Sets Avoiding Full-Rank Three-Point Patterns in $({\mathbb{F}}_q^n{)}^k$ Are Exponentially Small

Mohamed Omar

We prove that if a subset of $({\mathbb{F}}_q^n{)}^k$ (with $q$ an odd prime power) avoids a full-rank three-point pattern $\vec{x},\vec{x}+M_1\vec{d},\vec{x}+M_2\vec{d}$ then it is ex…