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Classification Results for Hyperovals of Generalized Quadrangles [PDF]
Mathematical Software – ICMS 2020, 2020 A hyperoval of a point-line geometry is a nonempty set of points meeting each line in either 0 or 2 points. We discuss a combination of theoretical and practical techniques that are helpful for classifying hyperovals of generalized quadrangles. These techniques are based on the connection between hyperovals, even sets and pseudo-embeddings of point ...
De Bruyn B.
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Topology in generalized quadrangles [PDF]
Topology and Its Applications, 1990 The study of topological generalized quadrangles, in particular 3- dimensional generalized quadrangles, was first taken up by \textit{M. Forst} [Mitt. Math. Semin. Gießen 147, 65-129 (1981; Zbl 0478.51013)]. The authors resume this subject and lay the basis for the study of topological generalized quadrangles in general dimension.
Norbert Knarr, Theo Grundhöfer
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Domesticity in Generalized Quadrangles [PDF]
Annals of Combinatorics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Temmermans, Beukje +2 more
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Classification of skew translation generalized quadrangles, I [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Combinatorics
Koen Thas
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Extending generalized quadrangles [PDF]
Journal of Combinatorial Theory, Series A, 1989 Let P be any point of a finite incidence structure S and denote by \(S_ P\) the incidence structure which consists of all points of S joined to P and all lines of S containing P. S is called an extended generalized quadrangle of order (s,t) if S is connected and \(S_ P\) is a generalized quadrangle of order (s,t) for all points P of S.
Fisher, P.H
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COVERS OF GENERALIZED QUADRANGLES [PDF]
Glasgow Mathematical Journal, 2018 AbstractWe solve a problem posed by Cardinali and Sastry (Elliptic ovoids and their rosettes in a classical generalized quadrangle of even order.Proc. Indian Acad. Sci. Math. Sci.126(2016), 591–612) about factorization of 2-covers of finite classical generalized quadrangles (GQs). To that end, we develop a general theory of cover factorization for GQs,
Thas, Joseph, Thas, Koen
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Generalized Quadrangles with a Spread of Symmetry [PDF]
European Journal of Combinatorics, 1999 An incidence system of points and blocks is called a Steiner system \(S(t,k,v)\) if there exactly \(v\) points, every block is incident with exactly \(k\) points and every \(t\) different points are incident with exactly one block. A partial spread of a Steiner system is a set of mutually disjoint blocks.
De Bruyn, Bart
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Generalized Hexagons as Amalgamations of Generalized Quadrangles
European Journal of Combinatorics, 1993 The paper investigates generalized hexagons with regular points and, in particular, generalized hexagons with an incident regular point-line pair. The first main result states that if \(p\) is a regular point of a finite generalized quadrangle of order \((s,t)\), then \(s \geq t\).
Hendrik Van Maldeghem, I. Bloemen
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Small Extended Generalized Quadrangles [PDF]
European Journal of Combinatorics, 1990 An extended generalized quadrangle (EGQ) is a connected point-block incidence structure \({\mathcal G}\) with the property that for any point P the points collinear with P (and different from P) and the blocks incident with P form a generalized quadrangle known as the (point) residue at P.
Peter J. Cameron, P. H. Fisher
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Generalized quadrangles and regularity [PDF]
Discrete Mathematics, 2005 The point \(X\) of a generalized quadrangle (GQ) of order \((s,t)\) is regular if \(|(\{X,Y\}^\bot)^\bot|=t+1\) for every point \(Y\) not collinear with \(X\). Let the generalized quadrangle \(\mathcal S\) of order \((s,t)\) contain a regular point \(X\). Then the incidence structure \({\mathcal N}_X\) with pointset \(X^\bot-\{X\}\), with lineset \(\{(\
Brown, Matthew R., Brown, M.
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