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arXiv · 2109.13992

Special directions on the finite affine plane

Gergely Kiss·Gábor Somlai
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Abstract

In this paper we study the number of special directions of sets of cardinality divisible by $p$ on a finite plane of characteristic $p$, where $p$ is a prime. We show that there is no such a set with exactly two special directions. We characterise sets with exactly 3 special directions which answers a question of Ghidelli in negative. Further we introduce methods to construct sets of minimal cardinality that has exactly 4 special directions for small values of $p$.

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Gergely Kiss, Gábor Somlai. 2023-02-27. Special directions on the finite affine plane. https://arxiv.org/abs/2109.13992

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