A lower bound on blocking semiovals
type: Item
instance of: scholarly article
title: A lower bound on blocking semiovals
zbMATH Open document ID: 0970.51007
author: Jeremy M. Dover
published in: European Journal of Combinatorics
publication date: 2001-10-16T00:00:00Z
review text: A set of points \(S\) in a projective plane \(\Pi\) which is at the same time a semioval and a blocking set is called blocking semioval, i.e., a blocking semioval is a set of points of \(\Pi\) satisfying the following properties: for every point \(P\in S\), there exists a unique line \(l\) of \(\Pi\) such that \(l\cap S=\{P\}\); every line of \(\Pi\) contains at least one point of \(S\), but is not entirely contained in \(S\). In this paper the author gives some lower bounds on the size of a blocking semioval in a finite projective plane. He proves that if \(\Pi\) is a projective plane of order \(q\) and \(S\) is a blocking semioval in \(\Pi\), then \(|S|\geq 2q+1\), and if \(q\geq 7\), then \(|S|\geq 2q+2\). If \(q=5\) or \(q=7\), these bounds are sharp. Also he constructs a family of blocking semiovals of size \(3q-4\) in the projective plane \(PG(2,q)\) with \(q>5\) odd.
reviewed by: Guglielmo Lunardon
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 1512032
zbMATH Keywords: semioval
zbMATH Keywords: blocking set
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: eujc.1999.0371
OpenAlex ID: W2075026414
cites work: Blocking Sets in Finite Projective Planes
cites work: Arcs and blocking sets. II
cites work: Blocking sets
cites work: Q5602602
DOI: 10.1006/EUJC.1999.0371
description: scientific article; zbMATH DE number 1512032