Lower bounds for corner-free sets

Abstract

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 configuration $(x, y), (x + d, y), (x, y + d)$ with $d \neq 0$, where $c = 2 \sqrt{2 \log_2 \frac{4}{3}} \approx 1.822\dots$.

Locations

• New Zealand journal of mathematics - View - PDF
• arXiv (Cornell University) - View - PDF
• Oxford University Research Archive (ORA) (University of Oxford) - View - PDF