Corners over quasirandom groups
Pavel Zorin-Kranich

TL;DR
This paper proves that in large quasirandom groups, the proportion of corners within dense subsets approaches certainty as the group's quasirandomness increases, revealing a strong combinatorial structure.
Contribution
It establishes a new asymptotic result on the density of corners in dense subsets of quasirandom groups, extending combinatorial understanding in algebraic settings.
Findings
Density of corners approaches 1 as quasirandomness D increases
Large quasirandom groups contain many structured configurations
Results generalize classical combinatorial theorems to algebraic group contexts
Abstract
Let be a finite -quasirandom group and a -dense subset. Then the density of the set of side lengths of corners \[ \{(a_{1},\dots,a_{k}),(ga_{1},a_{2},\dots,a_{k}),\dots,(ga_{1},\dots,ga_{k})\} \subset A \] converges to as .
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