On maximal partial spreads in \(PG\)(\(n\), \(q\))
type: Item
instance of: scholarly article
title: On maximal partial spreads in \(PG\)(\(n\), \(q\))
zbMATH Open document ID: 1038.51005
DOI: 10.1023/A:1024148308054
author: András Gács
author: Tamás Szőnyi
published in: Designs, Codes and Cryptography
publication date: 2003-08-21T00:00:00Z
review text: The paper under review contains some constructions of maximal partial spreads in \(PG(n, q)\). A partial spread in \(PG(n, q)\) is a set of pairwise disjoint lines. It is called maximal if it is not contained properly in a larger partial spread. In Section 2 of the paper, using a result on bipartite graphs (Lemma 2.1), the authors obtain three important lemmas for their constructions of a maximal partial spreads in \(PG(n, q)\). Then, they consider the cases \(n = 3\), \(n\geq 5\) odd, and \(n\geq 6\) even. In each case they give a construction of a maximal partial spread. When \(n = 3\), as the authors observe, their Construction 3.1 is almost identical with the one of \textit{A. Beutelspacher} [Geom. Dedicata 9, 425--449 (1980; Zbl 0377.50007)], but it enables the authors to construct maximal partial spreads smaller than the spreads constructed by Beutelspacher. Finally, in the cases \(n\geq 5\), they construct maximal partial spread in \(PG(n, q)\) of each size between \(c n q^{n - 2}\log q\) and \(c' q^{n - 1}\). Reviewer's remark. In Sections 2 and 5 some misprints occur. For example, sometimes they refer to Lemma 1.3 and to Theorem 1.3, but in the paper there is no lemma or theorem called 1.3.
reviewed by: V. Napolitano
Mathematics Subject Classification ID: 51E14
Mathematics Subject Classification ID: 05B25
zbMATH DE Number: 1968861
zbMATH Keywords: fractional cover of hypergraphs
zbMATH Keywords: maximal partial spreads
MaRDI profile type: Publication
full work available at URL: a:1024148308054
OpenAlex ID: W47480194
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description: scientific article; zbMATH DE number 1968861