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Notes on elation generalized quadrangles [PDF]
European Journal of Combinatorics, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stanley E. Payne, Koen Thas
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Flocks, ovoids and generalized quadrangles
Le Matematiche, 2004 In this paper we will discuss some of the connections between flocks of quadratic cones, ovoids of PG(3, q) and generalized quadrangles.
Matthew Brown
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Generalized Quadrangles and Flocks of Cones
European Journal of Combinatorics, 1987 A flock of the quadratic cone K of PG(3,q) is a partition of K but its vertex into disjoint conics. It is called linear if the planes of the q conics of such a flock all contain a common line. A flock is linear if and only if there corresponds a Desarguesian translation plane to it. W. M.
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Generalized quadrangles and subconstituent algebra ¹
Cubo, 2010 The point graph of a generalized quadrangle GQ (s, t) is a strongly regular graph G = srg( ?, ?, ?, μ) whose parameters depend on s and t. By a detailed analysis of the adjacency matrix we compute the Terwilliger algebra of this kind of graphs (and ...
Fernando Levstein, Carolina Maldonado
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The Ghinelli–Löwe construction of generalized quadrangles
European Journal of Combinatorics, 2003 The authors dig up an old construction of some finite generalized quadrangles due to Ghinelli and Löwe, which was never published. No new examples arise, but the authors identify earlier examples of this method (and these examples were not identified before) as flock quadrangles of Cantor-Knuth type.
GHINELLI, Dina, PAYNE S. E.
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A New Family of Extended Generalized Quadrangles
European Journal of Combinatorics, 1997 In this paper, the authors construct in an entirely geometric way an infinite family of rank 3 geometries extending the generalized quadrangles \(T^*_2 (O)\), \(O\) a hyperoval in the projective plane \(PG (2,q)\) for some prime power \(q\). The construction uses two hyperovals in \(PG (4,q)\): one in a plane \(\pi\), and another one (as set of planes)
DEL FRA A. +2 more
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The Veldkamp Space of Two-Qubits
Symmetry, Integrability and Geometry: Methods and Applications, 2007 Given a remarkable representation of the generalized Pauli operators of two-qubits in terms of the points of the generalized quadrangle of order two, W(2), it is shown that specific subsets of these operators can also be associated with the points and ...
Metod Saniga +3 more
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Characterizations of generalized quadrangles by generalized homologies
Journal of Combinatorial Theory, Series A, 1985 Let \(S=(P,B,I)\) be a finite generalized quadrangle of order (s,t) and \({\mathcal H}(x,y)\) the group of all collineations of S fixing the noncollinear points x and y linewise. S is called (x,y)-transitive if \({\mathcal H}(x,y)\) is transitive on each set \(^{\sim}-\{x,z\}\) and \(^{\sim}-\{y,z\},\) where z is any point collinear with both x and y ...
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Monomial graphs and generalized quadrangles
Finite Fields and Their Applications, 2012 In this paper, the author proves the nonexistence of certain generalized quadrangles of order \((s,s)\), with \(s\) an odd prime power. This is achieved by considering the graph of points and lines far away from a flag of such a quadrangle, identifying the point and line sets with 3-dimensional vector space over \(\mathrm{GF}(s)\), coordinatizing, and ...
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Generalized Quadrangles and the Higman-Sims Technique
European Journal of Combinatorics, 1981 Let S be a generalized quadrangle of order (s, t). Let O = {x1, ..., xq} be a set of points of S, q ≥ 2, and put b1 equal to the number of points (≠x1) of O that are collinear with xi,b¯=∑bi/q. Suppose Δ = Δ1+ ⋯ + Δf is a partition of some set Δ of tangent lines to O satisfying the following: f ≥ 2; for 1, i ≤ i ≤ f, each point of O is on θ lines in Δi;
Joseph A. Thas, Stanley E. Payne
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