Open Collections

Description

In this talk we will discuss lower and upper bounds for the size of $k$-AP-free subsets of $\mathbb{Z}_m^n$, that is, for $r_k(\mathbb{Z}_m^n$, in certain cases. Specifically, we will discuss some lower bounds given by Elsholtz and myself. In the case $m=4,k=3$ we present a construction which gives the tight answer up to $n\leq 5$ and point out some connection with coding theory. We will also mention some open questions (and some partial answers) about related linear algebraic problems.