Notes on sum-free sets in abelian groups

TL;DR

This paper discusses open problems and asymptotically determines the number of maximal sum-free subsets in most even order abelian groups using the container method.

Contribution

It introduces new asymptotic results on the count of maximal sum-free sets in abelian groups and highlights open problems in the area.

Findings

Asymptotic enumeration of maximal sum-free sets in most even order abelian groups

Identification of open problems related to sum-free sets in abelian groups

Application of the container method to this combinatorial problem

Abstract

In this paper we highlight a few open problems concerning maximal sum-free sets in abelian groups. In addition, for most even order abelian groups $G$ we asymptotically determine the number of maximal distinct sum-free subsets in $G$. Our proof makes use of the container method.