Blocking sets of external lines to a conic in \(PG(2,q),q\) even
type: Item
instance of: scholarly article
title: Blocking sets of external lines to a conic in \(PG(2,q),q\) even
zbMATH Open document ID: 1113.51004
author: Massimo Giulietti
published in: European Journal of Combinatorics
publication date: 2006-12-07T00:00:00Z
review text: Let \(C\) be an irreducible conic in the Desarguesian plane \(PG(2, q)\). There are exactly \((q- 1)q/2\) lines of \(PG(2, q)\) which do not intersect \(C\) at any point in \(PG(2, q)\). Each of these lines is called an external line to \(C\). A point-set \(K\) in \(PG(2,q)\) which blocks the external lines to \(C\), i.e. incident with each external line to \(C\), is called a blocking set of external lines to \(C\). The main problem is to find the minimum size for blocking sets of external lines to a conic, and to give a geometric construction for those which attain such a limit. This problem has been solved so far for odd \(q\) by proving that the minimum size is \(q-1\), and that for \(p\geq 9\) any blocking set of external lines to \(C\) of size \(q-1\) consists of a chord \(r\) of \(C\) minus the two common points of \(r\) and \(C\). In the present article, there are classified all point-sets of minimum size in \(PG(2,q)\), \(q\) even, that meet every external line to a conic in \(PG(2, q)\).
reviewed by: Pavel Burda
Mathematics Subject Classification ID: 51E21
zbMATH DE Number: 5077685
MaRDI profile type: Publication
full work available at URL: j.ejc.2004.10.005
OpenAlex ID: W1994353476
cites work: Blocking sets of external lines to a conic in \(\text{PG}(2,q)\), \(q\) odd
cites work: Endliche Gruppen I
cites work: Q3216750
DOI: 10.1016/J.EJC.2004.10.005
description: scientific article; zbMATH DE number 5077685