On the directions determined by a Cartesian product in an affine Galois plane

2020/01/20 by Di Benedetto, Daniel, Solymosi, Jozsef, White, Ethan P.
#11T06 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2001.06994

Abstract

We prove that the number of directions contained in a set of the form A × B ⊂ AG(2,p), where p is prime, is at least |A||B| - min\|A|,|B|\ + 2. Here A and B are subsets of GF(p) each with at least two elements and |A||B|

Related

• A new proof of Rédei's theorem on the number of directions
• Special directions on the finite affine plane
• Point distribution and perfect directions in F_p²
• On directions determined by subsets of vector spaces over finite fields
• On rich and poor directions determined by a subset of a finite plane