On large sum-free sets: revised bounds and patterns

TL;DR

This paper revises previous results on large sum-free sets, providing a new upper bound for certain subsets and identifying all patterns for maximum sum-free sets.

Contribution

It offers a corrected upper bound for specific sum-free subsets and classifies all patterns for maximum sum-free sets, improving understanding of their structure.

Findings

New upper bound for sum-free subsets in [n/3, n/2]

Complete classification of patterns for maximum sum-free sets

Rectification of two previous literature results

Abstract

In this paper we rectify two previous results found in the literature. Our work leads to a new upper bound for the largest sum-free subset of $[1,n]$ with lowest value in $\left [\frac{n}{3},\frac{n}{2}\right ]$, and the identification of all patterns that can be used to form sum-free sets of maximum cardinality.