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Communications of the ACM

Communications of the ACM

Partioning algorithms for finite sets

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The partitions of a set with n elements are represented by certain n-tuples of positive integers. Algorithms are described which generate without repetitions the n-tuples corresponding to: (1) all partitions of the given set, (2) all partitions of the given set into m or fewer sets (1 ≨ mn), and (3) all partitions of the given set into exactly m sets (1 ≨ mn).

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