TY - JOUR AU - Green, Ben PY - 2021/07/29 Y2 - 2024/03/30 TI - Lower bounds for corner-free sets JF - New Zealand Journal of Mathematics JA - NZ J Math VL - 51 IS - SE - Articles DO - 10.53733/86 UR - https://www.nzjmath.org/index.php/NZJMATH/article/view/86 SP - 1-2 AB - <p>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 $d eq 0$, where $c = 2 \sqrt{2 \log_2 \frac{4}{3}} \approx 1.822\dots$.</p> ER -