Results 11 to 20 of about 636 (237)
Extending generalized quadrangles
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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Generalized Quadrangles with a Spread of Symmetry
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
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
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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Foundations of elation generalized quadrangles
European Journal of Combinatorics, 2006 The authors give a negative answer to the long-standing question whether or not the set of all elations about some point \(x\) forms a group for any thick generalized quadrangle \(S^{(x)}\) having \(x\) as an elation point or a center of transitivity. Furthermore, an answer is given for each of the known generalized quadrangles.
Koen Thas, Stanley E. Payne
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Notes on elation generalized quadrangles
European Journal of Combinatorics, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stanley E. Payne, Koen Thas
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Nonisomorphic generalized quadrangles
Journal of Algebra, 1971 AbstractFor each integer e > 2 a class of somewhat more than φ(e) pairwise non-isomorphic quadrangles is exhibited and shown to yield nonisomorphic (v, k, λ)-designs. The collineation groups of these quadrangles and designs are determined. Also a class of quadrangles with s = q − 1, t = q + l, q any prime power, is constructed.
Payne, Stanley E
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On the nonexistence of pseudo-generalized quadrangles [PDF]
European Journal of Combinatorics, 2020 In this paper we consider the question of when a strongly regular graph with parameters $((s+1)(st+1),s(t+1),s-1,t+1)$ can exist. These parameters arise when the graph is derived from a generalized quadrangle, but there are other examples which do not arise in this manner, and we term these {\it pseudo-generalized quadrangles}.
Ivan Guo +3 more
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