Gábor Somlai

Non-existence of sets with few special directions

Let $p$ be an odd prime and let $S\subseteq\mathbb{F}_p^2$ have cardinality divisible by $p$. We prove that, for all sufficiently large primes $p$, no such set has exactly four special directions, and obtain a conditional extension to larger numbers of special directions under an affine-independence assumption on the c...