Partioning algorithms for finite sets
George A. Hutchinson · Communications of the ACM · 1963
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 ≨ m ≨ n ), and (3) all partitions of the given set into exactly m sets (1 ≨ m ≨ n ).