Blocking sets of type \((1,k)\) in a finite projective plane
type: Item
instance of: scholarly article
title: Blocking sets of type \((1,k)\) in a finite projective plane
zbMATH Open document ID: 0948.51009
DOI: 10.1023/A:1005169032357
author: Mauro Biliotti
author: Eliana Francot
published in: Geometriae Dedicata
publication date: 2000-07-06T00:00:00Z
review text: In a finite projective plane \(\Pi\) of order \(n\), a set \(\mathcal B\) is called of type \((1,k)\), if any line intersects \(\mathcal B\) in 1 or \(k\) points. \textit{G. Tallini} [J. Geom. 29, 191-199 (1987; Zbl 0618.51004)] gave strong conditions on the values of \(n\) and \(|\mathcal B|\) in dependence of \(k\). The authors give several numerical results on Tallini's parameters. In particular, they give restrictions on the case \(|{\mathcal B}|=y^m\), \(m\geq 2\). Furthermore, they consider sets of type \((1,k)\) which are conserved by a ``large'' collineation group \(G\) of \(\Pi\). A classification is given in the case where \(G\) is transitive on the \(k\)-secants of \(\mathcal B\) and contains a nontrivial perspectivity, and in the case where \(G\) acts flag-transitively on \(\mathcal B\).
reviewed by: J. Eisfeld
Mathematics Subject Classification ID: 51E21
Mathematics Subject Classification ID: 51A35
Mathematics Subject Classification ID: 51E15
zbMATH DE Number: 1436008
zbMATH Keywords: blocking set
zbMATH Keywords: set of type \((1,k)\)
MaRDI profile type: Publication
full work available at URL: a:1005169032357
OpenAlex ID: W63120575
description: scientific article; zbMATH DE number 1436008