A binary tree representation and related algorithms for generating integer partitions

Abstract

A representation of the partitions of an integer as a binary tree is presented, and the structure of this tree is related to the lexicographic ordering of the set of partitions. The appropriate recursive traversal algorithm for this binary tree immediately yields a recursive algorithm for generating the set of partitions in lexicographic order. Further consideration of the structure of the tree enables us to transform this version of the algorithm into a non-recursive loop-free version. Similar consideration of another recursive traversal algorithm yields corresponding algorithms for generating the set of partitions in a different order.