Enumerating submultisets of multisets

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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.
Original languageEnglish
PublisherDepartment of Information and Computing Sciences, Utrecht University
Number of pages8
Publication statusPublished - 2001

Publication series

NameTechnical Report Series
ISSN (Print)0924-3275


  • Wiskunde en Informatica (WIIN)


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