Zero sum sets in abelian groups
Combinatorics
2021-02-09 v2
Abstract
The distribution of cardinalities of zero-sum sets in abelian groups is completely determined. A complex summation involving the M\"obius function is given for the general abelian group, while in many special cases, including the case of elementary abelian groups, solved earlier by Li and Wan, it has a compact form. The proof involves two different M\"obius transforms, on positive integers and on set partitions.
Keywords
Cite
@article{arxiv.2102.00011,
title = {Zero sum sets in abelian groups},
author = {Minjia Shi and Denis S. Krotov and Xiaoxiao Li and Patrick Solé},
journal= {arXiv preprint arXiv:2102.00011},
year = {2021}
}
Comments
The result is not new, see [J. Li and D. Wan, Counting subset sums of finite abelian groups, J. Combin. Theory, Ser. A, 119(1) (2012), 170-182]