Sum-full sets are not zero-sum-free

2021/01/07 by Lev, Vsevolod F., Nagy, Janos, Pach, Peter Pal
#11B30 #15A06 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2101.02586

Abstract

Let A be a finite, nonempty subset of an abelian group. We show that if every element of A is a sum of two other elements, then A has a nonempty zero-sum subset. That is, a (finite, nonempty) sum-full subset of an abelian group is not zero-sum-free.

Related

• On the structure of zero-sum free set with minimum subset sums in abelian groups
• On sum-free subsets of abelian groups
• Sum-free sets in abelian groups
• Sum-free set in finite abelian groups
• Zero-sum subsets of decomposable sets in Abelian groups