On the size of a blocking set in \(\text{PG}(2,p)\)
type: Item
instance of: scholarly article
title: On the size of a blocking set in \(\text{PG}(2,p)\)
zbMATH Open document ID: 0803.05011
DOI: 10.1007/BF01305953
published in: Combinatorica
publication date: 1995-01-02T00:00:00Z
review text: This short and elementary note contains a proof of the following: the size of a non-trivial blocking set in \(\text{PG}(2,p)\), the Desarguesian projective plane of order \(p\), where \(p\) is prime, is at least \(3(p+1)/2\), and this bound can be achieved. (A non-trivial blocking set in \(\text{PG}(2,p)\) is such that any line intersects it, but is not contained in it.) This settles a 25 years old conjecture of Di Paola. This contrasts other results for projective planes of order \(q\). If \(q\) is a square, the tight bound is \(q+ \sqrt q+1\), established by \textit{A. A. Bruen} [SIAM J. Appl. Math. 21, 380-392 (1971; Zbl 0252.05014)]. If the projective plane is Desarguesian, it is at least \(q+ \sqrt{2q}+ 1\), as proved by the author and \textit{A. E. Brouwer} [Bull. Lond. Math. Soc. 18, 132-134 (1986; Zbl 0563.05016)].
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 51E21
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 51A30
zbMATH DE Number: 567475
zbMATH Keywords: blocking set
zbMATH Keywords: Desarguesian projective plane
zbMATH Keywords: conjecture of Di Paola
zbMATH Keywords: projective planes
author: Aart Blokhuis
MaRDI profile type: Publication
Wikidata QID: Q60306524
cites work: The blocking number of an affine space
cites work: Blocking Sets in Finite Projective Planes
cites work: Arcs and blocking sets. II
cites work: On Minimum Blocking Coalitions in Small Projective Plane Games
cites work: Covering finite fields with cosets of subspaces
full work available at URL: https://doi.org/10.1007/bf01305953
OpenAlex ID: W2021647730
description: scientific article; zbMATH DE number 567475