Finite Generalized Quadrangles

  title={Finite Generalized Quadrangles},
  author={Stanley E. Payne and Joseph A. Thas},

Characterizations of symplectic polar spaces

A polar space S is called symplectic if it admits a projective embedding ε : S → PG( V ) such that the image ε ( S ) of S by ε is defined by an alternating form of V . In this paper we characterize

An obstruction relating locally finite polygons to translation quadrangles

One of the most fundamental open problems in Incidence Geometry, posed by Tits in the 1960s, asks for the existence of so-called "locally finite generalized polygons" | that is, generalized polygons

Local Sharply Transitive Actions on Finite Generalized Quadrangles

We classify the finite generalized quadrangles containing a line L such that some group of collineations acts sharply transitively on the ordered pentagons which start with two points of L. This can

Hearing shapes of drums — mathematical and physical aspects of isospectrality

In a celebrated paper ''Can one hear the shape of a drum?'' M. Kac [Am. Math. Monthly 73, 1 (1966)] asked his famous question about the existence of nonisometric billiards having the same spectrum of

On a Class of Hyperplanes of the Symplectic and Hermitian Dual Polar Spaces

  • B. Bruyn
  • Mathematics
    Electron. J. Comb.
  • 2009
The construction of these hyperplanes allows it to be proved that there exists an ovoid of the Hermitian dual polar space DH arising from its Grassmann-embedding if and only if there exist an empty -Hermitian variety in PG(n 1; K).

A classification of transitive ovoids, spreads, and m-systems of polar spaces

Abstract Many of the known ovoids and spreads of finite polar spaces admit a transitive group of collineations, and in 1988, P. Kleidman classified the ovoids admitting a 2-transitive group. A.

Virtual motives for synthetic geometries, A. Definition and properties of $K_0(\mathcal{Q}_\ell)$

In this note, we introduce the first basics on Grothendieck rings for incidence geometries as a new motivic way and tool to study synthetic geometry. In this first instance, we concentrate on

Ju n 20 07 On the Pauli graphs of N-qudits

A comprehensive graph theoretical and finite geometrical study of the commutation relations between the generalized Pauli operators of N -qudits is performed in which vertices/points correspond to

On the packing chromatic number of Moore graphs

A magic Veldkamp line for three qubits. Representations and geometry

We investigate the structure of the three-qubit magic Veldkamp line (MVL). This mathematical notion has recently shown up as a tool for understanding the structures of the set of Mermin pentagrams,



Finite geometries

On a combinatorial generalization of 27 lines associated with a cubic surface

Given integers 0 < λ < κ < ν, does there exist a nontrivial graph G with the following properties: G is of order ν (i.e. has ν vertices), is regular of degree κ (i.e. every vertex is adjacent to

Projective Geometries Over Finite Fields

1. Finite fields 2. Projective spaces and algebraic varieties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities 6. The line 7. First properties of the plane 8. Ovals 9.

Generalized Quadrangles Associated with G2(q)

  • W. Kantor
  • Mathematics
    J. Comb. Theory, Ser. A
  • 1980

Partial quadrangles

  • Quart. J. Math. Oxford, 25(3):1–13,
  • 1974

Combinatorial characterizations of the classical generalized quadrangles

Moufang Conditions for Finite Generalized Quadrangles

Sur la trialité et certains groupes qui s’en déduisent