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Portland Quadrangle Texas

, 2017

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Every Generalized Quadrangle of Order 5 Having a Regular Point Is Symplectic [PDF]

Experimental Mathematics, 2015
For many years now, one of the most important open problems in the theory of generalized quadrangles has been whether other classes of generalized quadrangles exist besides those that are currently known.
Bart de Bruyn
exaly   +2 more sources

Notes on binary codes related to the O(5, q) generalized quadrangle for odd q

Geometriae Dedicata, 1991
In this note we determine the dimensions of the binary codes spanned by the lines or by the point neighborhoods in the generalized quadrangle Sp(4, q) and its dual O(5, q), where q is odd. Several more general results are given.
A E Brouwer, B Bagchi
exaly   +2 more sources

An unusual generalized quadrangle of order sixteen [PDF]

Journal of Combinatorial Theory - Series A, 1978
The generalized quadrangle J associated by the method of Tits with the nonconical ovoid discovered by M. Hall, Jr., in PG(2, 16) is shown to contain no subquadrangle of order 4.
Stanley E Payne
exaly   +2 more sources

The association scheme on the set of flags of a finite generalized quadrangle [PDF]

Discrete Mathematics
In this paper, the association scheme defined on the flags of a finite generalized quadrangle is considered. All possible fusions of this scheme are listed, and a full description for those of classes 2 and 3 is given.
Alessandro Siciliano, Giusy Monzillo
exaly   +3 more sources

Pseudo-embeddings and hyperovals of the generalized quadrangle of order (3,5)

Discrete Mathematics, 2023
We determine explicit constructions for the five homogeneous pseudo-embeddings of the generalized quadrangle GQ(3, 5). We also discuss a number of applications to hyperovals and tight sets.
Mou Gao, Dibyayoti Jena, Bart de Bruyn   +2 more
exaly   +2 more sources

A generalized quadrangle with an automorphism group acting regularly on the points [PDF]

European Journal of Combinatorics, 2007
We develop several fundamental lemmas on a generalized quadrangle with an automorphism group acting regularly on its set of points. This can be thought of as an improvement of arguments originated in D. Ghinelli [Regular groups on generalized quadrangles
Satoshi Yoshiara
exaly   +2 more sources

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Symmetry in Generalized Quadrangles

Designs, Codes and Cryptography, 2003
In this paper some new points of view about Lenz(-Barlotti)-type classification of finite generalized quadrangles are described. Also, it is shown that each span-symmetric generalized quadrangle of order \(s>1\) with \(s\) even is isomorphic to \(Q(4,5)\) without using the canonical connection between groups of order \(s^3-s\) with a 4-gonal basis and ...
openaire   +2 more sources

Coordinate system and combinatorial objects (an example of a generalized quadrangle)

Ukrainian Mathematical Journal, 1994
На прикладі узагальненого чотирикутника підтверджується припущення про те, що системи координат (відмінні від звичайноі декартової) існують не лише в довільній проективній площи­ні, де вони визначаються невиродженим чотирикутником,.
Медведев, В.К.
exaly   +2 more sources

Characterizations of Translation Generalized Quadrangles

Designs, Codes and Cryptography, 2001
If \(x\) is a regular point of the generalized quadrangle \({\mathcal S}\) of order \((s,t)\), \(s\neq 1\neq t\), then \(x\) defines a dual net \({\mathcal N}^*_x\). In this paper a particular class of collineations, called transvections with axis \(x\), of the point-line dual of \({\mathcal N}^*_x\), has been introduced. If \({\mathcal S}\) contains a
openaire   +3 more sources