A new proof of Rédei's theorem on the number of directions

2022/12/24 by Gábor Somlai, Somlai, Gabor
Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2212.12823

openalex publication_date 2022/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Rédei and Megyesi proved that the number of directions determined by a p element subset of \mathbbF_p² is either 1 or at least (p+3)/(2). The same result was independently obtained by Dress, Klin and Muzychuk. We give a new and short proof of this result using a Lemma proved by Kiss and the author. The new proof further on a result on polynomials over finite fields.

Related

• On rich and poor directions determined by a subset of a finite plane
• Point distribution and perfect directions in F_p²
• On the directions determined by a Cartesian product in an affine Galois plane
• On polynomials of small range sum
• On directions determined by subsets of vector spaces over finite fields