Two versions of the Ajtai-Szemer\'edi Theorem are considered in the Cartesian square of a finite non-Abelian group $G$. In case $G$ is sufficiently quasirandom, we obtain strong forms of both versions: if $E \subseteq G\times G$ is fairly dense, then $E$ contains a large number of the desired patterns for most individual choices of `common difference'. For one of the versions, we also show that this set of good common differences is syndetic.
CITATION STYLE
Austin, T. (2016). Ajtai–Szemerédi Theorems over quasirandom groups (pp. 453–484). https://doi.org/10.1007/978-3-319-24298-9_19
Mendeley helps you to discover research relevant for your work.