The subset sum problem for finite abelian groups

Authors:
Michiel Kosters
Affiliations:
Mathematisch Instituut, P.O. Box 9512, 2300 RA, Leiden, The Netherlands
Venue:
Journal of Combinatorial Theory Series A
Year:
2013

Citing 2
Cited 0

Counting subset sums of finite abelian groups

Journal of Combinatorial Theory Series A
On the subset sum problem over finite fields

Finite Fields and Their Applications

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Abstract

Let G be a finite abelian group. A problem in combinatorics is to give an explicit formula for the number of subsets of G of size n which sum up to a given element of G. In this article we give a short proof, using character theory, of a formula for these numbers due to Li and Wan. We show that these numbers are nonzero except in four special cases. A similar formula is given when none of these subsets contain zero.