Sum-full sets are not zero-sum-free
Number Theory
2021-05-20 v2 Combinatorics
Abstract
Let be a finite, nonempty subset of an abelian group. We show that if every element of is a sum of two other elements, then has a nonempty zero-sum subset. That is, a (finite, nonempty) sum-full subset of an abelian group is not zero-sum-free.
Keywords
Cite
@article{arxiv.2101.02586,
title = {Sum-full sets are not zero-sum-free},
author = {Vsevolod F. Lev and Janos Nagy and Peter Pal Pach},
journal= {arXiv preprint arXiv:2101.02586},
year = {2021}
}
Comments
Slightly revised version