Enumerating submultisets of multisets

Abstract

In this paper we consider the problem of enumerating the submultisets of a multiset, in which each element has equal multiplicity. The crucial property is that consecutive submultisets in this listing differ one in the cardinality of only one of the elements. This is a generalization to k-ary numbers of the so-called Gray Codes for binary numbers. In the special case of binary numbers there is also a link to the Game Of Hanoi. We give an example where these results were put to good use, and indicate when in general the method described can be applied.