CycleDecomposition from Permutation
A permutation in cycle notation, fixed points kept: each cycle from its least point, cycles in order of those points.
Called as CombinatorialMap(x, "CycleDecomposition"). The head's page has its examples.
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Each element of Permutation at a size, and its image, applied in your browser; sizes past 7 are not offered.
Properties
Transport a statistic
Pick a statistic on CycleDecomposition. Its distribution over the images of Permutation at each size is computed, and compared with the 323 statistics on Permutation: those that share it are the ones the map sends it to, as far as the sizes computed show.
No statistic is declared on CycleDecomposition.