Gray Code Enumeration of Families of Integer Partitions

In this paper we show that the elements of certain families of integer partitions can be listed in a minimal change, or Gray code, order. In particular, we construct Gray code listings for the classes Pδ(n, k) and D(n, k) of partitions of n into parts of size at most k in which, for Pδ(n, k), the parts are congruent to one modulo δ and, for D(n, k), the parts are distinct. The change required between successive partitions is the increase of one part by δ (or the addition of δ ones) and the decrease of one part by δ (or the removal of δ ones), where, in the case of D(n, k), δ = 1.