Finite Generalized Quadrangles

  title={Finite Generalized Quadrangles},
  author={S. E. Payne and J. Thas},
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 polygonsExpand
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 canExpand
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 ofExpand
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.Expand
On a Class of Hyperplanes of the Symplectic and Hermitian Dual Polar Spaces
  • B. Bruyn
  • Mathematics, Computer Science
  • 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). Expand
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 toExpand
On the packing chromatic number of Moore graphs
The packing chromatic number of a $(q+1,g)$-Moore graph $G$ is studied and the exact value of $\chi_\rho (G)$ is presented in terms of the intersection of certain structures in generalized quadrangles. Expand
Magic three-qubit Veldkamp line: A finite geometric underpinning for form theories of gravity and black hole entropy
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,Expand
A Probabilistic Construction in Generalized Quadrangles
We study random constructions in incidence structures, and illustrate our techniques by means of a well-studied example from finite geometry. A maximal partial ovoid of a generalized quadrangle is aExpand
Algebraic Codes and Geometry of Some Classical Generalized Polygons
Some results about the geometry of, and the \(q\)-ary codes associated with the finite generalized polygons \(W(q), q=2^{n}\); \(H(q)\), \(q=3^{n}\); and \(\mathcal {O}(q)\) , \(q=2^{2m+1}\), areExpand


Finite geometries
Generalized Quadrangles Associated with G2(q)
  • W. Kantor
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 1980
Abstract If q ≡ 2 (mod 3), a generalized quadrangle with parameters q, q2 is constructed from the generalized hexagon associated with the group G2(q).
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.Expand
Einführung in die Kombinatorik : mit einem Anhang über formale Potenzreihen
Partial quadrangles
  • Quart. J. Math. Oxford, 25(3):1–13,
  • 1974
On a combinatorial generalization of 27 lines associated with a cubic surface
Given integers 0 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 exactly κ other vertices), and every pair of verticesExpand
Projective planes I
  • N. Singhi
  • Computer Science, Mathematics
  • Eur. J. Comb.
  • 2010
These methods are being developed to study the well known conjectures that every finite projective plane with no proper subplane is isomorphic to a prime field plane and that the order of a finite projectives plane is a power of a prime number. Expand
Classification of buildings of spherical types and Moufang polygons: A survey
Sur la trialité et certains groupes qui s’en déduisent
Moufang Conditions for Finite Generalized Quadrangles
Publisher Summary This chapter discusses the Moufang conditions for finite generalized quadrangles. The chapter reviews the efforts for finding an “elementary” proof of Tits' theorem. The chapterExpand