An Approximate Counting Version of the Multidimensional Szemerédi Theorem

Natalie Behague, Joseph Hyde, Natasha Morrison +2

For any fixed $d\ge 1$ and subset $X$ of ${\mathbb{N}}^d$, let $r_X(n)$ be the maximum cardinality of a subset $A$ of $\{1,\dots ,n{\}}^d$ which does not contain a subset of the form $\…