Refined bound for sum-free sets in groups of prime order

TL;DR

This paper improves bounds on sum-free subsets in large prime order groups, showing that sufficiently large sum-free sets are contained within a specific interval after dilation.

Contribution

It provides a refined bound for sum-free sets in prime groups, extending previous results and characterizing their structure for large primes.

Findings

Sum-free sets with size greater than 0.318p are contained in a dilated interval

The result applies to sufficiently large primes p

Improves previous bounds on sum-free subset structure

Abstract

Improving upon earlier results of Freiman and the present authors, we show that if $p$ is a sufficiently large prime and $A$ is a sum-free subset of the group of order $p$, such that $n:=|A|>0.318p$, then $A$ is contained in a dilation of the interval $[n,p-n]\pmod p$.