CutWord from IntegerComposition
A composition of n as the binary word of length n - 1 marking where it is cut.
Not order-preserving: IntegerCompositions lists compositions lex on their parts, while BinaryWords(n - 1) through IntegerComposition(word) gives them in their cut words' order.
Called as CombinatorialMap(x, "CutWord"). The head's page has its examples.
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Each element of IntegerComposition at a size, and its image, applied in your browser; sizes past 6 are not offered.
Properties
Transport a statistic
Pick a statistic on BinaryWord. Its distribution over the images of IntegerComposition at each size is computed, and compared with the 44 statistics on IntegerComposition: those that share it are the ones the map sends it to, as far as the sizes computed show.