The maximum size of a partial spread in \(H(5,q^{2})\) is \(q^{3}+1\)
type: Item
instance of: scholarly article
title: The maximum size of a partial spread in \(H(5,q^{2})\) is \(q^{3}+1\)
zbMATH Open document ID: 1116.51007
published in: Journal of Combinatorial Theory. Series A
publication date: 2007-05-10T00:00:00Z
review text: A spread of a polar space is a set of mutually skew generators that partition the polar space. According to \textit{J. A. Thas} the finite Hermitian polar space \(H(d,q^2)\), \(d\) odd, does not possess any spread [Ann. Discrete Math. 52, 529--544 (1992; Zbl 0767.51004)], and for \(d=5\) an upper bound for the size of a partial spread is given by \(q^4\) (D. Luyckx). The authors are able to reduce this bound down to \(q^3+1\). Moreover, they improve the lower bound \(q+1\) for the number of planes that a partial spread of \(H (5,q^2)\), \(q\geq7\), contains to \(2q+3\).
Mathematics Subject Classification ID: 51E14
zbMATH DE Number: 5151551
zbMATH Keywords: spread
zbMATH Keywords: polar space
zbMATH Keywords: Hermitian variety
author: Jan De Beule
author: Klaus Metsch
describes a project that uses: GAP
describes a project that uses: pg
MaRDI profile type: Publication
full work available at URL: j.jcta.2006.08.005
OpenAlex ID: W1511980337
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cites work: Q3960715
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DOI: 10.1016/J.JCTA.2006.08.005
description: scientific article; zbMATH DE number 5151551