Partioning algorithms for finite sets

Abstract

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). © 1963, ACM. All rights reserved.