Corners over quasirandom groups

Abstract

Let $G$ be a finite $D$-quasirandom group and $A\subset G^k$ a $\delta$-dense subset. Then the density of the set of side lengths $g$ of corners \[ \{(a_{1},\dots,a_{k}),(ga_{1},a_{2},\dots,a_{k}),\dots,(ga_{1},\dots,ga_{k})\} \subset A \] converges to $1$ as $D\to \infty$.

6 pages, with an expanded introduction

References in corpus (2)

• Quantitative equidistribution for certain quadruples in quasi-random groups
• Triangles in cartesian squares of quasirandom groups