A Gray Code for Combinations of a Multiset

LetC(k; n0, n1, . . . , nt)denote the set of allk-element combinations of the multiset consisting ofnioccurrences ofifori=0, 1, . . . , t.Each combination is itself a multiset. For example,C(2; 2, 1, 1)={{0, 0}, {0, 1}, {0, 2}, {1, 2}}. We show that multiset combinations can be listed so that successive combinations differ by one element. Multiset combinations simultaneously generalize compositions and combinations, for which minimal change listings, called Gray codes, are known.