Erd\H{o}s' minimum overlap problem

TL;DR

This paper improves the lower bounds for Erdős' minimum overlap problem by applying elementary Fourier analysis and convex optimization techniques.

Contribution

It introduces a novel approach using Fourier analysis and convex optimization to advance the understanding of Erdős' minimum overlap problem.

Findings

Significantly improved lower bounds for the problem.

Application of Fourier analysis to combinatorial overlap problems.

Use of convex optimization to derive bounds.

Abstract

We obtain a substantially improved lower bound for the minimum overlap problem asked by Erd\H{o}s. Our approach uses elementary Fourier analysis to translate the problem to a convex optimization program.