On multiple nuclei and a conjecture of Lunelli and Sce
type: Item
instance of: scholarly article
title: On multiple nuclei and a conjecture of Lunelli and Sce
zbMATH Open document ID: 0803.51012
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 1994-08-10T00:00:00Z
full work available at URL: https://eudml.org/doc/225979
review text: A point \(p \not \in S\) is called a \(t\)-fold nucleus of a point set \(S\) contained in an affine plane \(AG (2,q)\), if every line through \(p\) intersects \(S\) at least \(t\) points. The author obtains an upper bound on the number of points which is then applied to obtain an improved lower bound of \((t + 1)q - 1\) on the cardinality of a \(t\)-fold blocking set of \(AG (2,q)\), provided that \(t\) and \(q\) are relatively prime. As a further application, the truth of the Lunelli-Sce conjecture on maximal \((k,n)\)- arcs is established for affine planes.
Mathematics Subject Classification ID: 51E21
Mathematics Subject Classification ID: 05B25
zbMATH DE Number: 617009
zbMATH Keywords: projective plane
zbMATH Keywords: maximal arc
zbMATH Keywords: nucleus
zbMATH Keywords: blocking set
author: Aart Blokhuis
reviewed by: Dieter Jungnickel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 617009