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Identifier
Mp00311: Plane partitions —to partition⟶ Integer partitions
Images
=>
Cc0025;cc-rep-0Cc0002;cc-rep-1
[[1]]=>[1] [[1],[1]]=>[1,1] [[2]]=>[2] [[1,1]]=>[2] [[1],[1],[1]]=>[1,1,1] [[2],[1]]=>[2,1] [[1,1],[1]]=>[2,1] [[3]]=>[3] [[2,1]]=>[3] [[1,1,1]]=>[3] [[1],[1],[1],[1]]=>[1,1,1,1] [[2],[1],[1]]=>[2,1,1] [[2],[2]]=>[2,2] [[1,1],[1],[1]]=>[2,1,1] [[1,1],[1,1]]=>[2,2] [[3],[1]]=>[3,1] [[2,1],[1]]=>[3,1] [[1,1,1],[1]]=>[3,1] [[4]]=>[4] [[3,1]]=>[4] [[2,2]]=>[4] [[2,1,1]]=>[4] [[1,1,1,1]]=>[4] [[1],[1],[1],[1],[1]]=>[1,1,1,1,1] [[2],[1],[1],[1]]=>[2,1,1,1] [[2],[2],[1]]=>[2,2,1] [[1,1],[1],[1],[1]]=>[2,1,1,1] [[1,1],[1,1],[1]]=>[2,2,1] [[3],[1],[1]]=>[3,1,1] [[3],[2]]=>[3,2] [[2,1],[1],[1]]=>[3,1,1] [[2,1],[2]]=>[3,2] [[2,1],[1,1]]=>[3,2] [[1,1,1],[1],[1]]=>[3,1,1] [[1,1,1],[1,1]]=>[3,2] [[4],[1]]=>[4,1] [[3,1],[1]]=>[4,1] [[2,2],[1]]=>[4,1] [[2,1,1],[1]]=>[4,1] [[1,1,1,1],[1]]=>[4,1] [[5]]=>[5] [[4,1]]=>[5] [[3,2]]=>[5] [[3,1,1]]=>[5] [[2,2,1]]=>[5] [[2,1,1,1]]=>[5] [[1,1,1,1,1]]=>[5] [[1],[1],[1],[1],[1],[1]]=>[1,1,1,1,1,1] [[2],[1],[1],[1],[1]]=>[2,1,1,1,1] [[2],[2],[1],[1]]=>[2,2,1,1] [[2],[2],[2]]=>[2,2,2] [[1,1],[1],[1],[1],[1]]=>[2,1,1,1,1] [[1,1],[1,1],[1],[1]]=>[2,2,1,1] [[1,1],[1,1],[1,1]]=>[2,2,2] [[3],[1],[1],[1]]=>[3,1,1,1] [[3],[2],[1]]=>[3,2,1] [[3],[3]]=>[3,3] [[2,1],[1],[1],[1]]=>[3,1,1,1] [[2,1],[2],[1]]=>[3,2,1] [[2,1],[1,1],[1]]=>[3,2,1] [[2,1],[2,1]]=>[3,3] [[1,1,1],[1],[1],[1]]=>[3,1,1,1] [[1,1,1],[1,1],[1]]=>[3,2,1] [[1,1,1],[1,1,1]]=>[3,3] [[4],[1],[1]]=>[4,1,1] [[4],[2]]=>[4,2] [[3,1],[1],[1]]=>[4,1,1] [[3,1],[2]]=>[4,2] [[3,1],[1,1]]=>[4,2] [[2,2],[1],[1]]=>[4,1,1] [[2,2],[2]]=>[4,2] [[2,2],[1,1]]=>[4,2] [[2,1,1],[1],[1]]=>[4,1,1] [[2,1,1],[2]]=>[4,2] [[2,1,1],[1,1]]=>[4,2] [[1,1,1,1],[1],[1]]=>[4,1,1] [[1,1,1,1],[1,1]]=>[4,2] [[5],[1]]=>[5,1] [[4,1],[1]]=>[5,1] [[3,2],[1]]=>[5,1] [[3,1,1],[1]]=>[5,1] [[2,2,1],[1]]=>[5,1] [[2,1,1,1],[1]]=>[5,1] [[1,1,1,1,1],[1]]=>[5,1] [[6]]=>[6] [[5,1]]=>[6] [[4,2]]=>[6] [[4,1,1]]=>[6] [[3,3]]=>[6] [[3,2,1]]=>[6] [[3,1,1,1]]=>[6] [[2,2,2]]=>[6] [[2,2,1,1]]=>[6] [[2,1,1,1,1]]=>[6] [[1,1,1,1,1,1]]=>[6] [[1],[1],[1],[1],[1],[1],[1]]=>[1,1,1,1,1,1,1] [[2],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1] [[2],[2],[1],[1],[1]]=>[2,2,1,1,1] [[2],[2],[2],[1]]=>[2,2,2,1] [[1,1],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1] [[1,1],[1,1],[1],[1],[1]]=>[2,2,1,1,1] [[1,1],[1,1],[1,1],[1]]=>[2,2,2,1] [[3],[1],[1],[1],[1]]=>[3,1,1,1,1] [[3],[2],[1],[1]]=>[3,2,1,1] [[3],[2],[2]]=>[3,2,2] [[3],[3],[1]]=>[3,3,1] [[2,1],[1],[1],[1],[1]]=>[3,1,1,1,1] [[2,1],[2],[1],[1]]=>[3,2,1,1] [[2,1],[2],[2]]=>[3,2,2] [[2,1],[1,1],[1],[1]]=>[3,2,1,1] [[2,1],[1,1],[1,1]]=>[3,2,2] [[2,1],[2,1],[1]]=>[3,3,1] [[1,1,1],[1],[1],[1],[1]]=>[3,1,1,1,1] [[1,1,1],[1,1],[1],[1]]=>[3,2,1,1] [[1,1,1],[1,1],[1,1]]=>[3,2,2] [[1,1,1],[1,1,1],[1]]=>[3,3,1] [[4],[1],[1],[1]]=>[4,1,1,1] [[4],[2],[1]]=>[4,2,1] [[4],[3]]=>[4,3] [[3,1],[1],[1],[1]]=>[4,1,1,1] [[3,1],[2],[1]]=>[4,2,1] [[3,1],[1,1],[1]]=>[4,2,1] [[3,1],[3]]=>[4,3] [[3,1],[2,1]]=>[4,3] [[2,2],[1],[1],[1]]=>[4,1,1,1] [[2,2],[2],[1]]=>[4,2,1] [[2,2],[1,1],[1]]=>[4,2,1] [[2,2],[2,1]]=>[4,3] [[2,1,1],[1],[1],[1]]=>[4,1,1,1] [[2,1,1],[2],[1]]=>[4,2,1] [[2,1,1],[1,1],[1]]=>[4,2,1] [[2,1,1],[2,1]]=>[4,3] [[2,1,1],[1,1,1]]=>[4,3] [[1,1,1,1],[1],[1],[1]]=>[4,1,1,1] [[1,1,1,1],[1,1],[1]]=>[4,2,1] [[1,1,1,1],[1,1,1]]=>[4,3] [[5],[1],[1]]=>[5,1,1] [[5],[2]]=>[5,2] [[4,1],[1],[1]]=>[5,1,1] [[4,1],[2]]=>[5,2] [[4,1],[1,1]]=>[5,2] [[3,2],[1],[1]]=>[5,1,1] [[3,2],[2]]=>[5,2] [[3,2],[1,1]]=>[5,2] [[3,1,1],[1],[1]]=>[5,1,1] [[3,1,1],[2]]=>[5,2] [[3,1,1],[1,1]]=>[5,2] [[2,2,1],[1],[1]]=>[5,1,1] [[2,2,1],[2]]=>[5,2] [[2,2,1],[1,1]]=>[5,2] [[2,1,1,1],[1],[1]]=>[5,1,1] [[2,1,1,1],[2]]=>[5,2] [[2,1,1,1],[1,1]]=>[5,2] [[1,1,1,1,1],[1],[1]]=>[5,1,1] [[1,1,1,1,1],[1,1]]=>[5,2] [[6],[1]]=>[6,1] [[5,1],[1]]=>[6,1] [[4,2],[1]]=>[6,1] [[4,1,1],[1]]=>[6,1] [[3,3],[1]]=>[6,1] [[3,2,1],[1]]=>[6,1] [[3,1,1,1],[1]]=>[6,1] [[2,2,2],[1]]=>[6,1] [[2,2,1,1],[1]]=>[6,1] [[2,1,1,1,1],[1]]=>[6,1] [[1,1,1,1,1,1],[1]]=>[6,1] [[7]]=>[7] [[6,1]]=>[7] [[5,2]]=>[7] [[5,1,1]]=>[7] [[4,3]]=>[7] [[4,2,1]]=>[7] [[4,1,1,1]]=>[7] [[3,3,1]]=>[7] [[3,2,2]]=>[7] [[3,2,1,1]]=>[7] [[3,1,1,1,1]]=>[7] [[2,2,2,1]]=>[7] [[2,2,1,1,1]]=>[7] [[2,1,1,1,1,1]]=>[7] [[1,1,1,1,1,1,1]]=>[7] [[1],[1],[1],[1],[1],[1],[1],[1]]=>[1,1,1,1,1,1,1,1] [[2],[1],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1,1] [[2],[2],[1],[1],[1],[1]]=>[2,2,1,1,1,1] [[2],[2],[2],[1],[1]]=>[2,2,2,1,1] [[2],[2],[2],[2]]=>[2,2,2,2] [[1,1],[1],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1,1] [[1,1],[1,1],[1],[1],[1],[1]]=>[2,2,1,1,1,1] [[1,1],[1,1],[1,1],[1],[1]]=>[2,2,2,1,1] [[1,1],[1,1],[1,1],[1,1]]=>[2,2,2,2] [[3],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1] [[3],[2],[1],[1],[1]]=>[3,2,1,1,1] [[3],[2],[2],[1]]=>[3,2,2,1] [[3],[3],[1],[1]]=>[3,3,1,1] [[3],[3],[2]]=>[3,3,2] [[2,1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1] [[2,1],[2],[1],[1],[1]]=>[3,2,1,1,1] [[2,1],[2],[2],[1]]=>[3,2,2,1] [[2,1],[1,1],[1],[1],[1]]=>[3,2,1,1,1] [[2,1],[1,1],[1,1],[1]]=>[3,2,2,1] [[2,1],[2,1],[1],[1]]=>[3,3,1,1] [[2,1],[2,1],[2]]=>[3,3,2] [[2,1],[2,1],[1,1]]=>[3,3,2] [[1,1,1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1] [[1,1,1],[1,1],[1],[1],[1]]=>[3,2,1,1,1] [[1,1,1],[1,1],[1,1],[1]]=>[3,2,2,1] [[1,1,1],[1,1,1],[1],[1]]=>[3,3,1,1] [[1,1,1],[1,1,1],[1,1]]=>[3,3,2] [[4],[1],[1],[1],[1]]=>[4,1,1,1,1] [[4],[2],[1],[1]]=>[4,2,1,1] [[4],[2],[2]]=>[4,2,2] [[4],[3],[1]]=>[4,3,1] [[4],[4]]=>[4,4] [[3,1],[1],[1],[1],[1]]=>[4,1,1,1,1] [[3,1],[2],[1],[1]]=>[4,2,1,1] [[3,1],[2],[2]]=>[4,2,2] [[3,1],[1,1],[1],[1]]=>[4,2,1,1] [[3,1],[1,1],[1,1]]=>[4,2,2] [[3,1],[3],[1]]=>[4,3,1] [[3,1],[2,1],[1]]=>[4,3,1] [[3,1],[3,1]]=>[4,4] [[2,2],[1],[1],[1],[1]]=>[4,1,1,1,1] [[2,2],[2],[1],[1]]=>[4,2,1,1] [[2,2],[2],[2]]=>[4,2,2] [[2,2],[1,1],[1],[1]]=>[4,2,1,1] [[2,2],[1,1],[1,1]]=>[4,2,2] [[2,2],[2,1],[1]]=>[4,3,1] [[2,2],[2,2]]=>[4,4] [[2,1,1],[1],[1],[1],[1]]=>[4,1,1,1,1] [[2,1,1],[2],[1],[1]]=>[4,2,1,1] [[2,1,1],[2],[2]]=>[4,2,2] [[2,1,1],[1,1],[1],[1]]=>[4,2,1,1] [[2,1,1],[1,1],[1,1]]=>[4,2,2] [[2,1,1],[2,1],[1]]=>[4,3,1] [[2,1,1],[1,1,1],[1]]=>[4,3,1] [[2,1,1],[2,1,1]]=>[4,4] [[1,1,1,1],[1],[1],[1],[1]]=>[4,1,1,1,1] [[1,1,1,1],[1,1],[1],[1]]=>[4,2,1,1] [[1,1,1,1],[1,1],[1,1]]=>[4,2,2] [[1,1,1,1],[1,1,1],[1]]=>[4,3,1] [[1,1,1,1],[1,1,1,1]]=>[4,4] [[5],[1],[1],[1]]=>[5,1,1,1] [[5],[2],[1]]=>[5,2,1] [[5],[3]]=>[5,3] [[4,1],[1],[1],[1]]=>[5,1,1,1] [[4,1],[2],[1]]=>[5,2,1] [[4,1],[1,1],[1]]=>[5,2,1] [[4,1],[3]]=>[5,3] [[4,1],[2,1]]=>[5,3] [[3,2],[1],[1],[1]]=>[5,1,1,1] [[3,2],[2],[1]]=>[5,2,1] [[3,2],[1,1],[1]]=>[5,2,1] [[3,2],[3]]=>[5,3] [[3,2],[2,1]]=>[5,3] [[3,1,1],[1],[1],[1]]=>[5,1,1,1] [[3,1,1],[2],[1]]=>[5,2,1] [[3,1,1],[1,1],[1]]=>[5,2,1] [[3,1,1],[3]]=>[5,3] [[3,1,1],[2,1]]=>[5,3] [[3,1,1],[1,1,1]]=>[5,3] [[2,2,1],[1],[1],[1]]=>[5,1,1,1] [[2,2,1],[2],[1]]=>[5,2,1] [[2,2,1],[1,1],[1]]=>[5,2,1] [[2,2,1],[2,1]]=>[5,3] [[2,2,1],[1,1,1]]=>[5,3] [[2,1,1,1],[1],[1],[1]]=>[5,1,1,1] [[2,1,1,1],[2],[1]]=>[5,2,1] [[2,1,1,1],[1,1],[1]]=>[5,2,1] [[2,1,1,1],[2,1]]=>[5,3] [[2,1,1,1],[1,1,1]]=>[5,3] [[1,1,1,1,1],[1],[1],[1]]=>[5,1,1,1] [[1,1,1,1,1],[1,1],[1]]=>[5,2,1] [[1,1,1,1,1],[1,1,1]]=>[5,3] [[6],[1],[1]]=>[6,1,1] [[6],[2]]=>[6,2] [[5,1],[1],[1]]=>[6,1,1] [[5,1],[2]]=>[6,2] [[5,1],[1,1]]=>[6,2] [[4,2],[1],[1]]=>[6,1,1] [[4,2],[2]]=>[6,2] [[4,2],[1,1]]=>[6,2] [[4,1,1],[1],[1]]=>[6,1,1] [[4,1,1],[2]]=>[6,2] [[4,1,1],[1,1]]=>[6,2] [[3,3],[1],[1]]=>[6,1,1] [[3,3],[2]]=>[6,2] [[3,3],[1,1]]=>[6,2] [[3,2,1],[1],[1]]=>[6,1,1] [[3,2,1],[2]]=>[6,2] [[3,2,1],[1,1]]=>[6,2] [[3,1,1,1],[1],[1]]=>[6,1,1] [[3,1,1,1],[2]]=>[6,2] [[3,1,1,1],[1,1]]=>[6,2] [[2,2,2],[1],[1]]=>[6,1,1] [[2,2,2],[2]]=>[6,2] [[2,2,2],[1,1]]=>[6,2] [[2,2,1,1],[1],[1]]=>[6,1,1] [[2,2,1,1],[2]]=>[6,2] [[2,2,1,1],[1,1]]=>[6,2] [[2,1,1,1,1],[1],[1]]=>[6,1,1] [[2,1,1,1,1],[2]]=>[6,2] [[2,1,1,1,1],[1,1]]=>[6,2] [[1,1,1,1,1,1],[1],[1]]=>[6,1,1] [[1,1,1,1,1,1],[1,1]]=>[6,2] [[7],[1]]=>[7,1] [[6,1],[1]]=>[7,1] [[5,2],[1]]=>[7,1] [[5,1,1],[1]]=>[7,1] [[4,3],[1]]=>[7,1] [[4,2,1],[1]]=>[7,1] [[4,1,1,1],[1]]=>[7,1] [[3,3,1],[1]]=>[7,1] [[3,2,2],[1]]=>[7,1] [[3,2,1,1],[1]]=>[7,1] [[3,1,1,1,1],[1]]=>[7,1] [[2,2,2,1],[1]]=>[7,1] [[2,2,1,1,1],[1]]=>[7,1] [[2,1,1,1,1,1],[1]]=>[7,1] [[1,1,1,1,1,1,1],[1]]=>[7,1] [[8]]=>[8] [[7,1]]=>[8] [[6,2]]=>[8] [[6,1,1]]=>[8] [[5,3]]=>[8] [[5,2,1]]=>[8] [[5,1,1,1]]=>[8] [[4,4]]=>[8] [[4,3,1]]=>[8] [[4,2,2]]=>[8] [[4,2,1,1]]=>[8] [[4,1,1,1,1]]=>[8] [[3,3,2]]=>[8] [[3,3,1,1]]=>[8] [[3,2,2,1]]=>[8] [[3,2,1,1,1]]=>[8] [[3,1,1,1,1,1]]=>[8] [[2,2,2,2]]=>[8] [[2,2,2,1,1]]=>[8] [[2,2,1,1,1,1]]=>[8] [[2,1,1,1,1,1,1]]=>[8] [[1,1,1,1,1,1,1,1]]=>[8] [[1],[1],[1],[1],[1],[1],[1],[1],[1]]=>[1,1,1,1,1,1,1,1,1] [[2],[1],[1],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1,1,1] [[2],[2],[1],[1],[1],[1],[1]]=>[2,2,1,1,1,1,1] [[2],[2],[2],[1],[1],[1]]=>[2,2,2,1,1,1] [[2],[2],[2],[2],[1]]=>[2,2,2,2,1] [[1,1],[1],[1],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1,1,1] [[1,1],[1,1],[1],[1],[1],[1],[1]]=>[2,2,1,1,1,1,1] [[1,1],[1,1],[1,1],[1],[1],[1]]=>[2,2,2,1,1,1] [[1,1],[1,1],[1,1],[1,1],[1]]=>[2,2,2,2,1] [[3],[1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1,1] [[3],[2],[1],[1],[1],[1]]=>[3,2,1,1,1,1] [[3],[2],[2],[1],[1]]=>[3,2,2,1,1] [[3],[2],[2],[2]]=>[3,2,2,2] [[3],[3],[1],[1],[1]]=>[3,3,1,1,1] [[3],[3],[2],[1]]=>[3,3,2,1] [[3],[3],[3]]=>[3,3,3] [[2,1],[1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1,1] [[2,1],[2],[1],[1],[1],[1]]=>[3,2,1,1,1,1] [[2,1],[2],[2],[1],[1]]=>[3,2,2,1,1] [[2,1],[2],[2],[2]]=>[3,2,2,2] [[2,1],[1,1],[1],[1],[1],[1]]=>[3,2,1,1,1,1] [[2,1],[1,1],[1,1],[1],[1]]=>[3,2,2,1,1] [[2,1],[1,1],[1,1],[1,1]]=>[3,2,2,2] [[2,1],[2,1],[1],[1],[1]]=>[3,3,1,1,1] [[2,1],[2,1],[2],[1]]=>[3,3,2,1] [[2,1],[2,1],[1,1],[1]]=>[3,3,2,1] [[2,1],[2,1],[2,1]]=>[3,3,3] [[1,1,1],[1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1,1] [[1,1,1],[1,1],[1],[1],[1],[1]]=>[3,2,1,1,1,1] [[1,1,1],[1,1],[1,1],[1],[1]]=>[3,2,2,1,1] [[1,1,1],[1,1],[1,1],[1,1]]=>[3,2,2,2] [[1,1,1],[1,1,1],[1],[1],[1]]=>[3,3,1,1,1] [[1,1,1],[1,1,1],[1,1],[1]]=>[3,3,2,1] [[1,1,1],[1,1,1],[1,1,1]]=>[3,3,3] [[4],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1] [[4],[2],[1],[1],[1]]=>[4,2,1,1,1] [[4],[2],[2],[1]]=>[4,2,2,1] [[4],[3],[1],[1]]=>[4,3,1,1] [[4],[3],[2]]=>[4,3,2] [[4],[4],[1]]=>[4,4,1] [[3,1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1] [[3,1],[2],[1],[1],[1]]=>[4,2,1,1,1] [[3,1],[2],[2],[1]]=>[4,2,2,1] [[3,1],[1,1],[1],[1],[1]]=>[4,2,1,1,1] [[3,1],[1,1],[1,1],[1]]=>[4,2,2,1] [[3,1],[3],[1],[1]]=>[4,3,1,1] [[3,1],[3],[2]]=>[4,3,2] [[3,1],[2,1],[1],[1]]=>[4,3,1,1] [[3,1],[2,1],[2]]=>[4,3,2] [[3,1],[2,1],[1,1]]=>[4,3,2] [[3,1],[3,1],[1]]=>[4,4,1] [[2,2],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1] [[2,2],[2],[1],[1],[1]]=>[4,2,1,1,1] [[2,2],[2],[2],[1]]=>[4,2,2,1] [[2,2],[1,1],[1],[1],[1]]=>[4,2,1,1,1] [[2,2],[1,1],[1,1],[1]]=>[4,2,2,1] [[2,2],[2,1],[1],[1]]=>[4,3,1,1] [[2,2],[2,1],[2]]=>[4,3,2] [[2,2],[2,1],[1,1]]=>[4,3,2] [[2,2],[2,2],[1]]=>[4,4,1] [[2,1,1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1] [[2,1,1],[2],[1],[1],[1]]=>[4,2,1,1,1] [[2,1,1],[2],[2],[1]]=>[4,2,2,1] [[2,1,1],[1,1],[1],[1],[1]]=>[4,2,1,1,1] [[2,1,1],[1,1],[1,1],[1]]=>[4,2,2,1] [[2,1,1],[2,1],[1],[1]]=>[4,3,1,1] [[2,1,1],[2,1],[2]]=>[4,3,2] [[2,1,1],[2,1],[1,1]]=>[4,3,2] [[2,1,1],[1,1,1],[1],[1]]=>[4,3,1,1] [[2,1,1],[1,1,1],[1,1]]=>[4,3,2] [[2,1,1],[2,1,1],[1]]=>[4,4,1] [[1,1,1,1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1] [[1,1,1,1],[1,1],[1],[1],[1]]=>[4,2,1,1,1] [[1,1,1,1],[1,1],[1,1],[1]]=>[4,2,2,1] [[1,1,1,1],[1,1,1],[1],[1]]=>[4,3,1,1] [[1,1,1,1],[1,1,1],[1,1]]=>[4,3,2] [[1,1,1,1],[1,1,1,1],[1]]=>[4,4,1] [[5],[1],[1],[1],[1]]=>[5,1,1,1,1] [[5],[2],[1],[1]]=>[5,2,1,1] [[5],[2],[2]]=>[5,2,2] [[5],[3],[1]]=>[5,3,1] [[5],[4]]=>[5,4] [[4,1],[1],[1],[1],[1]]=>[5,1,1,1,1] [[4,1],[2],[1],[1]]=>[5,2,1,1] [[4,1],[2],[2]]=>[5,2,2] [[4,1],[1,1],[1],[1]]=>[5,2,1,1] [[4,1],[1,1],[1,1]]=>[5,2,2] [[4,1],[3],[1]]=>[5,3,1] [[4,1],[2,1],[1]]=>[5,3,1] [[4,1],[4]]=>[5,4] [[4,1],[3,1]]=>[5,4] [[3,2],[1],[1],[1],[1]]=>[5,1,1,1,1] [[3,2],[2],[1],[1]]=>[5,2,1,1] [[3,2],[2],[2]]=>[5,2,2] [[3,2],[1,1],[1],[1]]=>[5,2,1,1] [[3,2],[1,1],[1,1]]=>[5,2,2] [[3,2],[3],[1]]=>[5,3,1] [[3,2],[2,1],[1]]=>[5,3,1] [[3,2],[3,1]]=>[5,4] [[3,2],[2,2]]=>[5,4] [[3,1,1],[1],[1],[1],[1]]=>[5,1,1,1,1] [[3,1,1],[2],[1],[1]]=>[5,2,1,1] [[3,1,1],[2],[2]]=>[5,2,2] [[3,1,1],[1,1],[1],[1]]=>[5,2,1,1] [[3,1,1],[1,1],[1,1]]=>[5,2,2] [[3,1,1],[3],[1]]=>[5,3,1] [[3,1,1],[2,1],[1]]=>[5,3,1] [[3,1,1],[1,1,1],[1]]=>[5,3,1] [[3,1,1],[3,1]]=>[5,4] [[3,1,1],[2,1,1]]=>[5,4] [[2,2,1],[1],[1],[1],[1]]=>[5,1,1,1,1] [[2,2,1],[2],[1],[1]]=>[5,2,1,1] [[2,2,1],[2],[2]]=>[5,2,2] [[2,2,1],[1,1],[1],[1]]=>[5,2,1,1] [[2,2,1],[1,1],[1,1]]=>[5,2,2] [[2,2,1],[2,1],[1]]=>[5,3,1] [[2,2,1],[1,1,1],[1]]=>[5,3,1] [[2,2,1],[2,2]]=>[5,4] [[2,2,1],[2,1,1]]=>[5,4] [[2,1,1,1],[1],[1],[1],[1]]=>[5,1,1,1,1] [[2,1,1,1],[2],[1],[1]]=>[5,2,1,1] [[2,1,1,1],[2],[2]]=>[5,2,2] [[2,1,1,1],[1,1],[1],[1]]=>[5,2,1,1] [[2,1,1,1],[1,1],[1,1]]=>[5,2,2] [[2,1,1,1],[2,1],[1]]=>[5,3,1] [[2,1,1,1],[1,1,1],[1]]=>[5,3,1] [[2,1,1,1],[2,1,1]]=>[5,4] [[2,1,1,1],[1,1,1,1]]=>[5,4] [[1,1,1,1,1],[1],[1],[1],[1]]=>[5,1,1,1,1] [[1,1,1,1,1],[1,1],[1],[1]]=>[5,2,1,1] [[1,1,1,1,1],[1,1],[1,1]]=>[5,2,2] [[1,1,1,1,1],[1,1,1],[1]]=>[5,3,1] [[1,1,1,1,1],[1,1,1,1]]=>[5,4] [[6],[1],[1],[1]]=>[6,1,1,1] [[6],[2],[1]]=>[6,2,1] [[6],[3]]=>[6,3] [[5,1],[1],[1],[1]]=>[6,1,1,1] [[5,1],[2],[1]]=>[6,2,1] [[5,1],[1,1],[1]]=>[6,2,1] [[5,1],[3]]=>[6,3] [[5,1],[2,1]]=>[6,3] [[4,2],[1],[1],[1]]=>[6,1,1,1] [[4,2],[2],[1]]=>[6,2,1] [[4,2],[1,1],[1]]=>[6,2,1] [[4,2],[3]]=>[6,3] [[4,2],[2,1]]=>[6,3] [[4,1,1],[1],[1],[1]]=>[6,1,1,1] [[4,1,1],[2],[1]]=>[6,2,1] [[4,1,1],[1,1],[1]]=>[6,2,1] [[4,1,1],[3]]=>[6,3] [[4,1,1],[2,1]]=>[6,3] [[4,1,1],[1,1,1]]=>[6,3] [[3,3],[1],[1],[1]]=>[6,1,1,1] [[3,3],[2],[1]]=>[6,2,1] [[3,3],[1,1],[1]]=>[6,2,1] [[3,3],[3]]=>[6,3] [[3,3],[2,1]]=>[6,3] [[3,2,1],[1],[1],[1]]=>[6,1,1,1] [[3,2,1],[2],[1]]=>[6,2,1] [[3,2,1],[1,1],[1]]=>[6,2,1] [[3,2,1],[3]]=>[6,3] [[3,2,1],[2,1]]=>[6,3] [[3,2,1],[1,1,1]]=>[6,3] [[3,1,1,1],[1],[1],[1]]=>[6,1,1,1] [[3,1,1,1],[2],[1]]=>[6,2,1] [[3,1,1,1],[1,1],[1]]=>[6,2,1] [[3,1,1,1],[3]]=>[6,3] [[3,1,1,1],[2,1]]=>[6,3] [[3,1,1,1],[1,1,1]]=>[6,3] [[2,2,2],[1],[1],[1]]=>[6,1,1,1] [[2,2,2],[2],[1]]=>[6,2,1] [[2,2,2],[1,1],[1]]=>[6,2,1] [[2,2,2],[2,1]]=>[6,3] [[2,2,2],[1,1,1]]=>[6,3] [[2,2,1,1],[1],[1],[1]]=>[6,1,1,1] [[2,2,1,1],[2],[1]]=>[6,2,1] [[2,2,1,1],[1,1],[1]]=>[6,2,1] [[2,2,1,1],[2,1]]=>[6,3] [[2,2,1,1],[1,1,1]]=>[6,3] [[2,1,1,1,1],[1],[1],[1]]=>[6,1,1,1] [[2,1,1,1,1],[2],[1]]=>[6,2,1] [[2,1,1,1,1],[1,1],[1]]=>[6,2,1] [[2,1,1,1,1],[2,1]]=>[6,3] [[2,1,1,1,1],[1,1,1]]=>[6,3] [[1,1,1,1,1,1],[1],[1],[1]]=>[6,1,1,1] [[1,1,1,1,1,1],[1,1],[1]]=>[6,2,1] [[1,1,1,1,1,1],[1,1,1]]=>[6,3] [[7],[1],[1]]=>[7,1,1] [[7],[2]]=>[7,2] [[6,1],[1],[1]]=>[7,1,1] [[6,1],[2]]=>[7,2] [[6,1],[1,1]]=>[7,2] [[5,2],[1],[1]]=>[7,1,1] [[5,2],[2]]=>[7,2] [[5,2],[1,1]]=>[7,2] [[5,1,1],[1],[1]]=>[7,1,1] [[5,1,1],[2]]=>[7,2] [[5,1,1],[1,1]]=>[7,2] [[4,3],[1],[1]]=>[7,1,1] [[4,3],[2]]=>[7,2] [[4,3],[1,1]]=>[7,2] [[4,2,1],[1],[1]]=>[7,1,1] [[4,2,1],[2]]=>[7,2] [[4,2,1],[1,1]]=>[7,2] [[4,1,1,1],[1],[1]]=>[7,1,1] [[4,1,1,1],[2]]=>[7,2] [[4,1,1,1],[1,1]]=>[7,2] [[3,3,1],[1],[1]]=>[7,1,1] [[3,3,1],[2]]=>[7,2] [[3,3,1],[1,1]]=>[7,2] [[3,2,2],[1],[1]]=>[7,1,1] [[3,2,2],[2]]=>[7,2] [[3,2,2],[1,1]]=>[7,2] [[3,2,1,1],[1],[1]]=>[7,1,1] [[3,2,1,1],[2]]=>[7,2] [[3,2,1,1],[1,1]]=>[7,2] [[3,1,1,1,1],[1],[1]]=>[7,1,1] [[3,1,1,1,1],[2]]=>[7,2] [[3,1,1,1,1],[1,1]]=>[7,2] [[2,2,2,1],[1],[1]]=>[7,1,1] [[2,2,2,1],[2]]=>[7,2] [[2,2,2,1],[1,1]]=>[7,2] [[2,2,1,1,1],[1],[1]]=>[7,1,1] [[2,2,1,1,1],[2]]=>[7,2] [[2,2,1,1,1],[1,1]]=>[7,2] [[2,1,1,1,1,1],[1],[1]]=>[7,1,1] [[2,1,1,1,1,1],[2]]=>[7,2] [[2,1,1,1,1,1],[1,1]]=>[7,2] [[1,1,1,1,1,1,1],[1],[1]]=>[7,1,1] [[1,1,1,1,1,1,1],[1,1]]=>[7,2] [[8],[1]]=>[8,1] [[7,1],[1]]=>[8,1] [[6,2],[1]]=>[8,1] [[6,1,1],[1]]=>[8,1] [[5,3],[1]]=>[8,1] [[5,2,1],[1]]=>[8,1] [[5,1,1,1],[1]]=>[8,1] [[4,4],[1]]=>[8,1] [[4,3,1],[1]]=>[8,1] [[4,2,2],[1]]=>[8,1] [[4,2,1,1],[1]]=>[8,1] [[4,1,1,1,1],[1]]=>[8,1] [[3,3,2],[1]]=>[8,1] [[3,3,1,1],[1]]=>[8,1] [[3,2,2,1],[1]]=>[8,1] [[3,2,1,1,1],[1]]=>[8,1] [[3,1,1,1,1,1],[1]]=>[8,1] [[2,2,2,2],[1]]=>[8,1] [[2,2,2,1,1],[1]]=>[8,1] [[2,2,1,1,1,1],[1]]=>[8,1] [[2,1,1,1,1,1,1],[1]]=>[8,1] [[1,1,1,1,1,1,1,1],[1]]=>[8,1] [[9]]=>[9] [[8,1]]=>[9] [[7,2]]=>[9] [[7,1,1]]=>[9] [[6,3]]=>[9] [[6,2,1]]=>[9] [[6,1,1,1]]=>[9] [[5,4]]=>[9] [[5,3,1]]=>[9] [[5,2,2]]=>[9] [[5,2,1,1]]=>[9] [[5,1,1,1,1]]=>[9] [[4,4,1]]=>[9] [[4,3,2]]=>[9] [[4,3,1,1]]=>[9] [[4,2,2,1]]=>[9] [[4,2,1,1,1]]=>[9] [[4,1,1,1,1,1]]=>[9] [[3,3,3]]=>[9] [[3,3,2,1]]=>[9] [[3,3,1,1,1]]=>[9] [[3,2,2,2]]=>[9] [[3,2,2,1,1]]=>[9] [[3,2,1,1,1,1]]=>[9] [[3,1,1,1,1,1,1]]=>[9] [[2,2,2,2,1]]=>[9] [[2,2,2,1,1,1]]=>[9] [[2,2,1,1,1,1,1]]=>[9] [[2,1,1,1,1,1,1,1]]=>[9] [[1,1,1,1,1,1,1,1,1]]=>[9] [[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]]=>[1,1,1,1,1,1,1,1,1,1] [[2],[1],[1],[1],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1,1,1,1] [[2],[2],[1],[1],[1],[1],[1],[1]]=>[2,2,1,1,1,1,1,1] [[2],[2],[2],[1],[1],[1],[1]]=>[2,2,2,1,1,1,1] [[2],[2],[2],[2],[1],[1]]=>[2,2,2,2,1,1] [[2],[2],[2],[2],[2]]=>[2,2,2,2,2] [[1,1],[1],[1],[1],[1],[1],[1],[1],[1]]=>[2,1,1,1,1,1,1,1,1] [[1,1],[1,1],[1],[1],[1],[1],[1],[1]]=>[2,2,1,1,1,1,1,1] [[1,1],[1,1],[1,1],[1],[1],[1],[1]]=>[2,2,2,1,1,1,1] [[1,1],[1,1],[1,1],[1,1],[1],[1]]=>[2,2,2,2,1,1] [[1,1],[1,1],[1,1],[1,1],[1,1]]=>[2,2,2,2,2] [[3],[1],[1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1,1,1] [[3],[2],[1],[1],[1],[1],[1]]=>[3,2,1,1,1,1,1] [[3],[2],[2],[1],[1],[1]]=>[3,2,2,1,1,1] [[3],[2],[2],[2],[1]]=>[3,2,2,2,1] [[3],[3],[1],[1],[1],[1]]=>[3,3,1,1,1,1] [[3],[3],[2],[1],[1]]=>[3,3,2,1,1] [[3],[3],[2],[2]]=>[3,3,2,2] [[3],[3],[3],[1]]=>[3,3,3,1] [[2,1],[1],[1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1,1,1] [[2,1],[2],[1],[1],[1],[1],[1]]=>[3,2,1,1,1,1,1] [[2,1],[2],[2],[1],[1],[1]]=>[3,2,2,1,1,1] [[2,1],[2],[2],[2],[1]]=>[3,2,2,2,1] [[2,1],[1,1],[1],[1],[1],[1],[1]]=>[3,2,1,1,1,1,1] [[2,1],[1,1],[1,1],[1],[1],[1]]=>[3,2,2,1,1,1] [[2,1],[1,1],[1,1],[1,1],[1]]=>[3,2,2,2,1] [[2,1],[2,1],[1],[1],[1],[1]]=>[3,3,1,1,1,1] [[2,1],[2,1],[2],[1],[1]]=>[3,3,2,1,1] [[2,1],[2,1],[2],[2]]=>[3,3,2,2] [[2,1],[2,1],[1,1],[1],[1]]=>[3,3,2,1,1] [[2,1],[2,1],[1,1],[1,1]]=>[3,3,2,2] [[2,1],[2,1],[2,1],[1]]=>[3,3,3,1] [[1,1,1],[1],[1],[1],[1],[1],[1],[1]]=>[3,1,1,1,1,1,1,1] [[1,1,1],[1,1],[1],[1],[1],[1],[1]]=>[3,2,1,1,1,1,1] [[1,1,1],[1,1],[1,1],[1],[1],[1]]=>[3,2,2,1,1,1] [[1,1,1],[1,1],[1,1],[1,1],[1]]=>[3,2,2,2,1] [[1,1,1],[1,1,1],[1],[1],[1],[1]]=>[3,3,1,1,1,1] [[1,1,1],[1,1,1],[1,1],[1],[1]]=>[3,3,2,1,1] [[1,1,1],[1,1,1],[1,1],[1,1]]=>[3,3,2,2] [[1,1,1],[1,1,1],[1,1,1],[1]]=>[3,3,3,1] [[4],[1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1,1] [[4],[2],[1],[1],[1],[1]]=>[4,2,1,1,1,1] [[4],[2],[2],[1],[1]]=>[4,2,2,1,1] [[4],[2],[2],[2]]=>[4,2,2,2] [[4],[3],[1],[1],[1]]=>[4,3,1,1,1] [[4],[3],[2],[1]]=>[4,3,2,1] [[4],[3],[3]]=>[4,3,3] [[4],[4],[1],[1]]=>[4,4,1,1] [[4],[4],[2]]=>[4,4,2] [[3,1],[1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1,1] [[3,1],[2],[1],[1],[1],[1]]=>[4,2,1,1,1,1] [[3,1],[2],[2],[1],[1]]=>[4,2,2,1,1] [[3,1],[2],[2],[2]]=>[4,2,2,2] [[3,1],[1,1],[1],[1],[1],[1]]=>[4,2,1,1,1,1] [[3,1],[1,1],[1,1],[1],[1]]=>[4,2,2,1,1] [[3,1],[1,1],[1,1],[1,1]]=>[4,2,2,2] [[3,1],[3],[1],[1],[1]]=>[4,3,1,1,1] [[3,1],[3],[2],[1]]=>[4,3,2,1] [[3,1],[3],[3]]=>[4,3,3] [[3,1],[2,1],[1],[1],[1]]=>[4,3,1,1,1] [[3,1],[2,1],[2],[1]]=>[4,3,2,1] [[3,1],[2,1],[1,1],[1]]=>[4,3,2,1] [[3,1],[2,1],[2,1]]=>[4,3,3] [[3,1],[3,1],[1],[1]]=>[4,4,1,1] [[3,1],[3,1],[2]]=>[4,4,2] [[3,1],[3,1],[1,1]]=>[4,4,2] [[2,2],[1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1,1] [[2,2],[2],[1],[1],[1],[1]]=>[4,2,1,1,1,1] [[2,2],[2],[2],[1],[1]]=>[4,2,2,1,1] [[2,2],[2],[2],[2]]=>[4,2,2,2] [[2,2],[1,1],[1],[1],[1],[1]]=>[4,2,1,1,1,1] [[2,2],[1,1],[1,1],[1],[1]]=>[4,2,2,1,1] [[2,2],[1,1],[1,1],[1,1]]=>[4,2,2,2] [[2,2],[2,1],[1],[1],[1]]=>[4,3,1,1,1] [[2,2],[2,1],[2],[1]]=>[4,3,2,1] [[2,2],[2,1],[1,1],[1]]=>[4,3,2,1] [[2,2],[2,1],[2,1]]=>[4,3,3] [[2,2],[2,2],[1],[1]]=>[4,4,1,1] [[2,2],[2,2],[2]]=>[4,4,2] [[2,2],[2,2],[1,1]]=>[4,4,2] [[2,1,1],[1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1,1] [[2,1,1],[2],[1],[1],[1],[1]]=>[4,2,1,1,1,1] [[2,1,1],[2],[2],[1],[1]]=>[4,2,2,1,1] [[2,1,1],[2],[2],[2]]=>[4,2,2,2] [[2,1,1],[1,1],[1],[1],[1],[1]]=>[4,2,1,1,1,1] [[2,1,1],[1,1],[1,1],[1],[1]]=>[4,2,2,1,1] [[2,1,1],[1,1],[1,1],[1,1]]=>[4,2,2,2] [[2,1,1],[2,1],[1],[1],[1]]=>[4,3,1,1,1] [[2,1,1],[2,1],[2],[1]]=>[4,3,2,1] [[2,1,1],[2,1],[1,1],[1]]=>[4,3,2,1] [[2,1,1],[2,1],[2,1]]=>[4,3,3] [[2,1,1],[1,1,1],[1],[1],[1]]=>[4,3,1,1,1] [[2,1,1],[1,1,1],[1,1],[1]]=>[4,3,2,1] [[2,1,1],[1,1,1],[1,1,1]]=>[4,3,3] [[2,1,1],[2,1,1],[1],[1]]=>[4,4,1,1] [[2,1,1],[2,1,1],[2]]=>[4,4,2] [[2,1,1],[2,1,1],[1,1]]=>[4,4,2] [[1,1,1,1],[1],[1],[1],[1],[1],[1]]=>[4,1,1,1,1,1,1] [[1,1,1,1],[1,1],[1],[1],[1],[1]]=>[4,2,1,1,1,1] [[1,1,1,1],[1,1],[1,1],[1],[1]]=>[4,2,2,1,1] [[1,1,1,1],[1,1],[1,1],[1,1]]=>[4,2,2,2] [[1,1,1,1],[1,1,1],[1],[1],[1]]=>[4,3,1,1,1] [[1,1,1,1],[1,1,1],[1,1],[1]]=>[4,3,2,1] [[1,1,1,1],[1,1,1],[1,1,1]]=>[4,3,3] [[1,1,1,1],[1,1,1,1],[1],[1]]=>[4,4,1,1] [[1,1,1,1],[1,1,1,1],[1,1]]=>[4,4,2] [[5],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1] [[5],[2],[1],[1],[1]]=>[5,2,1,1,1] [[5],[2],[2],[1]]=>[5,2,2,1] [[5],[3],[1],[1]]=>[5,3,1,1] [[5],[3],[2]]=>[5,3,2] [[5],[4],[1]]=>[5,4,1] [[5],[5]]=>[5,5] [[4,1],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1] [[4,1],[2],[1],[1],[1]]=>[5,2,1,1,1] [[4,1],[2],[2],[1]]=>[5,2,2,1] [[4,1],[1,1],[1],[1],[1]]=>[5,2,1,1,1] [[4,1],[1,1],[1,1],[1]]=>[5,2,2,1] [[4,1],[3],[1],[1]]=>[5,3,1,1] [[4,1],[3],[2]]=>[5,3,2] [[4,1],[2,1],[1],[1]]=>[5,3,1,1] [[4,1],[2,1],[2]]=>[5,3,2] [[4,1],[2,1],[1,1]]=>[5,3,2] [[4,1],[4],[1]]=>[5,4,1] [[4,1],[3,1],[1]]=>[5,4,1] [[4,1],[4,1]]=>[5,5] [[3,2],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1] [[3,2],[2],[1],[1],[1]]=>[5,2,1,1,1] [[3,2],[2],[2],[1]]=>[5,2,2,1] [[3,2],[1,1],[1],[1],[1]]=>[5,2,1,1,1] [[3,2],[1,1],[1,1],[1]]=>[5,2,2,1] [[3,2],[3],[1],[1]]=>[5,3,1,1] [[3,2],[3],[2]]=>[5,3,2] [[3,2],[2,1],[1],[1]]=>[5,3,1,1] [[3,2],[2,1],[2]]=>[5,3,2] [[3,2],[2,1],[1,1]]=>[5,3,2] [[3,2],[3,1],[1]]=>[5,4,1] [[3,2],[2,2],[1]]=>[5,4,1] [[3,2],[3,2]]=>[5,5] [[3,1,1],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1] [[3,1,1],[2],[1],[1],[1]]=>[5,2,1,1,1] [[3,1,1],[2],[2],[1]]=>[5,2,2,1] [[3,1,1],[1,1],[1],[1],[1]]=>[5,2,1,1,1] [[3,1,1],[1,1],[1,1],[1]]=>[5,2,2,1] [[3,1,1],[3],[1],[1]]=>[5,3,1,1] [[3,1,1],[3],[2]]=>[5,3,2] [[3,1,1],[2,1],[1],[1]]=>[5,3,1,1] [[3,1,1],[2,1],[2]]=>[5,3,2] [[3,1,1],[2,1],[1,1]]=>[5,3,2] [[3,1,1],[1,1,1],[1],[1]]=>[5,3,1,1] [[3,1,1],[1,1,1],[1,1]]=>[5,3,2] [[3,1,1],[3,1],[1]]=>[5,4,1] [[3,1,1],[2,1,1],[1]]=>[5,4,1] [[3,1,1],[3,1,1]]=>[5,5] [[2,2,1],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1] [[2,2,1],[2],[1],[1],[1]]=>[5,2,1,1,1] [[2,2,1],[2],[2],[1]]=>[5,2,2,1] [[2,2,1],[1,1],[1],[1],[1]]=>[5,2,1,1,1] [[2,2,1],[1,1],[1,1],[1]]=>[5,2,2,1] [[2,2,1],[2,1],[1],[1]]=>[5,3,1,1] [[2,2,1],[2,1],[2]]=>[5,3,2] [[2,2,1],[2,1],[1,1]]=>[5,3,2] [[2,2,1],[1,1,1],[1],[1]]=>[5,3,1,1] [[2,2,1],[1,1,1],[1,1]]=>[5,3,2] [[2,2,1],[2,2],[1]]=>[5,4,1] [[2,2,1],[2,1,1],[1]]=>[5,4,1] [[2,2,1],[2,2,1]]=>[5,5] [[2,1,1,1],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1] [[2,1,1,1],[2],[1],[1],[1]]=>[5,2,1,1,1] [[2,1,1,1],[2],[2],[1]]=>[5,2,2,1] [[2,1,1,1],[1,1],[1],[1],[1]]=>[5,2,1,1,1] [[2,1,1,1],[1,1],[1,1],[1]]=>[5,2,2,1] [[2,1,1,1],[2,1],[1],[1]]=>[5,3,1,1] [[2,1,1,1],[2,1],[2]]=>[5,3,2] [[2,1,1,1],[2,1],[1,1]]=>[5,3,2] [[2,1,1,1],[1,1,1],[1],[1]]=>[5,3,1,1] [[2,1,1,1],[1,1,1],[1,1]]=>[5,3,2] [[2,1,1,1],[2,1,1],[1]]=>[5,4,1] [[2,1,1,1],[1,1,1,1],[1]]=>[5,4,1] [[2,1,1,1],[2,1,1,1]]=>[5,5] [[1,1,1,1,1],[1],[1],[1],[1],[1]]=>[5,1,1,1,1,1] [[1,1,1,1,1],[1,1],[1],[1],[1]]=>[5,2,1,1,1] [[1,1,1,1,1],[1,1],[1,1],[1]]=>[5,2,2,1] [[1,1,1,1,1],[1,1,1],[1],[1]]=>[5,3,1,1] [[1,1,1,1,1],[1,1,1],[1,1]]=>[5,3,2] [[1,1,1,1,1],[1,1,1,1],[1]]=>[5,4,1] [[1,1,1,1,1],[1,1,1,1,1]]=>[5,5] [[6],[1],[1],[1],[1]]=>[6,1,1,1,1] [[6],[2],[1],[1]]=>[6,2,1,1] [[6],[2],[2]]=>[6,2,2] [[6],[3],[1]]=>[6,3,1] [[6],[4]]=>[6,4] [[5,1],[1],[1],[1],[1]]=>[6,1,1,1,1] [[5,1],[2],[1],[1]]=>[6,2,1,1] [[5,1],[2],[2]]=>[6,2,2] [[5,1],[1,1],[1],[1]]=>[6,2,1,1] [[5,1],[1,1],[1,1]]=>[6,2,2] [[5,1],[3],[1]]=>[6,3,1] [[5,1],[2,1],[1]]=>[6,3,1] [[5,1],[4]]=>[6,4] [[5,1],[3,1]]=>[6,4] [[4,2],[1],[1],[1],[1]]=>[6,1,1,1,1] [[4,2],[2],[1],[1]]=>[6,2,1,1] [[4,2],[2],[2]]=>[6,2,2] [[4,2],[1,1],[1],[1]]=>[6,2,1,1] [[4,2],[1,1],[1,1]]=>[6,2,2] [[4,2],[3],[1]]=>[6,3,1] [[4,2],[2,1],[1]]=>[6,3,1] [[4,2],[4]]=>[6,4] [[4,2],[3,1]]=>[6,4] [[4,2],[2,2]]=>[6,4] [[4,1,1],[1],[1],[1],[1]]=>[6,1,1,1,1] [[4,1,1],[2],[1],[1]]=>[6,2,1,1] [[4,1,1],[2],[2]]=>[6,2,2] [[4,1,1],[1,1],[1],[1]]=>[6,2,1,1] [[4,1,1],[1,1],[1,1]]=>[6,2,2] [[4,1,1],[3],[1]]=>[6,3,1] [[4,1,1],[2,1],[1]]=>[6,3,1] [[4,1,1],[1,1,1],[1]]=>[6,3,1] [[4,1,1],[4]]=>[6,4] [[4,1,1],[3,1]]=>[6,4] [[4,1,1],[2,1,1]]=>[6,4] [[3,3],[1],[1],[1],[1]]=>[6,1,1,1,1] [[3,3],[2],[1],[1]]=>[6,2,1,1] [[3,3],[2],[2]]=>[6,2,2] [[3,3],[1,1],[1],[1]]=>[6,2,1,1] [[3,3],[1,1],[1,1]]=>[6,2,2] [[3,3],[3],[1]]=>[6,3,1] [[3,3],[2,1],[1]]=>[6,3,1] [[3,3],[3,1]]=>[6,4] [[3,3],[2,2]]=>[6,4] [[3,2,1],[1],[1],[1],[1]]=>[6,1,1,1,1] [[3,2,1],[2],[1],[1]]=>[6,2,1,1] [[3,2,1],[2],[2]]=>[6,2,2] [[3,2,1],[1,1],[1],[1]]=>[6,2,1,1] [[3,2,1],[1,1],[1,1]]=>[6,2,2] [[3,2,1],[3],[1]]=>[6,3,1] [[3,2,1],[2,1],[1]]=>[6,3,1] [[3,2,1],[1,1,1],[1]]=>[6,3,1] [[3,2,1],[3,1]]=>[6,4] [[3,2,1],[2,2]]=>[6,4] [[3,2,1],[2,1,1]]=>[6,4] [[3,1,1,1],[1],[1],[1],[1]]=>[6,1,1,1,1] [[3,1,1,1],[2],[1],[1]]=>[6,2,1,1] [[3,1,1,1],[2],[2]]=>[6,2,2] [[3,1,1,1],[1,1],[1],[1]]=>[6,2,1,1] [[3,1,1,1],[1,1],[1,1]]=>[6,2,2] [[3,1,1,1],[3],[1]]=>[6,3,1] [[3,1,1,1],[2,1],[1]]=>[6,3,1] [[3,1,1,1],[1,1,1],[1]]=>[6,3,1] [[3,1,1,1],[3,1]]=>[6,4] [[3,1,1,1],[2,1,1]]=>[6,4] [[3,1,1,1],[1,1,1,1]]=>[6,4] [[2,2,2],[1],[1],[1],[1]]=>[6,1,1,1,1] [[2,2,2],[2],[1],[1]]=>[6,2,1,1] [[2,2,2],[2],[2]]=>[6,2,2] [[2,2,2],[1,1],[1],[1]]=>[6,2,1,1] [[2,2,2],[1,1],[1,1]]=>[6,2,2] [[2,2,2],[2,1],[1]]=>[6,3,1] [[2,2,2],[1,1,1],[1]]=>[6,3,1] [[2,2,2],[2,2]]=>[6,4] [[2,2,2],[2,1,1]]=>[6,4] [[2,2,1,1],[1],[1],[1],[1]]=>[6,1,1,1,1] [[2,2,1,1],[2],[1],[1]]=>[6,2,1,1] [[2,2,1,1],[2],[2]]=>[6,2,2] [[2,2,1,1],[1,1],[1],[1]]=>[6,2,1,1] [[2,2,1,1],[1,1],[1,1]]=>[6,2,2] [[2,2,1,1],[2,1],[1]]=>[6,3,1] [[2,2,1,1],[1,1,1],[1]]=>[6,3,1] [[2,2,1,1],[2,2]]=>[6,4] [[2,2,1,1],[2,1,1]]=>[6,4] [[2,2,1,1],[1,1,1,1]]=>[6,4] [[2,1,1,1,1],[1],[1],[1],[1]]=>[6,1,1,1,1] [[2,1,1,1,1],[2],[1],[1]]=>[6,2,1,1] [[2,1,1,1,1],[2],[2]]=>[6,2,2] [[2,1,1,1,1],[1,1],[1],[1]]=>[6,2,1,1] [[2,1,1,1,1],[1,1],[1,1]]=>[6,2,2] [[2,1,1,1,1],[2,1],[1]]=>[6,3,1] [[2,1,1,1,1],[1,1,1],[1]]=>[6,3,1] [[2,1,1,1,1],[2,1,1]]=>[6,4] [[2,1,1,1,1],[1,1,1,1]]=>[6,4] [[1,1,1,1,1,1],[1],[1],[1],[1]]=>[6,1,1,1,1] [[1,1,1,1,1,1],[1,1],[1],[1]]=>[6,2,1,1] [[1,1,1,1,1,1],[1,1],[1,1]]=>[6,2,2] [[1,1,1,1,1,1],[1,1,1],[1]]=>[6,3,1] [[1,1,1,1,1,1],[1,1,1,1]]=>[6,4] [[7],[1],[1],[1]]=>[7,1,1,1] [[7],[2],[1]]=>[7,2,1] [[7],[3]]=>[7,3] [[6,1],[1],[1],[1]]=>[7,1,1,1] [[6,1],[2],[1]]=>[7,2,1] [[6,1],[1,1],[1]]=>[7,2,1] [[6,1],[3]]=>[7,3] [[6,1],[2,1]]=>[7,3] [[5,2],[1],[1],[1]]=>[7,1,1,1] [[5,2],[2],[1]]=>[7,2,1] [[5,2],[1,1],[1]]=>[7,2,1] [[5,2],[3]]=>[7,3] [[5,2],[2,1]]=>[7,3] [[5,1,1],[1],[1],[1]]=>[7,1,1,1] [[5,1,1],[2],[1]]=>[7,2,1] [[5,1,1],[1,1],[1]]=>[7,2,1] [[5,1,1],[3]]=>[7,3] [[5,1,1],[2,1]]=>[7,3] [[5,1,1],[1,1,1]]=>[7,3] [[4,3],[1],[1],[1]]=>[7,1,1,1] [[4,3],[2],[1]]=>[7,2,1] [[4,3],[1,1],[1]]=>[7,2,1] [[4,3],[3]]=>[7,3] [[4,3],[2,1]]=>[7,3] [[4,2,1],[1],[1],[1]]=>[7,1,1,1] [[4,2,1],[2],[1]]=>[7,2,1] [[4,2,1],[1,1],[1]]=>[7,2,1] [[4,2,1],[3]]=>[7,3] [[4,2,1],[2,1]]=>[7,3] [[4,2,1],[1,1,1]]=>[7,3] [[4,1,1,1],[1],[1],[1]]=>[7,1,1,1] [[4,1,1,1],[2],[1]]=>[7,2,1] [[4,1,1,1],[1,1],[1]]=>[7,2,1] [[4,1,1,1],[3]]=>[7,3] [[4,1,1,1],[2,1]]=>[7,3] [[4,1,1,1],[1,1,1]]=>[7,3] [[3,3,1],[1],[1],[1]]=>[7,1,1,1] [[3,3,1],[2],[1]]=>[7,2,1] [[3,3,1],[1,1],[1]]=>[7,2,1] [[3,3,1],[3]]=>[7,3] [[3,3,1],[2,1]]=>[7,3] [[3,3,1],[1,1,1]]=>[7,3] [[3,2,2],[1],[1],[1]]=>[7,1,1,1] [[3,2,2],[2],[1]]=>[7,2,1] [[3,2,2],[1,1],[1]]=>[7,2,1] [[3,2,2],[3]]=>[7,3] [[3,2,2],[2,1]]=>[7,3] [[3,2,2],[1,1,1]]=>[7,3] [[3,2,1,1],[1],[1],[1]]=>[7,1,1,1] [[3,2,1,1],[2],[1]]=>[7,2,1] [[3,2,1,1],[1,1],[1]]=>[7,2,1] [[3,2,1,1],[3]]=>[7,3] [[3,2,1,1],[2,1]]=>[7,3] [[3,2,1,1],[1,1,1]]=>[7,3] [[3,1,1,1,1],[1],[1],[1]]=>[7,1,1,1] [[3,1,1,1,1],[2],[1]]=>[7,2,1] [[3,1,1,1,1],[1,1],[1]]=>[7,2,1] [[3,1,1,1,1],[3]]=>[7,3] [[3,1,1,1,1],[2,1]]=>[7,3] [[3,1,1,1,1],[1,1,1]]=>[7,3] [[2,2,2,1],[1],[1],[1]]=>[7,1,1,1] [[2,2,2,1],[2],[1]]=>[7,2,1] [[2,2,2,1],[1,1],[1]]=>[7,2,1] [[2,2,2,1],[2,1]]=>[7,3] [[2,2,2,1],[1,1,1]]=>[7,3] [[2,2,1,1,1],[1],[1],[1]]=>[7,1,1,1] [[2,2,1,1,1],[2],[1]]=>[7,2,1] [[2,2,1,1,1],[1,1],[1]]=>[7,2,1] [[2,2,1,1,1],[2,1]]=>[7,3] [[2,2,1,1,1],[1,1,1]]=>[7,3] [[2,1,1,1,1,1],[1],[1],[1]]=>[7,1,1,1] [[2,1,1,1,1,1],[2],[1]]=>[7,2,1] [[2,1,1,1,1,1],[1,1],[1]]=>[7,2,1] [[2,1,1,1,1,1],[2,1]]=>[7,3] [[2,1,1,1,1,1],[1,1,1]]=>[7,3] [[1,1,1,1,1,1,1],[1],[1],[1]]=>[7,1,1,1] [[1,1,1,1,1,1,1],[1,1],[1]]=>[7,2,1] [[1,1,1,1,1,1,1],[1,1,1]]=>[7,3] [[8],[1],[1]]=>[8,1,1] [[8],[2]]=>[8,2] [[7,1],[1],[1]]=>[8,1,1] [[7,1],[2]]=>[8,2] [[7,1],[1,1]]=>[8,2] [[6,2],[1],[1]]=>[8,1,1] [[6,2],[2]]=>[8,2] [[6,2],[1,1]]=>[8,2] [[6,1,1],[1],[1]]=>[8,1,1] [[6,1,1],[2]]=>[8,2] [[6,1,1],[1,1]]=>[8,2] [[5,3],[1],[1]]=>[8,1,1] [[5,3],[2]]=>[8,2] [[5,3],[1,1]]=>[8,2] [[5,2,1],[1],[1]]=>[8,1,1] [[5,2,1],[2]]=>[8,2] [[5,2,1],[1,1]]=>[8,2] [[5,1,1,1],[1],[1]]=>[8,1,1] [[5,1,1,1],[2]]=>[8,2] [[5,1,1,1],[1,1]]=>[8,2] [[4,4],[1],[1]]=>[8,1,1] [[4,4],[2]]=>[8,2] [[4,4],[1,1]]=>[8,2] [[4,3,1],[1],[1]]=>[8,1,1] [[4,3,1],[2]]=>[8,2] [[4,3,1],[1,1]]=>[8,2] [[4,2,2],[1],[1]]=>[8,1,1] [[4,2,2],[2]]=>[8,2] [[4,2,2],[1,1]]=>[8,2] [[4,2,1,1],[1],[1]]=>[8,1,1] [[4,2,1,1],[2]]=>[8,2] [[4,2,1,1],[1,1]]=>[8,2] [[4,1,1,1,1],[1],[1]]=>[8,1,1] [[4,1,1,1,1],[2]]=>[8,2] [[4,1,1,1,1],[1,1]]=>[8,2] [[3,3,2],[1],[1]]=>[8,1,1] [[3,3,2],[2]]=>[8,2] [[3,3,2],[1,1]]=>[8,2] [[3,3,1,1],[1],[1]]=>[8,1,1] [[3,3,1,1],[2]]=>[8,2] [[3,3,1,1],[1,1]]=>[8,2] [[3,2,2,1],[1],[1]]=>[8,1,1] [[3,2,2,1],[2]]=>[8,2] [[3,2,2,1],[1,1]]=>[8,2] [[3,2,1,1,1],[1],[1]]=>[8,1,1] [[3,2,1,1,1],[2]]=>[8,2] [[3,2,1,1,1],[1,1]]=>[8,2] [[3,1,1,1,1,1],[1],[1]]=>[8,1,1] [[3,1,1,1,1,1],[2]]=>[8,2] [[3,1,1,1,1,1],[1,1]]=>[8,2] [[2,2,2,2],[1],[1]]=>[8,1,1] [[2,2,2,2],[2]]=>[8,2] [[2,2,2,2],[1,1]]=>[8,2] [[2,2,2,1,1],[1],[1]]=>[8,1,1] [[2,2,2,1,1],[2]]=>[8,2] [[2,2,2,1,1],[1,1]]=>[8,2] [[2,2,1,1,1,1],[1],[1]]=>[8,1,1] [[2,2,1,1,1,1],[2]]=>[8,2] [[2,2,1,1,1,1],[1,1]]=>[8,2] [[2,1,1,1,1,1,1],[1],[1]]=>[8,1,1] [[2,1,1,1,1,1,1],[2]]=>[8,2] [[2,1,1,1,1,1,1],[1,1]]=>[8,2] [[1,1,1,1,1,1,1,1],[1],[1]]=>[8,1,1] [[1,1,1,1,1,1,1,1],[1,1]]=>[8,2] [[9],[1]]=>[9,1] [[8,1],[1]]=>[9,1] [[7,2],[1]]=>[9,1] [[7,1,1],[1]]=>[9,1] [[6,3],[1]]=>[9,1] [[6,2,1],[1]]=>[9,1] [[6,1,1,1],[1]]=>[9,1] [[5,4],[1]]=>[9,1] [[5,3,1],[1]]=>[9,1] [[5,2,2],[1]]=>[9,1] [[5,2,1,1],[1]]=>[9,1] [[5,1,1,1,1],[1]]=>[9,1] [[4,4,1],[1]]=>[9,1] [[4,3,2],[1]]=>[9,1] [[4,3,1,1],[1]]=>[9,1] [[4,2,2,1],[1]]=>[9,1] [[4,2,1,1,1],[1]]=>[9,1] [[4,1,1,1,1,1],[1]]=>[9,1] [[3,3,3],[1]]=>[9,1] [[3,3,2,1],[1]]=>[9,1] [[3,3,1,1,1],[1]]=>[9,1] [[3,2,2,2],[1]]=>[9,1] [[3,2,2,1,1],[1]]=>[9,1] [[3,2,1,1,1,1],[1]]=>[9,1] [[3,1,1,1,1,1,1],[1]]=>[9,1] [[2,2,2,2,1],[1]]=>[9,1] [[2,2,2,1,1,1],[1]]=>[9,1] [[2,2,1,1,1,1,1],[1]]=>[9,1] [[2,1,1,1,1,1,1,1],[1]]=>[9,1] [[1,1,1,1,1,1,1,1,1],[1]]=>[9,1] [[10]]=>[10] [[9,1]]=>[10] [[8,2]]=>[10] [[8,1,1]]=>[10] [[7,3]]=>[10] [[7,2,1]]=>[10] [[7,1,1,1]]=>[10] [[6,4]]=>[10] [[6,3,1]]=>[10] [[6,2,2]]=>[10] [[6,2,1,1]]=>[10] [[6,1,1,1,1]]=>[10] [[5,5]]=>[10] [[5,4,1]]=>[10] [[5,3,2]]=>[10] [[5,3,1,1]]=>[10] [[5,2,2,1]]=>[10] [[5,2,1,1,1]]=>[10] [[5,1,1,1,1,1]]=>[10] [[4,4,2]]=>[10] [[4,4,1,1]]=>[10] [[4,3,3]]=>[10] [[4,3,2,1]]=>[10] [[4,3,1,1,1]]=>[10] [[4,2,2,2]]=>[10] [[4,2,2,1,1]]=>[10] [[4,2,1,1,1,1]]=>[10] [[4,1,1,1,1,1,1]]=>[10] [[3,3,3,1]]=>[10] [[3,3,2,2]]=>[10] [[3,3,2,1,1]]=>[10] [[3,3,1,1,1,1]]=>[10] [[3,2,2,2,1]]=>[10] [[3,2,2,1,1,1]]=>[10] [[3,2,1,1,1,1,1]]=>[10] [[3,1,1,1,1,1,1,1]]=>[10] [[2,2,2,2,2]]=>[10] [[2,2,2,2,1,1]]=>[10] [[2,2,2,1,1,1,1]]=>[10] [[2,2,1,1,1,1,1,1]]=>[10] [[2,1,1,1,1,1,1,1,1]]=>[10] [[1,1,1,1,1,1,1,1,1,1]]=>[10]
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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.
Properties
graded
Sage code
def mapping(p):
    return Partition(sum(row) for row in p)
Weight
40
Created
Aug 28, 2023 at 10:00 by Martin Rubey
Updated
Aug 28, 2023 at 10:00 by Martin Rubey