Lower bounds for corner-free sets

Abstract

A corner is a set of three points in ${\mathbf{Z}}^2$ of the form $(x,y),(x+d,y),(x,y+d)$ with $d\ne 0$. We show that for infinitely many $N$ there is a set $A\subset [N{]}^2$ of size $2^{-(c+o(1))\sqrt{{\log }_{2}N}}{N}^2$ not containing any corner, where $c=2\sqrt{2{\log }_2\frac{4}{3}}\approx 1.822\dots$.

2 pages, very minor elaboration of the exposition. Accepted for publication in New Zealand Journal of Mathematics

References in corpus (1)

• Larger Corner-Free Sets from Better NOF Exactly-$N$ Protocols

Cited by in corpus (2)

• Larger Corner-Free Sets from Better NOF Exactly-$N$ Protocols
• Removal lemmas and approximate homomorphisms