,4,4,4,4],[3,2,1]]
[2,2,2,2,2,2,2,2,2] => [9,9] => [[9,9],[]] => [[9,9],[]]
[3,3,3,3,3,3] => [6,6,6] => [[6,6,6],[]] => [[6,6,6],[]]
[3,3,3,3,3,3,3,3] => [8,8,8] => [[8,8,8],[]] => [[8,8,8],[]]
[3,3,3,3,3,3,3] => [7,7,7] => [[7,7,7],[]] => [[7,7,7],[]]
[4,4,4,4,4] => [5,5,5,5] => [[5,5,5,5],[]] => [[5,5,5,5],[]]
[4,4,4,4,4,4] => [6,6,6,6] => [[6,6,6,6],[]] => [[6,6,6,6],[]]
[5,5,5,5] => [4,4,4,4,4] => [[4,4,4,4,4],[]] => [[4,4,4,4,4],[]]
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [16,16] => [[16,16],[]] => [[16,16],[]]
[6,6,6,6] => [4,4,4,4,4,4] => [[4,4,4,4,4,4],[]] => [[4,4,4,4,4,4],[]]
[6,2,2,2,2,2,2] => [7,7,1,1,1,1] => [[7,7,1,1,1,1],[]] => [[7,7,7,7,7,7],[6,6,6,6]]
[6,6,6] => [3,3,3,3,3,3] => [[3,3,3,3,3,3],[]] => [[3,3,3,3,3,3],[]]
[10,4,4] => [3,3,3,3,1,1,1,1,1,1] => [[3,3,3,3,1,1,1,1,1,1],[]] => [[3,3,3,3,3,3,3,3,3,3],[2,2,2,2,2,2]]
[10,10] => [2,2,2,2,2,2,2,2,2,2] => [[2,2,2,2,2,2,2,2,2,2],[]] => [[2,2,2,2,2,2,2,2,2,2],[]]
[6,6,6,6,6] => [5,5,5,5,5,5] => [[5,5,5,5,5,5],[]] => [[5,5,5,5,5,5],[]]
[10,10,10,10] => [4,4,4,4,4,4,4,4,4,4] => [[4,4,4,4,4,4,4,4,4,4],[]] => [[4,4,4,4,4,4,4,4,4,4],[]]
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => [24,24,24,24,24] => [[24,24,24,24,24],[]] => [[24,24,24,24,24],[]]
[5,5,5,5,5,5,5,5,5,5,5,5] => [12,12,12,12,12] => [[12,12,12,12,12],[]] => [[12,12,12,12,12],[]]
[15,15] => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2],[]] => [[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2],[]]
[5,5,5,5,5,5] => [6,6,6,6,6] => [[6,6,6,6,6],[]] => [[6,6,6,6,6],[]]
[15,5,5] => [3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] => [[3,3,3,3,3,1,1,1,1,1,1,1,1,1,1],[]] => [[3,3,3,3,3,3,3,3,3,3,3,3,3,3,3],[2,2,2,2,2,2,2,2,2,2]]
[7,7,7] => [3,3,3,3,3,3,3] => [[3,3,3,3,3,3,3],[]] => [[3,3,3,3,3,3,3],[]]
[11,7,5,1] => [4,3,3,3,3,2,2,1,1,1,1] => [[4,3,3,3,3,2,2,1,1,1,1],[]] => [[4,4,4,4,4,4,4,4,4,4,4],[3,3,3,3,2,2,1,1,1,1]]
[9,7,5,3,1] => [5,4,4,3,3,2,2,1,1] => [[5,4,4,3,3,2,2,1,1],[]] => [[5,5,5,5,5,5,5,5,5],[4,4,3,3,2,2,1,1]]
[11,9,7,5,3,1] => [6,5,5,4,4,3,3,2,2,1,1] => [[6,5,5,4,4,3,3,2,2,1,1],[]] => [[6,6,6,6,6,6,6,6,6,6,6],[5,5,4,4,3,3,2,2,1,1]]
[9,7,5,5,3,1] => [6,5,5,4,4,2,2,1,1] => [[6,5,5,4,4,2,2,1,1],[]] => [[6,6,6,6,6,6,6,6,6],[5,5,4,4,2,2,1,1]]
[11,8,7,5,4,1] => [6,5,5,5,4,3,3,2,1,1,1] => [[6,5,5,5,4,3,3,2,1,1,1],[]] => [[6,6,6,6,6,6,6,6,6,6,6],[5,5,5,4,3,3,2,1,1,1]]
[8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => [[8,7,6,5,4,3,2,1],[]] => [[8,8,8,8,8,8,8,8],[7,6,5,4,3,2,1]]
[7,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2] => [[8,7,6,5,4,3,2],[]] => [[8,8,8,8,8,8,8],[6,5,4,3,2,1]]
[7,6,6,5,4,3,2,1] => [8,7,6,5,4,3,1] => [[8,7,6,5,4,3,1],[]] => [[8,8,8,8,8,8,8],[7,5,4,3,2,1]]
[7,6,5,5,4,3,2,1] => [8,7,6,5,4,2,1] => [[8,7,6,5,4,2,1],[]] => [[8,8,8,8,8,8,8],[7,6,4,3,2,1]]
[7,6,5,4,4,3,2,1] => [8,7,6,5,3,2,1] => [[8,7,6,5,3,2,1],[]] => [[8,8,8,8,8,8,8],[7,6,5,3,2,1]]
[7,6,5,4,3,3,2,1] => [8,7,6,4,3,2,1] => [[8,7,6,4,3,2,1],[]] => [[8,8,8,8,8,8,8],[7,6,5,4,2,1]]
[7,6,5,4,3,2,2,1] => [8,7,5,4,3,2,1] => [[8,7,5,4,3,2,1],[]] => [[8,8,8,8,8,8,8],[7,6,5,4,3,1]]
[7,6,5,4,3,2,1,1] => [8,6,5,4,3,2,1] => [[8,6,5,4,3,2,1],[]] => [[8,8,8,8,8,8,8],[7,6,5,4,3,2]]
[9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => [[9,8,7,6,5,4,3,2,1],[]] => [[9,9,9,9,9,9,9,9,9],[8,7,6,5,4,3,2,1]]
[8,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2] => [[9,8,7,6,5,4,3,2],[]] => [[9,9,9,9,9,9,9,9],[7,6,5,4,3,2,1]]
[6,6,6,5,4,3,2,1] => [8,7,6,5,4,3] => [[8,7,6,5,4,3],[]] => [[8,8,8,8,8,8],[5,4,3,2,1]]
[8,7,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,1] => [[9,8,7,6,5,4,3,1],[]] => [[9,9,9,9,9,9,9,9],[8,6,5,4,3,2,1]]
[7,5,5,5,4,3,2,1] => [8,7,6,5,4,1,1] => [[8,7,6,5,4,1,1],[]] => [[8,8,8,8,8,8,8],[7,7,4,3,2,1]]
[8,7,6,6,5,4,3,2,1] => [9,8,7,6,5,4,2,1] => [[9,8,7,6,5,4,2,1],[]] => [[9,9,9,9,9,9,9,9],[8,7,5,4,3,2,1]]
[7,6,4,4,4,3,2,1] => [8,7,6,5,2,2,1] => [[8,7,6,5,2,2,1],[]] => [[8,8,8,8,8,8,8],[7,6,6,3,2,1]]
[8,7,6,5,5,4,3,2,1] => [9,8,7,6,5,3,2,1] => [[9,8,7,6,5,3,2,1],[]] => [[9,9,9,9,9,9,9,9],[8,7,6,4,3,2,1]]
[7,6,5,3,3,3,2,1] => [8,7,6,3,3,2,1] => [[8,7,6,3,3,2,1],[]] => [[8,8,8,8,8,8,8],[7,6,5,5,2,1]]
[8,7,6,5,4,4,3,2,1] => [9,8,7,6,4,3,2,1] => [[9,8,7,6,4,3,2,1],[]] => [[9,9,9,9,9,9,9,9],[8,7,6,5,3,2,1]]
[7,6,5,4,2,2,2,1] => [8,7,4,4,3,2,1] => [[8,7,4,4,3,2,1],[]] => [[8,8,8,8,8,8,8],[7,6,5,4,4,1]]
[8,7,6,5,4,3,3,2,1] => [9,8,7,5,4,3,2,1] => [[9,8,7,5,4,3,2,1],[]] => [[9,9,9,9,9,9,9,9],[8,7,6,5,4,2,1]]
[7,6,5,4,3,1,1,1] => [8,5,5,4,3,2,1] => [[8,5,5,4,3,2,1],[]] => [[8,8,8,8,8,8,8],[7,6,5,4,3,3]]
[8,7,6,5,4,3,2,2,1] => [9,8,6,5,4,3,2,1] => [[9,8,6,5,4,3,2,1],[]] => [[9,9,9,9,9,9,9,9],[8,7,6,5,4,3,1]]
[8,7,6,5,4,3,2,1,1] => [9,7,6,5,4,3,2,1] => [[9,7,6,5,4,3,2,1],[]] => [[9,9,9,9,9,9,9,9],[8,7,6,5,4,3,2]]
[8,7,6,5,4,3,2] => [7,7,6,5,4,3,2,1] => [[7,7,6,5,4,3,2,1],[]] => [[7,7,7,7,7,7,7,7],[6,5,4,3,2,1]]
[8,7,6,5,4,3,1] => [7,6,6,5,4,3,2,1] => [[7,6,6,5,4,3,2,1],[]] => [[7,7,7,7,7,7,7,7],[6,5,4,3,2,1,1]]
[8,7,6,5,4,2,1] => [7,6,5,5,4,3,2,1] => [[7,6,5,5,4,3,2,1],[]] => [[7,7,7,7,7,7,7,7],[6,5,4,3,2,2,1]]
[8,7,6,5,3,2,1] => [7,6,5,4,4,3,2,1] => [[7,6,5,4,4,3,2,1],[]] => [[7,7,7,7,7,7,7,7],[6,5,4,3,3,2,1]]
[8,7,6,4,3,2,1] => [7,6,5,4,3,3,2,1] => [[7,6,5,4,3,3,2,1],[]] => [[7,7,7,7,7,7,7,7],[6,5,4,4,3,2,1]]
[8,7,5,4,3,2,1] => [7,6,5,4,3,2,2,1] => [[7,6,5,4,3,2,2,1],[]] => [[7,7,7,7,7,7,7,7],[6,5,5,4,3,2,1]]
[8,6,5,4,3,2,1] => [7,6,5,4,3,2,1,1] => [[7,6,5,4,3,2,1,1],[]] => [[7,7,7,7,7,7,7,7],[6,6,5,4,3,2,1]]
[9,8,7,6,5,4,3,2] => [8,8,7,6,5,4,3,2,1] => [[8,8,7,6,5,4,3,2,1],[]] => [[8,8,8,8,8,8,8,8,8],[7,6,5,4,3,2,1]]
[8,7,6,5,4,3] => [6,6,6,5,4,3,2,1] => [[6,6,6,5,4,3,2,1],[]] => [[6,6,6,6,6,6,6,6],[5,4,3,2,1]]
[8,7,6,5,4,1,1] => [7,5,5,5,4,3,2,1] => [[7,5,5,5,4,3,2,1],[]] => [[7,7,7,7,7,7,7,7],[6,5,4,3,2,2,2]]
[8,7,6,5,2,2,1] => [7,6,4,4,4,3,2,1] => [[7,6,4,4,4,3,2,1],[]] => [[7,7,7,7,7,7,7,7],[6,5,4,3,3,3,1]]
[8,7,6,3,3,2,1] => [7,6,5,3,3,3,2,1] => [[7,6,5,3,3,3,2,1],[]] => [[7,7,7,7,7,7,7,7],[6,5,4,4,4,2,1]]
[8,7,4,4,3,2,1] => [7,6,5,4,2,2,2,1] => [[7,6,5,4,2,2,2,1],[]] => [[7,7,7,7,7,7,7,7],[6,5,5,5,3,2,1]]
[8,5,5,4,3,2,1] => [7,6,5,4,3,1,1,1] => [[7,6,5,4,3,1,1,1],[]] => [[7,7,7,7,7,7,7,7],[6,6,6,4,3,2,1]]
[9,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1,1] => [[8,7,6,5,4,3,2,1,1],[]] => [[8,8,8,8,8,8,8,8,8],[7,7,6,5,4,3,2,1]]
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [15,15] => [[15,15],[]] => [[15,15],[]]
[5,5,5,5,5] => [5,5,5,5,5] => [[5,5,5,5,5],[]] => [[5,5,5,5,5],[]]
[7,7,1,1,1,1] => [6,2,2,2,2,2,2] => [[6,2,2,2,2,2,2],[]] => [[6,6,6,6,6,6,6],[4,4,4,4,4,4]]
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
Map
to skew partition
Description
The partition regarded as a skew partition.
Map
rotate
Description
The rotation of a skew partition.
This is the skew partition obtained by rotating the diagram by 180 degrees. Equivalently, given a skew partition $\lambda/\mu$, its rotation $(\lambda/\mu)^\natural$ is the skew partition with cells $\{(a-i, b-j)| (i, j) \in \lambda/\mu\}$, where $b$ and $a$ are the first part and the number of parts of $\lambda$ respectively.