On generalized corners and matrix multiplication

Kevin Pratt

Suppose that $S\subseteq [n{]}^2$ contains no three points of the form $(x,y),(x,y+\delta ),(x+\delta ,y^{\prime })$, where $\delta \ne 0$. How big can $S$ be? Trivially, $n\le |S|\le n^2$. Slight improv…