On the number of directions determined by a set of points in an affine Galois plane
type: Item
instance of: scholarly article
title: On the number of directions determined by a set of points in an affine Galois plane
zbMATH Open document ID: 0852.51006
published in: Journal of Combinatorial Theory. Series A
publication date: 1996-07-09T00:00:00Z
review text: In \(AG (2,q)\), let \(U\) be a set of \(q-n\) points. The author studies the set of ``points at infinity'' \((m)\) such that \(m\) is the slope of some line \(PQ\) where \(P\) and \(Q\) are distinct points of \(U\). Let \(N\) be the number of such points at infinity. Let \(D\) be a set of points at infinity and let \(W\) be a set of affine points. Then \(W\) is said to be a \(D\)-set if \(w\) determines precisely the points of \(D\). The \(D\)-set \(W\) is complete (with respect to \(D)\) if \(W\) is maximal. The main result: If \(U\) is a \(D\)-set with \(q - n\) points, \(n \leq {1 \over 2} \sqrt q\) and if \(|D |< {1 \over 2} (q + 1)\) then \(U\) is incomplete.
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 883806
zbMATH Keywords: directions
zbMATH Keywords: points at infinity
author: Tamás Szőnyi
reviewed by: Theodore G. Ostrom
MaRDI profile type: Publication
full work available at URL: jcta.1996.0042
OpenAlex ID: W2166882067
DOI: 10.1006/JCTA.1996.0042
description: scientific article; zbMATH DE number 883806