A new approach to arcs
type: Item
instance of: scholarly article
title: A new approach to arcs
zbMATH Open document ID: 0932.05016
DOI: 10.1023/A:1006620816691
author: Aleksander Malnič
author: Dragan Marušič
author: Gy. Kiss
published in: Acta Mathematica Hungarica
publication date: 2000-02-21T00:00:00Z
review text: The authors consider the Desarguesian plane \(\text{PG}(2,q)\) represented via a difference set in the cyclic group of order \(q^2+q+1\), and define the covering number of a set \(S\) of points as the smallest number of lines needed to cover the set \(-S\). They use this notion to study \(k\)-arcs and call such an arc flat when its covering number is 1. In particular, they focus on hyperovals in even order planes and consider those with covering numbers 1 and 2. Small order planes are examined and some classical results are recovered. An algorithm is suggested which tests whether a \(k\)-set of points forms an arc.
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51E21
Mathematics Subject Classification ID: 51D20
zbMATH DE Number: 1404417
zbMATH Keywords: arcs
zbMATH Keywords: hyperovals
zbMATH Keywords: finite projective planes
MaRDI profile type: Publication
full work available at URL: a:1006620816691
OpenAlex ID: W1794043882
description: scientific article; zbMATH DE number 1404417