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Identifier
Mp00177: Plane partitions —transpose⟶ Plane partitions
Images
=>
Cc0025;cc-rep-0Cc0025;cc-rep-1
[[1]]=>[[1]] [[1],[1]]=>[[1,1]] [[2]]=>[[2]] [[1,1]]=>[[1],[1]] [[1],[1],[1]]=>[[1,1,1]] [[2],[1]]=>[[2,1]] [[1,1],[1]]=>[[1,1],[1]] [[3]]=>[[3]] [[2,1]]=>[[2],[1]] [[1,1,1]]=>[[1],[1],[1]] [[1],[1],[1],[1]]=>[[1,1,1,1]] [[2],[1],[1]]=>[[2,1,1]] [[2],[2]]=>[[2,2]] [[1,1],[1],[1]]=>[[1,1,1],[1]] [[1,1],[1,1]]=>[[1,1],[1,1]] [[3],[1]]=>[[3,1]] [[2,1],[1]]=>[[2,1],[1]] [[1,1,1],[1]]=>[[1,1],[1],[1]] [[4]]=>[[4]] [[3,1]]=>[[3],[1]] [[2,2]]=>[[2],[2]] [[2,1,1]]=>[[2],[1],[1]] [[1,1,1,1]]=>[[1],[1],[1],[1]] [[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]]=>[[1,1,1,1],[1]] [[1,1],[1,1],[1]]=>[[1,1,1],[1,1]] [[3],[1],[1]]=>[[3,1,1]] [[3],[2]]=>[[3,2]] [[2,1],[1],[1]]=>[[2,1,1],[1]] [[2,1],[2]]=>[[2,2],[1]] [[2,1],[1,1]]=>[[2,1],[1,1]] [[1,1,1],[1],[1]]=>[[1,1,1],[1],[1]] [[1,1,1],[1,1]]=>[[1,1],[1,1],[1]] [[4],[1]]=>[[4,1]] [[3,1],[1]]=>[[3,1],[1]] [[2,2],[1]]=>[[2,1],[2]] [[2,1,1],[1]]=>[[2,1],[1],[1]] [[1,1,1,1],[1]]=>[[1,1],[1],[1],[1]] [[5]]=>[[5]] [[4,1]]=>[[4],[1]] [[3,2]]=>[[3],[2]] [[3,1,1]]=>[[3],[1],[1]] [[2,2,1]]=>[[2],[2],[1]] [[2,1,1,1]]=>[[2],[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]] [[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]]=>[[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]] [[3],[1],[1],[1]]=>[[3,1,1,1]] [[3],[2],[1]]=>[[3,2,1]] [[3],[3]]=>[[3,3]] [[2,1],[1],[1],[1]]=>[[2,1,1,1],[1]] [[2,1],[2],[1]]=>[[2,2,1],[1]] [[2,1],[1,1],[1]]=>[[2,1,1],[1,1]] [[2,1],[2,1]]=>[[2,2],[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]] [[4],[1],[1]]=>[[4,1,1]] [[4],[2]]=>[[4,2]] [[3,1],[1],[1]]=>[[3,1,1],[1]] [[3,1],[2]]=>[[3,2],[1]] [[3,1],[1,1]]=>[[3,1],[1,1]] [[2,2],[1],[1]]=>[[2,1,1],[2]] [[2,2],[2]]=>[[2,2],[2]] [[2,2],[1,1]]=>[[2,1],[2,1]] [[2,1,1],[1],[1]]=>[[2,1,1],[1],[1]] [[2,1,1],[2]]=>[[2,2],[1],[1]] [[2,1,1],[1,1]]=>[[2,1],[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]] [[5],[1]]=>[[5,1]] [[4,1],[1]]=>[[4,1],[1]] [[3,2],[1]]=>[[3,1],[2]] [[3,1,1],[1]]=>[[3,1],[1],[1]] [[2,2,1],[1]]=>[[2,1],[2],[1]] [[2,1,1,1],[1]]=>[[2,1],[1],[1],[1]] [[1,1,1,1,1],[1]]=>[[1,1],[1],[1],[1],[1]] [[6]]=>[[6]] [[5,1]]=>[[5],[1]] [[4,2]]=>[[4],[2]] [[4,1,1]]=>[[4],[1],[1]] [[3,3]]=>[[3],[3]] [[3,2,1]]=>[[3],[2],[1]] [[3,1,1,1]]=>[[3],[1],[1],[1]] [[2,2,2]]=>[[2],[2],[2]] [[2,2,1,1]]=>[[2],[2],[1],[1]] [[2,1,1,1,1]]=>[[2],[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]] [[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]]=>[[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]] [[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]]=>[[2,1,1,1,1],[1]] [[2,1],[2],[1],[1]]=>[[2,2,1,1],[1]] [[2,1],[2],[2]]=>[[2,2,2],[1]] [[2,1],[1,1],[1],[1]]=>[[2,1,1,1],[1,1]] [[2,1],[1,1],[1,1]]=>[[2,1,1],[1,1,1]] [[2,1],[2,1],[1]]=>[[2,2,1],[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]] [[1,1,1],[1,1,1],[1]]=>[[1,1,1],[1,1],[1,1]] [[4],[1],[1],[1]]=>[[4,1,1,1]] [[4],[2],[1]]=>[[4,2,1]] [[4],[3]]=>[[4,3]] [[3,1],[1],[1],[1]]=>[[3,1,1,1],[1]] [[3,1],[2],[1]]=>[[3,2,1],[1]] [[3,1],[1,1],[1]]=>[[3,1,1],[1,1]] [[3,1],[3]]=>[[3,3],[1]] [[3,1],[2,1]]=>[[3,2],[1,1]] [[2,2],[1],[1],[1]]=>[[2,1,1,1],[2]] [[2,2],[2],[1]]=>[[2,2,1],[2]] [[2,2],[1,1],[1]]=>[[2,1,1],[2,1]] [[2,2],[2,1]]=>[[2,2],[2,1]] [[2,1,1],[1],[1],[1]]=>[[2,1,1,1],[1],[1]] [[2,1,1],[2],[1]]=>[[2,2,1],[1],[1]] [[2,1,1],[1,1],[1]]=>[[2,1,1],[1,1],[1]] [[2,1,1],[2,1]]=>[[2,2],[1,1],[1]] [[2,1,1],[1,1,1]]=>[[2,1],[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],[1,1],[1]] [[5],[1],[1]]=>[[5,1,1]] [[5],[2]]=>[[5,2]] [[4,1],[1],[1]]=>[[4,1,1],[1]] [[4,1],[2]]=>[[4,2],[1]] [[4,1],[1,1]]=>[[4,1],[1,1]] [[3,2],[1],[1]]=>[[3,1,1],[2]] [[3,2],[2]]=>[[3,2],[2]] [[3,2],[1,1]]=>[[3,1],[2,1]] [[3,1,1],[1],[1]]=>[[3,1,1],[1],[1]] [[3,1,1],[2]]=>[[3,2],[1],[1]] [[3,1,1],[1,1]]=>[[3,1],[1,1],[1]] [[2,2,1],[1],[1]]=>[[2,1,1],[2],[1]] [[2,2,1],[2]]=>[[2,2],[2],[1]] [[2,2,1],[1,1]]=>[[2,1],[2,1],[1]] [[2,1,1,1],[1],[1]]=>[[2,1,1],[1],[1],[1]] [[2,1,1,1],[2]]=>[[2,2],[1],[1],[1]] [[2,1,1,1],[1,1]]=>[[2,1],[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],[1]]=>[[6,1]] [[5,1],[1]]=>[[5,1],[1]] [[4,2],[1]]=>[[4,1],[2]] [[4,1,1],[1]]=>[[4,1],[1],[1]] [[3,3],[1]]=>[[3,1],[3]] [[3,2,1],[1]]=>[[3,1],[2],[1]] [[3,1,1,1],[1]]=>[[3,1],[1],[1],[1]] [[2,2,2],[1]]=>[[2,1],[2],[2]] [[2,2,1,1],[1]]=>[[2,1],[2],[1],[1]] [[2,1,1,1,1],[1]]=>[[2,1],[1],[1],[1],[1]] [[1,1,1,1,1,1],[1]]=>[[1,1],[1],[1],[1],[1],[1]] [[7]]=>[[7]] [[6,1]]=>[[6],[1]] [[5,2]]=>[[5],[2]] [[5,1,1]]=>[[5],[1],[1]] [[4,3]]=>[[4],[3]] [[4,2,1]]=>[[4],[2],[1]] [[4,1,1,1]]=>[[4],[1],[1],[1]] [[3,3,1]]=>[[3],[3],[1]] [[3,2,2]]=>[[3],[2],[2]] [[3,2,1,1]]=>[[3],[2],[1],[1]] [[3,1,1,1,1]]=>[[3],[1],[1],[1],[1]] [[2,2,2,1]]=>[[2],[2],[2],[1]] [[2,2,1,1,1]]=>[[2],[2],[1],[1],[1]] [[2,1,1,1,1,1]]=>[[2],[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]] [[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]]=>[[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],[1,1],[1,1]]=>[[1,1,1,1],[1,1,1,1]] [[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]]=>[[2,1,1,1,1,1],[1]] [[2,1],[2],[1],[1],[1]]=>[[2,2,1,1,1],[1]] [[2,1],[2],[2],[1]]=>[[2,2,2,1],[1]] [[2,1],[1,1],[1],[1],[1]]=>[[2,1,1,1,1],[1,1]] [[2,1],[1,1],[1,1],[1]]=>[[2,1,1,1],[1,1,1]] [[2,1],[2,1],[1],[1]]=>[[2,2,1,1],[1,1]] [[2,1],[2,1],[2]]=>[[2,2,2],[1,1]] [[2,1],[2,1],[1,1]]=>[[2,2,1],[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]]=>[[1,1,1,1],[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]] [[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]]=>[[3,1,1,1,1],[1]] [[3,1],[2],[1],[1]]=>[[3,2,1,1],[1]] [[3,1],[2],[2]]=>[[3,2,2],[1]] [[3,1],[1,1],[1],[1]]=>[[3,1,1,1],[1,1]] [[3,1],[1,1],[1,1]]=>[[3,1,1],[1,1,1]] [[3,1],[3],[1]]=>[[3,3,1],[1]] [[3,1],[2,1],[1]]=>[[3,2,1],[1,1]] [[3,1],[3,1]]=>[[3,3],[1,1]] [[2,2],[1],[1],[1],[1]]=>[[2,1,1,1,1],[2]] [[2,2],[2],[1],[1]]=>[[2,2,1,1],[2]] [[2,2],[2],[2]]=>[[2,2,2],[2]] [[2,2],[1,1],[1],[1]]=>[[2,1,1,1],[2,1]] [[2,2],[1,1],[1,1]]=>[[2,1,1],[2,1,1]] [[2,2],[2,1],[1]]=>[[2,2,1],[2,1]] [[2,2],[2,2]]=>[[2,2],[2,2]] [[2,1,1],[1],[1],[1],[1]]=>[[2,1,1,1,1],[1],[1]] [[2,1,1],[2],[1],[1]]=>[[2,2,1,1],[1],[1]] [[2,1,1],[2],[2]]=>[[2,2,2],[1],[1]] [[2,1,1],[1,1],[1],[1]]=>[[2,1,1,1],[1,1],[1]] [[2,1,1],[1,1],[1,1]]=>[[2,1,1],[1,1,1],[1]] [[2,1,1],[2,1],[1]]=>[[2,2,1],[1,1],[1]] [[2,1,1],[1,1,1],[1]]=>[[2,1,1],[1,1],[1,1]] [[2,1,1],[2,1,1]]=>[[2,2],[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]]=>[[1,1,1],[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]] [[5],[1],[1],[1]]=>[[5,1,1,1]] [[5],[2],[1]]=>[[5,2,1]] [[5],[3]]=>[[5,3]] [[4,1],[1],[1],[1]]=>[[4,1,1,1],[1]] [[4,1],[2],[1]]=>[[4,2,1],[1]] [[4,1],[1,1],[1]]=>[[4,1,1],[1,1]] [[4,1],[3]]=>[[4,3],[1]] [[4,1],[2,1]]=>[[4,2],[1,1]] [[3,2],[1],[1],[1]]=>[[3,1,1,1],[2]] [[3,2],[2],[1]]=>[[3,2,1],[2]] [[3,2],[1,1],[1]]=>[[3,1,1],[2,1]] [[3,2],[3]]=>[[3,3],[2]] [[3,2],[2,1]]=>[[3,2],[2,1]] [[3,1,1],[1],[1],[1]]=>[[3,1,1,1],[1],[1]] [[3,1,1],[2],[1]]=>[[3,2,1],[1],[1]] [[3,1,1],[1,1],[1]]=>[[3,1,1],[1,1],[1]] [[3,1,1],[3]]=>[[3,3],[1],[1]] [[3,1,1],[2,1]]=>[[3,2],[1,1],[1]] [[3,1,1],[1,1,1]]=>[[3,1],[1,1],[1,1]] [[2,2,1],[1],[1],[1]]=>[[2,1,1,1],[2],[1]] [[2,2,1],[2],[1]]=>[[2,2,1],[2],[1]] [[2,2,1],[1,1],[1]]=>[[2,1,1],[2,1],[1]] [[2,2,1],[2,1]]=>[[2,2],[2,1],[1]] [[2,2,1],[1,1,1]]=>[[2,1],[2,1],[1,1]] [[2,1,1,1],[1],[1],[1]]=>[[2,1,1,1],[1],[1],[1]] [[2,1,1,1],[2],[1]]=>[[2,2,1],[1],[1],[1]] [[2,1,1,1],[1,1],[1]]=>[[2,1,1],[1,1],[1],[1]] [[2,1,1,1],[2,1]]=>[[2,2],[1,1],[1],[1]] [[2,1,1,1],[1,1,1]]=>[[2,1],[1,1],[1,1],[1]] [[1,1,1,1,1],[1],[1],[1]]=>[[1,1,1,1],[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],[1],[1]]=>[[6,1,1]] [[6],[2]]=>[[6,2]] [[5,1],[1],[1]]=>[[5,1,1],[1]] [[5,1],[2]]=>[[5,2],[1]] [[5,1],[1,1]]=>[[5,1],[1,1]] [[4,2],[1],[1]]=>[[4,1,1],[2]] [[4,2],[2]]=>[[4,2],[2]] [[4,2],[1,1]]=>[[4,1],[2,1]] [[4,1,1],[1],[1]]=>[[4,1,1],[1],[1]] [[4,1,1],[2]]=>[[4,2],[1],[1]] [[4,1,1],[1,1]]=>[[4,1],[1,1],[1]] [[3,3],[1],[1]]=>[[3,1,1],[3]] [[3,3],[2]]=>[[3,2],[3]] [[3,3],[1,1]]=>[[3,1],[3,1]] [[3,2,1],[1],[1]]=>[[3,1,1],[2],[1]] [[3,2,1],[2]]=>[[3,2],[2],[1]] [[3,2,1],[1,1]]=>[[3,1],[2,1],[1]] [[3,1,1,1],[1],[1]]=>[[3,1,1],[1],[1],[1]] [[3,1,1,1],[2]]=>[[3,2],[1],[1],[1]] [[3,1,1,1],[1,1]]=>[[3,1],[1,1],[1],[1]] [[2,2,2],[1],[1]]=>[[2,1,1],[2],[2]] [[2,2,2],[2]]=>[[2,2],[2],[2]] [[2,2,2],[1,1]]=>[[2,1],[2,1],[2]] [[2,2,1,1],[1],[1]]=>[[2,1,1],[2],[1],[1]] [[2,2,1,1],[2]]=>[[2,2],[2],[1],[1]] [[2,2,1,1],[1,1]]=>[[2,1],[2,1],[1],[1]] [[2,1,1,1,1],[1],[1]]=>[[2,1,1],[1],[1],[1],[1]] [[2,1,1,1,1],[2]]=>[[2,2],[1],[1],[1],[1]] [[2,1,1,1,1],[1,1]]=>[[2,1],[1,1],[1],[1],[1]] [[1,1,1,1,1,1],[1],[1]]=>[[1,1,1],[1],[1],[1],[1],[1]] [[1,1,1,1,1,1],[1,1]]=>[[1,1],[1,1],[1],[1],[1],[1]] [[7],[1]]=>[[7,1]] [[6,1],[1]]=>[[6,1],[1]] [[5,2],[1]]=>[[5,1],[2]] [[5,1,1],[1]]=>[[5,1],[1],[1]] [[4,3],[1]]=>[[4,1],[3]] [[4,2,1],[1]]=>[[4,1],[2],[1]] [[4,1,1,1],[1]]=>[[4,1],[1],[1],[1]] [[3,3,1],[1]]=>[[3,1],[3],[1]] [[3,2,2],[1]]=>[[3,1],[2],[2]] [[3,2,1,1],[1]]=>[[3,1],[2],[1],[1]] [[3,1,1,1,1],[1]]=>[[3,1],[1],[1],[1],[1]] [[2,2,2,1],[1]]=>[[2,1],[2],[2],[1]] [[2,2,1,1,1],[1]]=>[[2,1],[2],[1],[1],[1]] [[2,1,1,1,1,1],[1]]=>[[2,1],[1],[1],[1],[1],[1]] [[1,1,1,1,1,1,1],[1]]=>[[1,1],[1],[1],[1],[1],[1],[1]] [[8]]=>[[8]] [[7,1]]=>[[7],[1]] [[6,2]]=>[[6],[2]] [[6,1,1]]=>[[6],[1],[1]] [[5,3]]=>[[5],[3]] [[5,2,1]]=>[[5],[2],[1]] [[5,1,1,1]]=>[[5],[1],[1],[1]] [[4,4]]=>[[4],[4]] [[4,3,1]]=>[[4],[3],[1]] [[4,2,2]]=>[[4],[2],[2]] [[4,2,1,1]]=>[[4],[2],[1],[1]] [[4,1,1,1,1]]=>[[4],[1],[1],[1],[1]] [[3,3,2]]=>[[3],[3],[2]] [[3,3,1,1]]=>[[3],[3],[1],[1]] [[3,2,2,1]]=>[[3],[2],[2],[1]] [[3,2,1,1,1]]=>[[3],[2],[1],[1],[1]] [[3,1,1,1,1,1]]=>[[3],[1],[1],[1],[1],[1]] [[2,2,2,2]]=>[[2],[2],[2],[2]] [[2,2,2,1,1]]=>[[2],[2],[2],[1],[1]] [[2,2,1,1,1,1]]=>[[2],[2],[1],[1],[1],[1]] [[2,1,1,1,1,1,1]]=>[[2],[1],[1],[1],[1],[1],[1]] [[1,1,1,1,1,1,1,1]]=>[[1],[1],[1],[1],[1],[1],[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]]=>[[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]]=>[[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]] [[1,1],[1,1],[1,1],[1,1],[1]]=>[[1,1,1,1,1],[1,1,1,1]] [[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]]=>[[2,1,1,1,1,1,1],[1]] [[2,1],[2],[1],[1],[1],[1]]=>[[2,2,1,1,1,1],[1]] [[2,1],[2],[2],[1],[1]]=>[[2,2,2,1,1],[1]] [[2,1],[2],[2],[2]]=>[[2,2,2,2],[1]] [[2,1],[1,1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1],[1,1]] [[2,1],[1,1],[1,1],[1],[1]]=>[[2,1,1,1,1],[1,1,1]] [[2,1],[1,1],[1,1],[1,1]]=>[[2,1,1,1],[1,1,1,1]] [[2,1],[2,1],[1],[1],[1]]=>[[2,2,1,1,1],[1,1]] [[2,1],[2,1],[2],[1]]=>[[2,2,2,1],[1,1]] [[2,1],[2,1],[1,1],[1]]=>[[2,2,1,1],[1,1,1]] [[2,1],[2,1],[2,1]]=>[[2,2,2],[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],[1,1],[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],[1,1],[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]] [[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]]=>[[3,1,1,1,1,1],[1]] [[3,1],[2],[1],[1],[1]]=>[[3,2,1,1,1],[1]] [[3,1],[2],[2],[1]]=>[[3,2,2,1],[1]] [[3,1],[1,1],[1],[1],[1]]=>[[3,1,1,1,1],[1,1]] [[3,1],[1,1],[1,1],[1]]=>[[3,1,1,1],[1,1,1]] [[3,1],[3],[1],[1]]=>[[3,3,1,1],[1]] [[3,1],[3],[2]]=>[[3,3,2],[1]] [[3,1],[2,1],[1],[1]]=>[[3,2,1,1],[1,1]] [[3,1],[2,1],[2]]=>[[3,2,2],[1,1]] [[3,1],[2,1],[1,1]]=>[[3,2,1],[1,1,1]] [[3,1],[3,1],[1]]=>[[3,3,1],[1,1]] [[2,2],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1],[2]] [[2,2],[2],[1],[1],[1]]=>[[2,2,1,1,1],[2]] [[2,2],[2],[2],[1]]=>[[2,2,2,1],[2]] [[2,2],[1,1],[1],[1],[1]]=>[[2,1,1,1,1],[2,1]] [[2,2],[1,1],[1,1],[1]]=>[[2,1,1,1],[2,1,1]] [[2,2],[2,1],[1],[1]]=>[[2,2,1,1],[2,1]] [[2,2],[2,1],[2]]=>[[2,2,2],[2,1]] [[2,2],[2,1],[1,1]]=>[[2,2,1],[2,1,1]] [[2,2],[2,2],[1]]=>[[2,2,1],[2,2]] [[2,1,1],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1],[1],[1]] [[2,1,1],[2],[1],[1],[1]]=>[[2,2,1,1,1],[1],[1]] [[2,1,1],[2],[2],[1]]=>[[2,2,2,1],[1],[1]] [[2,1,1],[1,1],[1],[1],[1]]=>[[2,1,1,1,1],[1,1],[1]] [[2,1,1],[1,1],[1,1],[1]]=>[[2,1,1,1],[1,1,1],[1]] [[2,1,1],[2,1],[1],[1]]=>[[2,2,1,1],[1,1],[1]] [[2,1,1],[2,1],[2]]=>[[2,2,2],[1,1],[1]] [[2,1,1],[2,1],[1,1]]=>[[2,2,1],[1,1,1],[1]] [[2,1,1],[1,1,1],[1],[1]]=>[[2,1,1,1],[1,1],[1,1]] [[2,1,1],[1,1,1],[1,1]]=>[[2,1,1],[1,1,1],[1,1]] [[2,1,1],[2,1,1],[1]]=>[[2,2,1],[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],[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],[1,1,1],[1,1],[1]] [[1,1,1,1],[1,1,1,1],[1]]=>[[1,1,1],[1,1],[1,1],[1,1]] [[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]]=>[[4,1,1,1,1],[1]] [[4,1],[2],[1],[1]]=>[[4,2,1,1],[1]] [[4,1],[2],[2]]=>[[4,2,2],[1]] [[4,1],[1,1],[1],[1]]=>[[4,1,1,1],[1,1]] [[4,1],[1,1],[1,1]]=>[[4,1,1],[1,1,1]] [[4,1],[3],[1]]=>[[4,3,1],[1]] [[4,1],[2,1],[1]]=>[[4,2,1],[1,1]] [[4,1],[4]]=>[[4,4],[1]] [[4,1],[3,1]]=>[[4,3],[1,1]] [[3,2],[1],[1],[1],[1]]=>[[3,1,1,1,1],[2]] [[3,2],[2],[1],[1]]=>[[3,2,1,1],[2]] [[3,2],[2],[2]]=>[[3,2,2],[2]] [[3,2],[1,1],[1],[1]]=>[[3,1,1,1],[2,1]] [[3,2],[1,1],[1,1]]=>[[3,1,1],[2,1,1]] [[3,2],[3],[1]]=>[[3,3,1],[2]] [[3,2],[2,1],[1]]=>[[3,2,1],[2,1]] [[3,2],[3,1]]=>[[3,3],[2,1]] [[3,2],[2,2]]=>[[3,2],[2,2]] [[3,1,1],[1],[1],[1],[1]]=>[[3,1,1,1,1],[1],[1]] [[3,1,1],[2],[1],[1]]=>[[3,2,1,1],[1],[1]] [[3,1,1],[2],[2]]=>[[3,2,2],[1],[1]] [[3,1,1],[1,1],[1],[1]]=>[[3,1,1,1],[1,1],[1]] [[3,1,1],[1,1],[1,1]]=>[[3,1,1],[1,1,1],[1]] [[3,1,1],[3],[1]]=>[[3,3,1],[1],[1]] [[3,1,1],[2,1],[1]]=>[[3,2,1],[1,1],[1]] [[3,1,1],[1,1,1],[1]]=>[[3,1,1],[1,1],[1,1]] [[3,1,1],[3,1]]=>[[3,3],[1,1],[1]] [[3,1,1],[2,1,1]]=>[[3,2],[1,1],[1,1]] [[2,2,1],[1],[1],[1],[1]]=>[[2,1,1,1,1],[2],[1]] [[2,2,1],[2],[1],[1]]=>[[2,2,1,1],[2],[1]] [[2,2,1],[2],[2]]=>[[2,2,2],[2],[1]] [[2,2,1],[1,1],[1],[1]]=>[[2,1,1,1],[2,1],[1]] [[2,2,1],[1,1],[1,1]]=>[[2,1,1],[2,1,1],[1]] [[2,2,1],[2,1],[1]]=>[[2,2,1],[2,1],[1]] [[2,2,1],[1,1,1],[1]]=>[[2,1,1],[2,1],[1,1]] [[2,2,1],[2,2]]=>[[2,2],[2,2],[1]] [[2,2,1],[2,1,1]]=>[[2,2],[2,1],[1,1]] [[2,1,1,1],[1],[1],[1],[1]]=>[[2,1,1,1,1],[1],[1],[1]] [[2,1,1,1],[2],[1],[1]]=>[[2,2,1,1],[1],[1],[1]] [[2,1,1,1],[2],[2]]=>[[2,2,2],[1],[1],[1]] [[2,1,1,1],[1,1],[1],[1]]=>[[2,1,1,1],[1,1],[1],[1]] [[2,1,1,1],[1,1],[1,1]]=>[[2,1,1],[1,1,1],[1],[1]] [[2,1,1,1],[2,1],[1]]=>[[2,2,1],[1,1],[1],[1]] [[2,1,1,1],[1,1,1],[1]]=>[[2,1,1],[1,1],[1,1],[1]] [[2,1,1,1],[2,1,1]]=>[[2,2],[1,1],[1,1],[1]] [[2,1,1,1],[1,1,1,1]]=>[[2,1],[1,1],[1,1],[1,1]] [[1,1,1,1,1],[1],[1],[1],[1]]=>[[1,1,1,1,1],[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]] [[1,1,1,1,1],[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],[1],[1],[1]]=>[[6,1,1,1]] [[6],[2],[1]]=>[[6,2,1]] [[6],[3]]=>[[6,3]] [[5,1],[1],[1],[1]]=>[[5,1,1,1],[1]] [[5,1],[2],[1]]=>[[5,2,1],[1]] [[5,1],[1,1],[1]]=>[[5,1,1],[1,1]] [[5,1],[3]]=>[[5,3],[1]] [[5,1],[2,1]]=>[[5,2],[1,1]] [[4,2],[1],[1],[1]]=>[[4,1,1,1],[2]] [[4,2],[2],[1]]=>[[4,2,1],[2]] [[4,2],[1,1],[1]]=>[[4,1,1],[2,1]] [[4,2],[3]]=>[[4,3],[2]] [[4,2],[2,1]]=>[[4,2],[2,1]] [[4,1,1],[1],[1],[1]]=>[[4,1,1,1],[1],[1]] [[4,1,1],[2],[1]]=>[[4,2,1],[1],[1]] [[4,1,1],[1,1],[1]]=>[[4,1,1],[1,1],[1]] [[4,1,1],[3]]=>[[4,3],[1],[1]] [[4,1,1],[2,1]]=>[[4,2],[1,1],[1]] [[4,1,1],[1,1,1]]=>[[4,1],[1,1],[1,1]] [[3,3],[1],[1],[1]]=>[[3,1,1,1],[3]] [[3,3],[2],[1]]=>[[3,2,1],[3]] [[3,3],[1,1],[1]]=>[[3,1,1],[3,1]] [[3,3],[3]]=>[[3,3],[3]] [[3,3],[2,1]]=>[[3,2],[3,1]] [[3,2,1],[1],[1],[1]]=>[[3,1,1,1],[2],[1]] [[3,2,1],[2],[1]]=>[[3,2,1],[2],[1]] [[3,2,1],[1,1],[1]]=>[[3,1,1],[2,1],[1]] [[3,2,1],[3]]=>[[3,3],[2],[1]] [[3,2,1],[2,1]]=>[[3,2],[2,1],[1]] [[3,2,1],[1,1,1]]=>[[3,1],[2,1],[1,1]] [[3,1,1,1],[1],[1],[1]]=>[[3,1,1,1],[1],[1],[1]] [[3,1,1,1],[2],[1]]=>[[3,2,1],[1],[1],[1]] [[3,1,1,1],[1,1],[1]]=>[[3,1,1],[1,1],[1],[1]] [[3,1,1,1],[3]]=>[[3,3],[1],[1],[1]] [[3,1,1,1],[2,1]]=>[[3,2],[1,1],[1],[1]] [[3,1,1,1],[1,1,1]]=>[[3,1],[1,1],[1,1],[1]] [[2,2,2],[1],[1],[1]]=>[[2,1,1,1],[2],[2]] [[2,2,2],[2],[1]]=>[[2,2,1],[2],[2]] [[2,2,2],[1,1],[1]]=>[[2,1,1],[2,1],[2]] [[2,2,2],[2,1]]=>[[2,2],[2,1],[2]] [[2,2,2],[1,1,1]]=>[[2,1],[2,1],[2,1]] [[2,2,1,1],[1],[1],[1]]=>[[2,1,1,1],[2],[1],[1]] [[2,2,1,1],[2],[1]]=>[[2,2,1],[2],[1],[1]] [[2,2,1,1],[1,1],[1]]=>[[2,1,1],[2,1],[1],[1]] [[2,2,1,1],[2,1]]=>[[2,2],[2,1],[1],[1]] [[2,2,1,1],[1,1,1]]=>[[2,1],[2,1],[1,1],[1]] [[2,1,1,1,1],[1],[1],[1]]=>[[2,1,1,1],[1],[1],[1],[1]] [[2,1,1,1,1],[2],[1]]=>[[2,2,1],[1],[1],[1],[1]] [[2,1,1,1,1],[1,1],[1]]=>[[2,1,1],[1,1],[1],[1],[1]] [[2,1,1,1,1],[2,1]]=>[[2,2],[1,1],[1],[1],[1]] [[2,1,1,1,1],[1,1,1]]=>[[2,1],[1,1],[1,1],[1],[1]] [[1,1,1,1,1,1],[1],[1],[1]]=>[[1,1,1,1],[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]] [[7],[1],[1]]=>[[7,1,1]] [[7],[2]]=>[[7,2]] [[6,1],[1],[1]]=>[[6,1,1],[1]] [[6,1],[2]]=>[[6,2],[1]] [[6,1],[1,1]]=>[[6,1],[1,1]] [[5,2],[1],[1]]=>[[5,1,1],[2]] [[5,2],[2]]=>[[5,2],[2]] [[5,2],[1,1]]=>[[5,1],[2,1]] [[5,1,1],[1],[1]]=>[[5,1,1],[1],[1]] [[5,1,1],[2]]=>[[5,2],[1],[1]] [[5,1,1],[1,1]]=>[[5,1],[1,1],[1]] [[4,3],[1],[1]]=>[[4,1,1],[3]] [[4,3],[2]]=>[[4,2],[3]] [[4,3],[1,1]]=>[[4,1],[3,1]] [[4,2,1],[1],[1]]=>[[4,1,1],[2],[1]] [[4,2,1],[2]]=>[[4,2],[2],[1]] [[4,2,1],[1,1]]=>[[4,1],[2,1],[1]] [[4,1,1,1],[1],[1]]=>[[4,1,1],[1],[1],[1]] [[4,1,1,1],[2]]=>[[4,2],[1],[1],[1]] [[4,1,1,1],[1,1]]=>[[4,1],[1,1],[1],[1]] [[3,3,1],[1],[1]]=>[[3,1,1],[3],[1]] [[3,3,1],[2]]=>[[3,2],[3],[1]] [[3,3,1],[1,1]]=>[[3,1],[3,1],[1]] [[3,2,2],[1],[1]]=>[[3,1,1],[2],[2]] [[3,2,2],[2]]=>[[3,2],[2],[2]] [[3,2,2],[1,1]]=>[[3,1],[2,1],[2]] [[3,2,1,1],[1],[1]]=>[[3,1,1],[2],[1],[1]] [[3,2,1,1],[2]]=>[[3,2],[2],[1],[1]] [[3,2,1,1],[1,1]]=>[[3,1],[2,1],[1],[1]] [[3,1,1,1,1],[1],[1]]=>[[3,1,1],[1],[1],[1],[1]] [[3,1,1,1,1],[2]]=>[[3,2],[1],[1],[1],[1]] [[3,1,1,1,1],[1,1]]=>[[3,1],[1,1],[1],[1],[1]] [[2,2,2,1],[1],[1]]=>[[2,1,1],[2],[2],[1]] [[2,2,2,1],[2]]=>[[2,2],[2],[2],[1]] [[2,2,2,1],[1,1]]=>[[2,1],[2,1],[2],[1]] [[2,2,1,1,1],[1],[1]]=>[[2,1,1],[2],[1],[1],[1]] [[2,2,1,1,1],[2]]=>[[2,2],[2],[1],[1],[1]] [[2,2,1,1,1],[1,1]]=>[[2,1],[2,1],[1],[1],[1]] [[2,1,1,1,1,1],[1],[1]]=>[[2,1,1],[1],[1],[1],[1],[1]] [[2,1,1,1,1,1],[2]]=>[[2,2],[1],[1],[1],[1],[1]] [[2,1,1,1,1,1],[1,1]]=>[[2,1],[1,1],[1],[1],[1],[1]] [[1,1,1,1,1,1,1],[1],[1]]=>[[1,1,1],[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]]=>[[8,1]] [[7,1],[1]]=>[[7,1],[1]] [[6,2],[1]]=>[[6,1],[2]] [[6,1,1],[1]]=>[[6,1],[1],[1]] [[5,3],[1]]=>[[5,1],[3]] [[5,2,1],[1]]=>[[5,1],[2],[1]] [[5,1,1,1],[1]]=>[[5,1],[1],[1],[1]] [[4,4],[1]]=>[[4,1],[4]] [[4,3,1],[1]]=>[[4,1],[3],[1]] [[4,2,2],[1]]=>[[4,1],[2],[2]] [[4,2,1,1],[1]]=>[[4,1],[2],[1],[1]] [[4,1,1,1,1],[1]]=>[[4,1],[1],[1],[1],[1]] [[3,3,2],[1]]=>[[3,1],[3],[2]] [[3,3,1,1],[1]]=>[[3,1],[3],[1],[1]] [[3,2,2,1],[1]]=>[[3,1],[2],[2],[1]] [[3,2,1,1,1],[1]]=>[[3,1],[2],[1],[1],[1]] [[3,1,1,1,1,1],[1]]=>[[3,1],[1],[1],[1],[1],[1]] [[2,2,2,2],[1]]=>[[2,1],[2],[2],[2]] [[2,2,2,1,1],[1]]=>[[2,1],[2],[2],[1],[1]] [[2,2,1,1,1,1],[1]]=>[[2,1],[2],[1],[1],[1],[1]] [[2,1,1,1,1,1,1],[1]]=>[[2,1],[1],[1],[1],[1],[1],[1]] [[1,1,1,1,1,1,1,1],[1]]=>[[1,1],[1],[1],[1],[1],[1],[1],[1]] [[9]]=>[[9]] [[8,1]]=>[[8],[1]] [[7,2]]=>[[7],[2]] [[7,1,1]]=>[[7],[1],[1]] [[6,3]]=>[[6],[3]] [[6,2,1]]=>[[6],[2],[1]] [[6,1,1,1]]=>[[6],[1],[1],[1]] [[5,4]]=>[[5],[4]] [[5,3,1]]=>[[5],[3],[1]] [[5,2,2]]=>[[5],[2],[2]] [[5,2,1,1]]=>[[5],[2],[1],[1]] [[5,1,1,1,1]]=>[[5],[1],[1],[1],[1]] [[4,4,1]]=>[[4],[4],[1]] [[4,3,2]]=>[[4],[3],[2]] [[4,3,1,1]]=>[[4],[3],[1],[1]] [[4,2,2,1]]=>[[4],[2],[2],[1]] [[4,2,1,1,1]]=>[[4],[2],[1],[1],[1]] [[4,1,1,1,1,1]]=>[[4],[1],[1],[1],[1],[1]] [[3,3,3]]=>[[3],[3],[3]] [[3,3,2,1]]=>[[3],[3],[2],[1]] [[3,3,1,1,1]]=>[[3],[3],[1],[1],[1]] [[3,2,2,2]]=>[[3],[2],[2],[2]] [[3,2,2,1,1]]=>[[3],[2],[2],[1],[1]] [[3,2,1,1,1,1]]=>[[3],[2],[1],[1],[1],[1]] [[3,1,1,1,1,1,1]]=>[[3],[1],[1],[1],[1],[1],[1]] [[2,2,2,2,1]]=>[[2],[2],[2],[2],[1]] [[2,2,2,1,1,1]]=>[[2],[2],[2],[1],[1],[1]] [[2,2,1,1,1,1,1]]=>[[2],[2],[1],[1],[1],[1],[1]] [[2,1,1,1,1,1,1,1]]=>[[2],[1],[1],[1],[1],[1],[1],[1]] [[1,1,1,1,1,1,1,1,1]]=>[[1],[1],[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]] [[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]]=>[[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]]=>[[1,1,1,1,1,1,1],[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]] [[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]]=>[[2,1,1,1,1,1,1,1],[1]] [[2,1],[2],[1],[1],[1],[1],[1]]=>[[2,2,1,1,1,1,1],[1]] [[2,1],[2],[2],[1],[1],[1]]=>[[2,2,2,1,1,1],[1]] [[2,1],[2],[2],[2],[1]]=>[[2,2,2,2,1],[1]] [[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]]=>[[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]] [[2,1],[2,1],[1],[1],[1],[1]]=>[[2,2,1,1,1,1],[1,1]] [[2,1],[2,1],[2],[1],[1]]=>[[2,2,2,1,1],[1,1]] [[2,1],[2,1],[2],[2]]=>[[2,2,2,2],[1,1]] [[2,1],[2,1],[1,1],[1],[1]]=>[[2,2,1,1,1],[1,1,1]] [[2,1],[2,1],[1,1],[1,1]]=>[[2,2,1,1],[1,1,1,1]] [[2,1],[2,1],[2,1],[1]]=>[[2,2,2,1],[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]] [[1,1,1],[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],[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]]=>[[1,1,1,1],[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]] [[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]]=>[[3,1,1,1,1,1,1],[1]] [[3,1],[2],[1],[1],[1],[1]]=>[[3,2,1,1,1,1],[1]] [[3,1],[2],[2],[1],[1]]=>[[3,2,2,1,1],[1]] [[3,1],[2],[2],[2]]=>[[3,2,2,2],[1]] [[3,1],[1,1],[1],[1],[1],[1]]=>[[3,1,1,1,1,1],[1,1]] [[3,1],[1,1],[1,1],[1],[1]]=>[[3,1,1,1,1],[1,1,1]] [[3,1],[1,1],[1,1],[1,1]]=>[[3,1,1,1],[1,1,1,1]] [[3,1],[3],[1],[1],[1]]=>[[3,3,1,1,1],[1]] [[3,1],[3],[2],[1]]=>[[3,3,2,1],[1]] [[3,1],[3],[3]]=>[[3,3,3],[1]] [[3,1],[2,1],[1],[1],[1]]=>[[3,2,1,1,1],[1,1]] [[3,1],[2,1],[2],[1]]=>[[3,2,2,1],[1,1]] [[3,1],[2,1],[1,1],[1]]=>[[3,2,1,1],[1,1,1]] [[3,1],[2,1],[2,1]]=>[[3,2,2],[1,1,1]] [[3,1],[3,1],[1],[1]]=>[[3,3,1,1],[1,1]] [[3,1],[3,1],[2]]=>[[3,3,2],[1,1]] [[3,1],[3,1],[1,1]]=>[[3,3,1],[1,1,1]] [[2,2],[1],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1,1],[2]] [[2,2],[2],[1],[1],[1],[1]]=>[[2,2,1,1,1,1],[2]] [[2,2],[2],[2],[1],[1]]=>[[2,2,2,1,1],[2]] [[2,2],[2],[2],[2]]=>[[2,2,2,2],[2]] [[2,2],[1,1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1],[2,1]] [[2,2],[1,1],[1,1],[1],[1]]=>[[2,1,1,1,1],[2,1,1]] [[2,2],[1,1],[1,1],[1,1]]=>[[2,1,1,1],[2,1,1,1]] [[2,2],[2,1],[1],[1],[1]]=>[[2,2,1,1,1],[2,1]] [[2,2],[2,1],[2],[1]]=>[[2,2,2,1],[2,1]] [[2,2],[2,1],[1,1],[1]]=>[[2,2,1,1],[2,1,1]] [[2,2],[2,1],[2,1]]=>[[2,2,2],[2,1,1]] [[2,2],[2,2],[1],[1]]=>[[2,2,1,1],[2,2]] [[2,2],[2,2],[2]]=>[[2,2,2],[2,2]] [[2,2],[2,2],[1,1]]=>[[2,2,1],[2,2,1]] [[2,1,1],[1],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1,1],[1],[1]] [[2,1,1],[2],[1],[1],[1],[1]]=>[[2,2,1,1,1,1],[1],[1]] [[2,1,1],[2],[2],[1],[1]]=>[[2,2,2,1,1],[1],[1]] [[2,1,1],[2],[2],[2]]=>[[2,2,2,2],[1],[1]] [[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]]=>[[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]] [[2,1,1],[2,1],[1],[1],[1]]=>[[2,2,1,1,1],[1,1],[1]] [[2,1,1],[2,1],[2],[1]]=>[[2,2,2,1],[1,1],[1]] [[2,1,1],[2,1],[1,1],[1]]=>[[2,2,1,1],[1,1,1],[1]] [[2,1,1],[2,1],[2,1]]=>[[2,2,2],[1,1,1],[1]] [[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]]=>[[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]] [[2,1,1],[2,1,1],[1],[1]]=>[[2,2,1,1],[1,1],[1,1]] [[2,1,1],[2,1,1],[2]]=>[[2,2,2],[1,1],[1,1]] [[2,1,1],[2,1,1],[1,1]]=>[[2,2,1],[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],[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],[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],[1,1,1]]=>[[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],[1,1,1],[1,1],[1,1]] [[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]]=>[[4,1,1,1,1,1],[1]] [[4,1],[2],[1],[1],[1]]=>[[4,2,1,1,1],[1]] [[4,1],[2],[2],[1]]=>[[4,2,2,1],[1]] [[4,1],[1,1],[1],[1],[1]]=>[[4,1,1,1,1],[1,1]] [[4,1],[1,1],[1,1],[1]]=>[[4,1,1,1],[1,1,1]] [[4,1],[3],[1],[1]]=>[[4,3,1,1],[1]] [[4,1],[3],[2]]=>[[4,3,2],[1]] [[4,1],[2,1],[1],[1]]=>[[4,2,1,1],[1,1]] [[4,1],[2,1],[2]]=>[[4,2,2],[1,1]] [[4,1],[2,1],[1,1]]=>[[4,2,1],[1,1,1]] [[4,1],[4],[1]]=>[[4,4,1],[1]] [[4,1],[3,1],[1]]=>[[4,3,1],[1,1]] [[4,1],[4,1]]=>[[4,4],[1,1]] [[3,2],[1],[1],[1],[1],[1]]=>[[3,1,1,1,1,1],[2]] [[3,2],[2],[1],[1],[1]]=>[[3,2,1,1,1],[2]] [[3,2],[2],[2],[1]]=>[[3,2,2,1],[2]] [[3,2],[1,1],[1],[1],[1]]=>[[3,1,1,1,1],[2,1]] [[3,2],[1,1],[1,1],[1]]=>[[3,1,1,1],[2,1,1]] [[3,2],[3],[1],[1]]=>[[3,3,1,1],[2]] [[3,2],[3],[2]]=>[[3,3,2],[2]] [[3,2],[2,1],[1],[1]]=>[[3,2,1,1],[2,1]] [[3,2],[2,1],[2]]=>[[3,2,2],[2,1]] [[3,2],[2,1],[1,1]]=>[[3,2,1],[2,1,1]] [[3,2],[3,1],[1]]=>[[3,3,1],[2,1]] [[3,2],[2,2],[1]]=>[[3,2,1],[2,2]] [[3,2],[3,2]]=>[[3,3],[2,2]] [[3,1,1],[1],[1],[1],[1],[1]]=>[[3,1,1,1,1,1],[1],[1]] [[3,1,1],[2],[1],[1],[1]]=>[[3,2,1,1,1],[1],[1]] [[3,1,1],[2],[2],[1]]=>[[3,2,2,1],[1],[1]] [[3,1,1],[1,1],[1],[1],[1]]=>[[3,1,1,1,1],[1,1],[1]] [[3,1,1],[1,1],[1,1],[1]]=>[[3,1,1,1],[1,1,1],[1]] [[3,1,1],[3],[1],[1]]=>[[3,3,1,1],[1],[1]] [[3,1,1],[3],[2]]=>[[3,3,2],[1],[1]] [[3,1,1],[2,1],[1],[1]]=>[[3,2,1,1],[1,1],[1]] [[3,1,1],[2,1],[2]]=>[[3,2,2],[1,1],[1]] [[3,1,1],[2,1],[1,1]]=>[[3,2,1],[1,1,1],[1]] [[3,1,1],[1,1,1],[1],[1]]=>[[3,1,1,1],[1,1],[1,1]] [[3,1,1],[1,1,1],[1,1]]=>[[3,1,1],[1,1,1],[1,1]] [[3,1,1],[3,1],[1]]=>[[3,3,1],[1,1],[1]] [[3,1,1],[2,1,1],[1]]=>[[3,2,1],[1,1],[1,1]] [[3,1,1],[3,1,1]]=>[[3,3],[1,1],[1,1]] [[2,2,1],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1],[2],[1]] [[2,2,1],[2],[1],[1],[1]]=>[[2,2,1,1,1],[2],[1]] [[2,2,1],[2],[2],[1]]=>[[2,2,2,1],[2],[1]] [[2,2,1],[1,1],[1],[1],[1]]=>[[2,1,1,1,1],[2,1],[1]] [[2,2,1],[1,1],[1,1],[1]]=>[[2,1,1,1],[2,1,1],[1]] [[2,2,1],[2,1],[1],[1]]=>[[2,2,1,1],[2,1],[1]] [[2,2,1],[2,1],[2]]=>[[2,2,2],[2,1],[1]] [[2,2,1],[2,1],[1,1]]=>[[2,2,1],[2,1,1],[1]] [[2,2,1],[1,1,1],[1],[1]]=>[[2,1,1,1],[2,1],[1,1]] [[2,2,1],[1,1,1],[1,1]]=>[[2,1,1],[2,1,1],[1,1]] [[2,2,1],[2,2],[1]]=>[[2,2,1],[2,2],[1]] [[2,2,1],[2,1,1],[1]]=>[[2,2,1],[2,1],[1,1]] [[2,2,1],[2,2,1]]=>[[2,2],[2,2],[1,1]] [[2,1,1,1],[1],[1],[1],[1],[1]]=>[[2,1,1,1,1,1],[1],[1],[1]] [[2,1,1,1],[2],[1],[1],[1]]=>[[2,2,1,1,1],[1],[1],[1]] [[2,1,1,1],[2],[2],[1]]=>[[2,2,2,1],[1],[1],[1]] [[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]]=>[[2,1,1,1],[1,1,1],[1],[1]] [[2,1,1,1],[2,1],[1],[1]]=>[[2,2,1,1],[1,1],[1],[1]] [[2,1,1,1],[2,1],[2]]=>[[2,2,2],[1,1],[1],[1]] [[2,1,1,1],[2,1],[1,1]]=>[[2,2,1],[1,1,1],[1],[1]] [[2,1,1,1],[1,1,1],[1],[1]]=>[[2,1,1,1],[1,1],[1,1],[1]] [[2,1,1,1],[1,1,1],[1,1]]=>[[2,1,1],[1,1,1],[1,1],[1]] [[2,1,1,1],[2,1,1],[1]]=>[[2,2,1],[1,1],[1,1],[1]] [[2,1,1,1],[1,1,1,1],[1]]=>[[2,1,1],[1,1],[1,1],[1,1]] [[2,1,1,1],[2,1,1,1]]=>[[2,2],[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],[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]] [[1,1,1,1,1],[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],[1,1,1,1,1]]=>[[1,1],[1,1],[1,1],[1,1],[1,1]] [[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]]=>[[5,1,1,1,1],[1]] [[5,1],[2],[1],[1]]=>[[5,2,1,1],[1]] [[5,1],[2],[2]]=>[[5,2,2],[1]] [[5,1],[1,1],[1],[1]]=>[[5,1,1,1],[1,1]] [[5,1],[1,1],[1,1]]=>[[5,1,1],[1,1,1]] [[5,1],[3],[1]]=>[[5,3,1],[1]] [[5,1],[2,1],[1]]=>[[5,2,1],[1,1]] [[5,1],[4]]=>[[5,4],[1]] [[5,1],[3,1]]=>[[5,3],[1,1]] [[4,2],[1],[1],[1],[1]]=>[[4,1,1,1,1],[2]] [[4,2],[2],[1],[1]]=>[[4,2,1,1],[2]] [[4,2],[2],[2]]=>[[4,2,2],[2]] [[4,2],[1,1],[1],[1]]=>[[4,1,1,1],[2,1]] [[4,2],[1,1],[1,1]]=>[[4,1,1],[2,1,1]] [[4,2],[3],[1]]=>[[4,3,1],[2]] [[4,2],[2,1],[1]]=>[[4,2,1],[2,1]] [[4,2],[4]]=>[[4,4],[2]] [[4,2],[3,1]]=>[[4,3],[2,1]] [[4,2],[2,2]]=>[[4,2],[2,2]] [[4,1,1],[1],[1],[1],[1]]=>[[4,1,1,1,1],[1],[1]] [[4,1,1],[2],[1],[1]]=>[[4,2,1,1],[1],[1]] [[4,1,1],[2],[2]]=>[[4,2,2],[1],[1]] [[4,1,1],[1,1],[1],[1]]=>[[4,1,1,1],[1,1],[1]] [[4,1,1],[1,1],[1,1]]=>[[4,1,1],[1,1,1],[1]] [[4,1,1],[3],[1]]=>[[4,3,1],[1],[1]] [[4,1,1],[2,1],[1]]=>[[4,2,1],[1,1],[1]] [[4,1,1],[1,1,1],[1]]=>[[4,1,1],[1,1],[1,1]] [[4,1,1],[4]]=>[[4,4],[1],[1]] [[4,1,1],[3,1]]=>[[4,3],[1,1],[1]] [[4,1,1],[2,1,1]]=>[[4,2],[1,1],[1,1]] [[3,3],[1],[1],[1],[1]]=>[[3,1,1,1,1],[3]] [[3,3],[2],[1],[1]]=>[[3,2,1,1],[3]] [[3,3],[2],[2]]=>[[3,2,2],[3]] [[3,3],[1,1],[1],[1]]=>[[3,1,1,1],[3,1]] [[3,3],[1,1],[1,1]]=>[[3,1,1],[3,1,1]] [[3,3],[3],[1]]=>[[3,3,1],[3]] [[3,3],[2,1],[1]]=>[[3,2,1],[3,1]] [[3,3],[3,1]]=>[[3,3],[3,1]] [[3,3],[2,2]]=>[[3,2],[3,2]] [[3,2,1],[1],[1],[1],[1]]=>[[3,1,1,1,1],[2],[1]] [[3,2,1],[2],[1],[1]]=>[[3,2,1,1],[2],[1]] [[3,2,1],[2],[2]]=>[[3,2,2],[2],[1]] [[3,2,1],[1,1],[1],[1]]=>[[3,1,1,1],[2,1],[1]] [[3,2,1],[1,1],[1,1]]=>[[3,1,1],[2,1,1],[1]] [[3,2,1],[3],[1]]=>[[3,3,1],[2],[1]] [[3,2,1],[2,1],[1]]=>[[3,2,1],[2,1],[1]] [[3,2,1],[1,1,1],[1]]=>[[3,1,1],[2,1],[1,1]] [[3,2,1],[3,1]]=>[[3,3],[2,1],[1]] [[3,2,1],[2,2]]=>[[3,2],[2,2],[1]] [[3,2,1],[2,1,1]]=>[[3,2],[2,1],[1,1]] [[3,1,1,1],[1],[1],[1],[1]]=>[[3,1,1,1,1],[1],[1],[1]] [[3,1,1,1],[2],[1],[1]]=>[[3,2,1,1],[1],[1],[1]] [[3,1,1,1],[2],[2]]=>[[3,2,2],[1],[1],[1]] [[3,1,1,1],[1,1],[1],[1]]=>[[3,1,1,1],[1,1],[1],[1]] [[3,1,1,1],[1,1],[1,1]]=>[[3,1,1],[1,1,1],[1],[1]] [[3,1,1,1],[3],[1]]=>[[3,3,1],[1],[1],[1]] [[3,1,1,1],[2,1],[1]]=>[[3,2,1],[1,1],[1],[1]] [[3,1,1,1],[1,1,1],[1]]=>[[3,1,1],[1,1],[1,1],[1]] [[3,1,1,1],[3,1]]=>[[3,3],[1,1],[1],[1]] [[3,1,1,1],[2,1,1]]=>[[3,2],[1,1],[1,1],[1]] [[3,1,1,1],[1,1,1,1]]=>[[3,1],[1,1],[1,1],[1,1]] [[2,2,2],[1],[1],[1],[1]]=>[[2,1,1,1,1],[2],[2]] [[2,2,2],[2],[1],[1]]=>[[2,2,1,1],[2],[2]] [[2,2,2],[2],[2]]=>[[2,2,2],[2],[2]] [[2,2,2],[1,1],[1],[1]]=>[[2,1,1,1],[2,1],[2]] [[2,2,2],[1,1],[1,1]]=>[[2,1,1],[2,1,1],[2]] [[2,2,2],[2,1],[1]]=>[[2,2,1],[2,1],[2]] [[2,2,2],[1,1,1],[1]]=>[[2,1,1],[2,1],[2,1]] [[2,2,2],[2,2]]=>[[2,2],[2,2],[2]] [[2,2,2],[2,1,1]]=>[[2,2],[2,1],[2,1]] [[2,2,1,1],[1],[1],[1],[1]]=>[[2,1,1,1,1],[2],[1],[1]] [[2,2,1,1],[2],[1],[1]]=>[[2,2,1,1],[2],[1],[1]] [[2,2,1,1],[2],[2]]=>[[2,2,2],[2],[1],[1]] [[2,2,1,1],[1,1],[1],[1]]=>[[2,1,1,1],[2,1],[1],[1]] [[2,2,1,1],[1,1],[1,1]]=>[[2,1,1],[2,1,1],[1],[1]] [[2,2,1,1],[2,1],[1]]=>[[2,2,1],[2,1],[1],[1]] [[2,2,1,1],[1,1,1],[1]]=>[[2,1,1],[2,1],[1,1],[1]] [[2,2,1,1],[2,2]]=>[[2,2],[2,2],[1],[1]] [[2,2,1,1],[2,1,1]]=>[[2,2],[2,1],[1,1],[1]] [[2,2,1,1],[1,1,1,1]]=>[[2,1],[2,1],[1,1],[1,1]] [[2,1,1,1,1],[1],[1],[1],[1]]=>[[2,1,1,1,1],[1],[1],[1],[1]] [[2,1,1,1,1],[2],[1],[1]]=>[[2,2,1,1],[1],[1],[1],[1]] [[2,1,1,1,1],[2],[2]]=>[[2,2,2],[1],[1],[1],[1]] [[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]]=>[[2,1,1],[1,1,1],[1],[1],[1]] [[2,1,1,1,1],[2,1],[1]]=>[[2,2,1],[1,1],[1],[1],[1]] [[2,1,1,1,1],[1,1,1],[1]]=>[[2,1,1],[1,1],[1,1],[1],[1]] [[2,1,1,1,1],[2,1,1]]=>[[2,2],[1,1],[1,1],[1],[1]] [[2,1,1,1,1],[1,1,1,1]]=>[[2,1],[1,1],[1,1],[1,1],[1]] [[1,1,1,1,1,1],[1],[1],[1],[1]]=>[[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],[1,1,1],[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]] [[7],[1],[1],[1]]=>[[7,1,1,1]] [[7],[2],[1]]=>[[7,2,1]] [[7],[3]]=>[[7,3]] [[6,1],[1],[1],[1]]=>[[6,1,1,1],[1]] [[6,1],[2],[1]]=>[[6,2,1],[1]] [[6,1],[1,1],[1]]=>[[6,1,1],[1,1]] [[6,1],[3]]=>[[6,3],[1]] [[6,1],[2,1]]=>[[6,2],[1,1]] [[5,2],[1],[1],[1]]=>[[5,1,1,1],[2]] [[5,2],[2],[1]]=>[[5,2,1],[2]] [[5,2],[1,1],[1]]=>[[5,1,1],[2,1]] [[5,2],[3]]=>[[5,3],[2]] [[5,2],[2,1]]=>[[5,2],[2,1]] [[5,1,1],[1],[1],[1]]=>[[5,1,1,1],[1],[1]] [[5,1,1],[2],[1]]=>[[5,2,1],[1],[1]] [[5,1,1],[1,1],[1]]=>[[5,1,1],[1,1],[1]] [[5,1,1],[3]]=>[[5,3],[1],[1]] [[5,1,1],[2,1]]=>[[5,2],[1,1],[1]] [[5,1,1],[1,1,1]]=>[[5,1],[1,1],[1,1]] [[4,3],[1],[1],[1]]=>[[4,1,1,1],[3]] [[4,3],[2],[1]]=>[[4,2,1],[3]] [[4,3],[1,1],[1]]=>[[4,1,1],[3,1]] [[4,3],[3]]=>[[4,3],[3]] [[4,3],[2,1]]=>[[4,2],[3,1]] [[4,2,1],[1],[1],[1]]=>[[4,1,1,1],[2],[1]] [[4,2,1],[2],[1]]=>[[4,2,1],[2],[1]] [[4,2,1],[1,1],[1]]=>[[4,1,1],[2,1],[1]] [[4,2,1],[3]]=>[[4,3],[2],[1]] [[4,2,1],[2,1]]=>[[4,2],[2,1],[1]] [[4,2,1],[1,1,1]]=>[[4,1],[2,1],[1,1]] [[4,1,1,1],[1],[1],[1]]=>[[4,1,1,1],[1],[1],[1]] [[4,1,1,1],[2],[1]]=>[[4,2,1],[1],[1],[1]] [[4,1,1,1],[1,1],[1]]=>[[4,1,1],[1,1],[1],[1]] [[4,1,1,1],[3]]=>[[4,3],[1],[1],[1]] [[4,1,1,1],[2,1]]=>[[4,2],[1,1],[1],[1]] [[4,1,1,1],[1,1,1]]=>[[4,1],[1,1],[1,1],[1]] [[3,3,1],[1],[1],[1]]=>[[3,1,1,1],[3],[1]] [[3,3,1],[2],[1]]=>[[3,2,1],[3],[1]] [[3,3,1],[1,1],[1]]=>[[3,1,1],[3,1],[1]] [[3,3,1],[3]]=>[[3,3],[3],[1]] [[3,3,1],[2,1]]=>[[3,2],[3,1],[1]] [[3,3,1],[1,1,1]]=>[[3,1],[3,1],[1,1]] [[3,2,2],[1],[1],[1]]=>[[3,1,1,1],[2],[2]] [[3,2,2],[2],[1]]=>[[3,2,1],[2],[2]] [[3,2,2],[1,1],[1]]=>[[3,1,1],[2,1],[2]] [[3,2,2],[3]]=>[[3,3],[2],[2]] [[3,2,2],[2,1]]=>[[3,2],[2,1],[2]] [[3,2,2],[1,1,1]]=>[[3,1],[2,1],[2,1]] [[3,2,1,1],[1],[1],[1]]=>[[3,1,1,1],[2],[1],[1]] [[3,2,1,1],[2],[1]]=>[[3,2,1],[2],[1],[1]] [[3,2,1,1],[1,1],[1]]=>[[3,1,1],[2,1],[1],[1]] [[3,2,1,1],[3]]=>[[3,3],[2],[1],[1]] [[3,2,1,1],[2,1]]=>[[3,2],[2,1],[1],[1]] [[3,2,1,1],[1,1,1]]=>[[3,1],[2,1],[1,1],[1]] [[3,1,1,1,1],[1],[1],[1]]=>[[3,1,1,1],[1],[1],[1],[1]] [[3,1,1,1,1],[2],[1]]=>[[3,2,1],[1],[1],[1],[1]] [[3,1,1,1,1],[1,1],[1]]=>[[3,1,1],[1,1],[1],[1],[1]] [[3,1,1,1,1],[3]]=>[[3,3],[1],[1],[1],[1]] [[3,1,1,1,1],[2,1]]=>[[3,2],[1,1],[1],[1],[1]] [[3,1,1,1,1],[1,1,1]]=>[[3,1],[1,1],[1,1],[1],[1]] [[2,2,2,1],[1],[1],[1]]=>[[2,1,1,1],[2],[2],[1]] [[2,2,2,1],[2],[1]]=>[[2,2,1],[2],[2],[1]] [[2,2,2,1],[1,1],[1]]=>[[2,1,1],[2,1],[2],[1]] [[2,2,2,1],[2,1]]=>[[2,2],[2,1],[2],[1]] [[2,2,2,1],[1,1,1]]=>[[2,1],[2,1],[2,1],[1]] [[2,2,1,1,1],[1],[1],[1]]=>[[2,1,1,1],[2],[1],[1],[1]] [[2,2,1,1,1],[2],[1]]=>[[2,2,1],[2],[1],[1],[1]] [[2,2,1,1,1],[1,1],[1]]=>[[2,1,1],[2,1],[1],[1],[1]] [[2,2,1,1,1],[2,1]]=>[[2,2],[2,1],[1],[1],[1]] [[2,2,1,1,1],[1,1,1]]=>[[2,1],[2,1],[1,1],[1],[1]] [[2,1,1,1,1,1],[1],[1],[1]]=>[[2,1,1,1],[1],[1],[1],[1],[1]] [[2,1,1,1,1,1],[2],[1]]=>[[2,2,1],[1],[1],[1],[1],[1]] [[2,1,1,1,1,1],[1,1],[1]]=>[[2,1,1],[1,1],[1],[1],[1],[1]] [[2,1,1,1,1,1],[2,1]]=>[[2,2],[1,1],[1],[1],[1],[1]] [[2,1,1,1,1,1],[1,1,1]]=>[[2,1],[1,1],[1,1],[1],[1],[1]] [[1,1,1,1,1,1,1],[1],[1],[1]]=>[[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],[1,1],[1],[1],[1],[1]] [[8],[1],[1]]=>[[8,1,1]] [[8],[2]]=>[[8,2]] [[7,1],[1],[1]]=>[[7,1,1],[1]] [[7,1],[2]]=>[[7,2],[1]] [[7,1],[1,1]]=>[[7,1],[1,1]] [[6,2],[1],[1]]=>[[6,1,1],[2]] [[6,2],[2]]=>[[6,2],[2]] [[6,2],[1,1]]=>[[6,1],[2,1]] [[6,1,1],[1],[1]]=>[[6,1,1],[1],[1]] [[6,1,1],[2]]=>[[6,2],[1],[1]] [[6,1,1],[1,1]]=>[[6,1],[1,1],[1]] [[5,3],[1],[1]]=>[[5,1,1],[3]] [[5,3],[2]]=>[[5,2],[3]] [[5,3],[1,1]]=>[[5,1],[3,1]] [[5,2,1],[1],[1]]=>[[5,1,1],[2],[1]] [[5,2,1],[2]]=>[[5,2],[2],[1]] [[5,2,1],[1,1]]=>[[5,1],[2,1],[1]] [[5,1,1,1],[1],[1]]=>[[5,1,1],[1],[1],[1]] [[5,1,1,1],[2]]=>[[5,2],[1],[1],[1]] [[5,1,1,1],[1,1]]=>[[5,1],[1,1],[1],[1]] [[4,4],[1],[1]]=>[[4,1,1],[4]] [[4,4],[2]]=>[[4,2],[4]] [[4,4],[1,1]]=>[[4,1],[4,1]] [[4,3,1],[1],[1]]=>[[4,1,1],[3],[1]] [[4,3,1],[2]]=>[[4,2],[3],[1]] [[4,3,1],[1,1]]=>[[4,1],[3,1],[1]] [[4,2,2],[1],[1]]=>[[4,1,1],[2],[2]] [[4,2,2],[2]]=>[[4,2],[2],[2]] [[4,2,2],[1,1]]=>[[4,1],[2,1],[2]] [[4,2,1,1],[1],[1]]=>[[4,1,1],[2],[1],[1]] [[4,2,1,1],[2]]=>[[4,2],[2],[1],[1]] [[4,2,1,1],[1,1]]=>[[4,1],[2,1],[1],[1]] [[4,1,1,1,1],[1],[1]]=>[[4,1,1],[1],[1],[1],[1]] [[4,1,1,1,1],[2]]=>[[4,2],[1],[1],[1],[1]] [[4,1,1,1,1],[1,1]]=>[[4,1],[1,1],[1],[1],[1]] [[3,3,2],[1],[1]]=>[[3,1,1],[3],[2]] [[3,3,2],[2]]=>[[3,2],[3],[2]] [[3,3,2],[1,1]]=>[[3,1],[3,1],[2]] [[3,3,1,1],[1],[1]]=>[[3,1,1],[3],[1],[1]] [[3,3,1,1],[2]]=>[[3,2],[3],[1],[1]] [[3,3,1,1],[1,1]]=>[[3,1],[3,1],[1],[1]] [[3,2,2,1],[1],[1]]=>[[3,1,1],[2],[2],[1]] [[3,2,2,1],[2]]=>[[3,2],[2],[2],[1]] [[3,2,2,1],[1,1]]=>[[3,1],[2,1],[2],[1]] [[3,2,1,1,1],[1],[1]]=>[[3,1,1],[2],[1],[1],[1]] [[3,2,1,1,1],[2]]=>[[3,2],[2],[1],[1],[1]] [[3,2,1,1,1],[1,1]]=>[[3,1],[2,1],[1],[1],[1]] [[3,1,1,1,1,1],[1],[1]]=>[[3,1,1],[1],[1],[1],[1],[1]] [[3,1,1,1,1,1],[2]]=>[[3,2],[1],[1],[1],[1],[1]] [[3,1,1,1,1,1],[1,1]]=>[[3,1],[1,1],[1],[1],[1],[1]] [[2,2,2,2],[1],[1]]=>[[2,1,1],[2],[2],[2]] [[2,2,2,2],[2]]=>[[2,2],[2],[2],[2]] [[2,2,2,2],[1,1]]=>[[2,1],[2,1],[2],[2]] [[2,2,2,1,1],[1],[1]]=>[[2,1,1],[2],[2],[1],[1]] [[2,2,2,1,1],[2]]=>[[2,2],[2],[2],[1],[1]] [[2,2,2,1,1],[1,1]]=>[[2,1],[2,1],[2],[1],[1]] [[2,2,1,1,1,1],[1],[1]]=>[[2,1,1],[2],[1],[1],[1],[1]] [[2,2,1,1,1,1],[2]]=>[[2,2],[2],[1],[1],[1],[1]] [[2,2,1,1,1,1],[1,1]]=>[[2,1],[2,1],[1],[1],[1],[1]] [[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],[2]]=>[[2,2],[1],[1],[1],[1],[1],[1]] [[2,1,1,1,1,1,1],[1,1]]=>[[2,1],[1,1],[1],[1],[1],[1],[1]] [[1,1,1,1,1,1,1,1],[1],[1]]=>[[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]]=>[[9,1]] [[8,1],[1]]=>[[8,1],[1]] [[7,2],[1]]=>[[7,1],[2]] [[7,1,1],[1]]=>[[7,1],[1],[1]] [[6,3],[1]]=>[[6,1],[3]] [[6,2,1],[1]]=>[[6,1],[2],[1]] [[6,1,1,1],[1]]=>[[6,1],[1],[1],[1]] [[5,4],[1]]=>[[5,1],[4]] [[5,3,1],[1]]=>[[5,1],[3],[1]] [[5,2,2],[1]]=>[[5,1],[2],[2]] [[5,2,1,1],[1]]=>[[5,1],[2],[1],[1]] [[5,1,1,1,1],[1]]=>[[5,1],[1],[1],[1],[1]] [[4,4,1],[1]]=>[[4,1],[4],[1]] [[4,3,2],[1]]=>[[4,1],[3],[2]] [[4,3,1,1],[1]]=>[[4,1],[3],[1],[1]] [[4,2,2,1],[1]]=>[[4,1],[2],[2],[1]] [[4,2,1,1,1],[1]]=>[[4,1],[2],[1],[1],[1]] [[4,1,1,1,1,1],[1]]=>[[4,1],[1],[1],[1],[1],[1]] [[3,3,3],[1]]=>[[3,1],[3],[3]] [[3,3,2,1],[1]]=>[[3,1],[3],[2],[1]] [[3,3,1,1,1],[1]]=>[[3,1],[3],[1],[1],[1]] [[3,2,2,2],[1]]=>[[3,1],[2],[2],[2]] [[3,2,2,1,1],[1]]=>[[3,1],[2],[2],[1],[1]] [[3,2,1,1,1,1],[1]]=>[[3,1],[2],[1],[1],[1],[1]] [[3,1,1,1,1,1,1],[1]]=>[[3,1],[1],[1],[1],[1],[1],[1]] [[2,2,2,2,1],[1]]=>[[2,1],[2],[2],[2],[1]] [[2,2,2,1,1,1],[1]]=>[[2,1],[2],[2],[1],[1],[1]] [[2,2,1,1,1,1,1],[1]]=>[[2,1],[2],[1],[1],[1],[1],[1]] [[2,1,1,1,1,1,1,1],[1]]=>[[2,1],[1],[1],[1],[1],[1],[1],[1]] [[1,1,1,1,1,1,1,1,1],[1]]=>[[1,1],[1],[1],[1],[1],[1],[1],[1],[1]] [[10]]=>[[10]] [[9,1]]=>[[9],[1]] [[8,2]]=>[[8],[2]] [[8,1,1]]=>[[8],[1],[1]] [[7,3]]=>[[7],[3]] [[7,2,1]]=>[[7],[2],[1]] [[7,1,1,1]]=>[[7],[1],[1],[1]] [[6,4]]=>[[6],[4]] [[6,3,1]]=>[[6],[3],[1]] [[6,2,2]]=>[[6],[2],[2]] [[6,2,1,1]]=>[[6],[2],[1],[1]] [[6,1,1,1,1]]=>[[6],[1],[1],[1],[1]] [[5,5]]=>[[5],[5]] [[5,4,1]]=>[[5],[4],[1]] [[5,3,2]]=>[[5],[3],[2]] [[5,3,1,1]]=>[[5],[3],[1],[1]] [[5,2,2,1]]=>[[5],[2],[2],[1]] [[5,2,1,1,1]]=>[[5],[2],[1],[1],[1]] [[5,1,1,1,1,1]]=>[[5],[1],[1],[1],[1],[1]] [[4,4,2]]=>[[4],[4],[2]] [[4,4,1,1]]=>[[4],[4],[1],[1]] [[4,3,3]]=>[[4],[3],[3]] [[4,3,2,1]]=>[[4],[3],[2],[1]] [[4,3,1,1,1]]=>[[4],[3],[1],[1],[1]] [[4,2,2,2]]=>[[4],[2],[2],[2]] [[4,2,2,1,1]]=>[[4],[2],[2],[1],[1]] [[4,2,1,1,1,1]]=>[[4],[2],[1],[1],[1],[1]] [[4,1,1,1,1,1,1]]=>[[4],[1],[1],[1],[1],[1],[1]] [[3,3,3,1]]=>[[3],[3],[3],[1]] [[3,3,2,2]]=>[[3],[3],[2],[2]] [[3,3,2,1,1]]=>[[3],[3],[2],[1],[1]] [[3,3,1,1,1,1]]=>[[3],[3],[1],[1],[1],[1]] [[3,2,2,2,1]]=>[[3],[2],[2],[2],[1]] [[3,2,2,1,1,1]]=>[[3],[2],[2],[1],[1],[1]] [[3,2,1,1,1,1,1]]=>[[3],[2],[1],[1],[1],[1],[1]] [[3,1,1,1,1,1,1,1]]=>[[3],[1],[1],[1],[1],[1],[1],[1]] [[2,2,2,2,2]]=>[[2],[2],[2],[2],[2]] [[2,2,2,2,1,1]]=>[[2],[2],[2],[2],[1],[1]] [[2,2,2,1,1,1,1]]=>[[2],[2],[2],[1],[1],[1],[1]] [[2,2,1,1,1,1,1,1]]=>[[2],[2],[1],[1],[1],[1],[1],[1]] [[2,1,1,1,1,1,1,1,1]]=>[[2],[1],[1],[1],[1],[1],[1],[1],[1]] [[1,1,1,1,1,1,1,1,1,1]]=>[[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]]
click to show experimental identities (only identities of compositions of up to three maps are shown)
Description
The transpose of a plane partition.
This is the mirror symmetry along the vertical axis.
Properties
graded, involutive
Sage code
def mapping(pp):
    return PlanePartition([Partition(la) for la in pp.transpose()])
Weight
11
Created
Sep 13, 2020 at 11:45 by Martin Rubey
Updated
Sep 13, 2020 at 11:45 by Martin Rubey