Weighted intriguing sets of finite generalised quadrangles
type: Item
instance of: scholarly article
title: Weighted intriguing sets of finite generalised quadrangles
zbMATH Open document ID: 1270.51005
author: John Bamberg
author: Alice Devillers
author: Jeroen Schillewaert
published in: Journal of Algebraic Combinatorics
publication date: 2012-07-31T00:00:00Z
review text: A set of points \(\mathcal T\) of a generalised quadrangle of order \((s,t)\) is an \(i\)-tight set if for every point \(p\in {\mathcal T}\), there are \(s+i\) points of \(\mathcal T\) collinear with \(p\) and for every point \(p\notin {\mathcal T}\), there are \(i\) points of \(\mathcal T\) collinear with \(p\). A set of points \(\mathcal M\) of a generalised quadrangle is an \(m\)-ovoid if every line meets \({\mathcal M}\) in \(m\) points. Lemma 4.1. Let \(S\) be a set of points of a generalised quadrangle such that \(\chi_S\in (V^\epsilon)^\bot\) where \(\epsilon\in \{-,+\}\). Then \(S\) is an \(m\)-ovoid or a tight set. Theorem 9.1 Let \(S\) be a non-trivial \(m\)-ovoid of \(H(4,q^2)\). If \(q>2\), then \[ m\geq \frac{1}{2}\frac{-3q-3+\sqrt{4q^5-4q^4+5q^2-2q+1}}{q^2-q-2} \] where for \(q=2\) we have \(m\geq 2\).
Mathematics Subject Classification ID: 51E12
zbMATH DE Number: 6062482
zbMATH Keywords: generalised quadrangle
zbMATH Keywords: hemisystem
zbMATH Keywords: \(m\)-ovoids
zbMATH Keywords: strongly regular graph
reviewed by: Alexandre A. Makhnev
describes a project that uses: Gurobi
MaRDI profile type: Publication
full work available at URL: s10801-011-0330-4
OpenAlex ID: W2018212353
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DOI: 10.1007/S10801-011-0330-4
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description: scientific article; zbMATH DE number 6062482