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. It is shown that the elements of these classes can be listed so that the only change 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.