Ajtai–Szemerédi Theorems over quasirandom groups
Ajtai–Szemerédi Theorems over quasirandom groups
Two versions of the Ajtai–Szemerédi 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 …