Special directions on the finite affine plane

2021/09/28 by Gergely Kiss, Kiss, Gergely, Gábor Somlai +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2109.13992

openalex publication_date 2021/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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