RestrictedGrowthString from SetPartition
A set partition's restricted growth string: each position labelled with its block's index, from 0.
An order isomorphism: the k-th set partition of n, in the order SetPartitions lists them, goes to the k-th restricted growth string of length n. So everything defined on one carrier is available on the other through it.
Called as CombinatorialMap(x, "RestrictedGrowthString"). The head's page has its examples.
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Each element of SetPartition at a size, and its image, applied in your browser; sizes past 7 are not offered.
Properties
Transport a statistic
Pick a statistic on RestrictedGrowthString. Its distribution over the images of SetPartition at each size is computed, and compared with the 111 statistics on SetPartition: those that share it are the ones the map sends it to, as far as the sizes computed show.
No statistic is declared on RestrictedGrowthString.