J. A. Thas

We show that every embedded finite thick generalized hexagon ℋ of order (s, t) in PG(n,q) which satisfies the conditions s = q the set of all points of ℋ … We show that every embedded finite thick generalized hexagon ℋ of order (s, t) in PG(n,q) which satisfies the conditions s = q the set of all points of ℋ generates PG(n, q) for any point x of ℋ, the set of all points collinear in ℋ with x is contained in a plane of PG(n, q) for any point x of ℋ, the set of all points of ℋ not opposite x in ℋ is contained in a hyperplane of PG,(n, q) is necessarily the standard representation of H(q) in PG(6, q) (on the quadric Q(6, q)), the standard representation of H(q) for q even in PG(5, q) (inside a symplectic space), or the standard representation of H(q, q 3 ) in PG(7, q) (where the lines of ℋ are the lines fixed by a triality on the quadric Q+(7, q)). This generalizes a result by Cameron and Kantor [3], which is used in our proof.

A restriction on the parameters of a subhexagon

1976-07-01

J. A. Thas

k-arcs and partial flocks

1995-09-01

Leo Storme , J. A. Thas

Flocks, maximal exterior sets, and inversive planes

1990-01-01

J. A. Thas

The Characterization of Projections of Quadrics over Finite Fields of Even Order

1980-10-01

J. W. P. Hirschfeld , J. A. Thas

Linear independence in finite spaces

1987-05-01

J. W. P. Hirschfeld , J. A. Thas

Combinatorics of Partial Geometries and Generalized Quadrangles

1977-01-01

J. A. Thas

Flat Lax and Weak Lax Embeddings of Finite Generalized Hexagons

1998-08-01

J. A. Thas , Hendrik Van Maldeghem

Classification of finite Veronesean caps

2003-09-12

J. A. Thas , Hendrik Van Maldeghem

Arcs, Caps and Generalisations in a Finite Projective Space

2025-04-30

J. W. P. Hirschfeld , J. A. Thas

Arcs and caps are fundamental structures in finite projective spaces. They can be generalised. Here, a survey is given of some important results on these objects, in particular on generalised … Arcs and caps are fundamental structures in finite projective spaces. They can be generalised. Here, a survey is given of some important results on these objects, in particular on generalised ovals and generalised ovoids. This paper also contains recent results and several open problems.

Epimorphisms of generalized polygons, B: The octagons

2023-09-13

J. A. Thas , Koen Thas

This is the second part of our study of epimorphisms with source a thick generalized m-gon and target a thin generalized m-gon.We classify the case m = 8 when the … This is the second part of our study of epimorphisms with source a thick generalized m-gon and target a thin generalized m-gon.We classify the case m = 8 when the polygons are finite (in the first part [15] we handled the cases m = 3, 4 and 6).Then we show that the infinite case is very different, and construct examples which strongly differ from the finite case.A number of general structure theorems are also obtained, and we also take a look at the infinite case for general gonality. CONTENTSRemark 1.2.A local variation on Theorem 1.1 by Bödi and Kramer [1] states that an epimorphism between thick generalized m-gons (m ≥ 3) is an isomorphism if and only if its restriction to at least one point row or line pencil is bijective.Later on, Gramlich and Van Maldeghem thoroughly studied epimorphisms from thick

View PDF Chat

Generalized quadrangles of order (s,s2). IV Translations, Moufang and Fong-Seitz

2023-08-21

J. A. Thas

View PDF Chat

Suzuki–Tits ovoids through the years

2023-07-14

J. A. Thas , Hendrik Van Maldeghem

Epimorphisms of generalized polygons B: The octagons

2023-01-01

J. A. Thas , Koen Thas

This is the second part of our study of epimorphisms with source a thick generalized $m$-gon and target a thin generalized $m$-gon. We classify the case $m = 8$ when … This is the second part of our study of epimorphisms with source a thick generalized $m$-gon and target a thin generalized $m$-gon. We classify the case $m = 8$ when the polygons are finite (in the first part [15] we handled the cases $m = 3, 4$ and $6$). Then we show that the infinite case is very different, and construct examples which strongly differ from the finite case. A number of general structure theorems are also obtained, and we also take a look at the infinite case for general gonality.

View PDF Chat

Epimorphisms of generalized polygons A: The planes, quadrangles and hexagons

2022-07-04

J. A. Thas , Koen Thas

View PDF Chat

Generalized Quadrangles Of Order $(s, s^2)$. IV. Translations, Moufang And Fong-Seitz

2022-01-01

J. A. Thas

In the period 1994-1999 Thas wrote a series of three papers on generalized quadrangles of order $(s, s^2)$. In this Part IV we classify all finite translation generalized quadrangles of … In the period 1994-1999 Thas wrote a series of three papers on generalized quadrangles of order $(s, s^2)$. In this Part IV we classify all finite translation generalized quadrangles of order $(s, s^2)$ having a kernel of size at least 3, containing a regular line not incident with the translation point. There are several applications on generalized quadrangles of order $(s, s^2)$ having at least 2 translation points, on Moufang quadrangles, and concerning the theorem of Fong and Seitz classifying all groups with a BN-pair of rank 2.

View PDF Chat

Covers of generalized quadrangles, 2. Kantor-Knuth covers and embedded ovoids

2020-12-29

J. A. Thas , Koen Thas

View PDF Chat

Covers of generalized quadrangles, 2. Kantor-Knuth covers and embedded ovoids

2020-01-01

J. A. Thas , Koen Thas

In this paper, which is a sequel to \cite{part1}, we proceed with our study of covers and decomposition laws for geometries related to generalized quadrangles. In particular, we obtain a … In this paper, which is a sequel to \cite{part1}, we proceed with our study of covers and decomposition laws for geometries related to generalized quadrangles. In particular, we obtain a higher decomposition law for all Kantor-Knuth generalized quadrangles which generalizes one of the main results in \cite{part1}. In a second part of the paper, we study the set of all Kantor-Knuth ovoids (with given parameter) in a fixed finite parabolic quadrangle, and relate this set to embeddings of parabolic quadrangles into Kantor-Knuth quadrangles. This point of view gives rise to an answer of a question posed in \cite{JATSEP}.

Regular pseudo-hyperovals and regular pseudo-ovals in even characteristic

2019-02-20

J. A. Thas

S. Rottey and G. Van de Voorde characterized regular pseudo-ovals of PG(3n - 1, q), q = 2^h, h >1 and n prime. Here an alternative proof is given and … S. Rottey and G. Van de Voorde characterized regular pseudo-ovals of PG(3n - 1, q), q = 2^h, h >1 and n prime. Here an alternative proof is given and slightly stronger results are obtained.

View PDF Chat

On <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:mi>k</mml:mi></mml:math>-caps in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml2" display="inline" overflow="scroll" altimg="si2.gif"><mml:mi mathvariant="bold">PG</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>, with <mml:math xmlns:mml="http://www.w3.org/1998/Math/…

2018-02-21

J. A. Thas

View PDF Chat

COVERS OF GENERALIZED QUADRANGLES

2018-01-25

J. A. Thas , Koen Thas

Abstract We solve a problem posed by Cardinali and Sastry (Elliptic ovoids and their rosettes in a classical generalized quadrangle of even order. Proc. Indian Acad. Sci. Math. Sci. 126 … Abstract We solve a problem posed by Cardinali and Sastry (Elliptic ovoids and their rosettes in a classical generalized quadrangle of even order. Proc. Indian Acad. Sci. Math. Sci. 126 (2016), 591–612) about factorization of 2-covers of finite classical generalized quadrangles (GQs). To that end, we develop a general theory of cover factorization for GQs, and in particular, we study the isomorphism problem for such covers and associated geometries. As a byproduct, we obtain new results about semi-partial geometries coming from θ-covers, and consider related problems.

View PDF Chat

On <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:mi>k</mml:mi></mml:math>-caps in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml2" display="inline" overflow="scroll" altimg="si2.gif"><mml:mi mathvariant="bold">PG</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>, with <mml:math xmlns:mml="http://www.w3.org/1998/Math/…

2017-11-01

J. A. Thas

View PDF Chat

On k-caps in PG(n, q), with q even and n \geq 4

2017-10-06

J. A. Thas

Let $m_2(n, q), n \geq 3$, be the maximum size of k for which there exists a complete k-cap in PG(n, q). In this paper the known bounds for $m_2(n, … Let $m_2(n, q), n \geq 3$, be the maximum size of k for which there exists a complete k-cap in PG(n, q). In this paper the known bounds for $m_2(n, q), n \geq 4$, q even and $q \geq 2048$, will be considerably improved.

50 years of finite geometry

2017-01-01

J. W. P. Hirschfeld , J. A. Thas , Hendrik Van Maldeghem

View PDF Chat

On k-caps in PG(n, q), with q even and n \geq 3

2017-01-01

J. A. Thas

Let m_2(n, q) be the maximum size of k for which there exists a k-cap in PG(n, q), and let m'_2(n, q) be the second largest value of k for … Let m_2(n, q) be the maximum size of k for which there exists a k-cap in PG(n, q), and let m'_2(n, q) be the second largest value of k for which there exists a complete k-cap in PG(n, q). In this paper Chao's upper bound q^2 - q + 5 for m'_2(3, q), q even and q \geq 8, will be improved. As a corollary new bounds for m_2(n, q), q even, q\geq 8 and n \geq 4, are obtained. Cao and Ou published a better bound but there seems to be a gap in their proof.

Counting points and acquiring flesh

2017-01-01

J. A. Thas

This set of notes is based on a lecture I gave at "50 years of Finite Geometry -A conference on the occasion of Jef Thas's 70th birthday," in November 2014.It … This set of notes is based on a lecture I gave at "50 years of Finite Geometry -A conference on the occasion of Jef Thas's 70th birthday," in November 2014.It consists essentially of three parts: in a first part, I introduce some ideas which are based in the combinatorial theory underlying F1, the field with one element.In a second part, I describe, in a nutshell, the fundamental scheme theory over F1 which was designed by Deitmar.The last part focuses on zeta functions of Deitmar schemes, and also presents more recent work done in this area.

View PDF Chat

On k-caps in PG(n, q), with q even and n \geq 4

2017-01-01

J. A. Thas

View PDF Chat

Covers of generalized quadrangles

2016-07-20

J. A. Thas , Koen Thas

We solve a problem posed by Cardinali and Sastry [2] about factorization of $2$-covers of finite classical generalized quadrangles. To that end, we develop a general theory of cover factorization … We solve a problem posed by Cardinali and Sastry [2] about factorization of $2$-covers of finite classical generalized quadrangles. To that end, we develop a general theory of cover factorization for generalized quadrangles, and in particular we study the isomorphism problem for such covers and associated geometries. As a byproduct, we obtain new results about semipartial geometries coming from $\theta$-covers, and consider related problems.

Finite affine planes in projective spaces

2016-06-17

J. A. Thas , Hendrik Van Maldeghem

View PDF Chat

Veronese and Segre varieties

2016-01-01

J. W. P. Hirschfeld , J. A. Thas

Arcs and caps

2016-01-01

J. W. P. Hirschfeld , J. A. Thas

Covers of generalized quadrangles

2016-01-01

J. A. Thas , Koen Thas

View PDF Chat

General Galois Geometries

2016-01-01

J. W. P. Hirschfeld , J. A. Thas

Open problems in finite projective spaces

2014-12-04

J. W. P. Hirschfeld , J. A. Thas

View PDF Chat

Characterizations of Segre varieties

2013-01-18

J. A. Thas , Hendrik Van Maldeghem

View PDF Chat

Editorial: Finite geometries

2012-12-17

Dina Ghinelli , J. W. P. Hirschfeld , D. Jungnickel +1 more

Domesticity in Generalized Quadrangles

2012-11-21

Beukje Temmermans , J. A. Thas , Hendrik Van Maldeghem

View PDF Chat

A Characterization of the Finite Veronesean by Intersection Properties

2012-01-28

Jeroen Schillewaert , J. A. Thas , Hendrik Van Maldeghem

View PDF Chat

Generalized Veronesean embeddings of projective spaces, part II: the lax case

2012-01-01

Ziya AKÇA , A. Bayar , S. Ekmekçi +3 more

We classify all embeddings theta : PG(n,K) -> PG(d, F), with d >= n(n+3)/2 and K, F skew fields with vertical bar K vertical bar > 2, such that 0 … We classify all embeddings theta : PG(n,K) -> PG(d, F), with d >= n(n+3)/2 and K, F skew fields with vertical bar K vertical bar > 2, such that 0 maps the set of points of each line of PG(n,K) to a set of coplanar points of PG(d, F), and such that the image of theta generates PG(d, F). It turns out that d = 1/2n(n + 3) and all examples essentially arise from a similar full embedding theta' : PG(n, K) -> PG(d,K) by identifying K with subfields of IF and embedding PG(d, K) into PG(d, F) by several ordinary field extensions. These full embeddings satisfy one more property and are classified in [5]. They relate to the quadric Veronesean of PG(n, K) in PG(d, K) and its projections from subspaces of PG(d, K) generated by sub-Veroneseans (the point sets corresponding to subspaces of PG(n,K)), if K is commutative, and to a degenerate analogue of this, if K is noncommutative.

Generalized Veronesean embeddings of projective spaces

2011-11-01

J. A. Thas , Hendrik Van Maldeghem

Characterizations of Veronese and Segre varieties

2011-08-01

J. A. Thas , Hendrik Van Maldeghem

View PDF Chat

An essay on self-dual generalized quadrangles

2011-06-18

Sam Payne , J. A. Thas

Collineations of polar spaces with restricted displacements

2011-04-30

Beukje Temmermans , J. A. Thas , Hendrik Van Maldeghem

View PDF Chat

4-Gonal Configurations

2011-01-01

J. A. Thas

Generalized Ovals in PG(3n - 1; q), with q Odd

2011-01-01

J. A. Thas

In 1954 Segre proved that every oval of PG(2, q), with q odd, is a nonsingular conic.The proof relies on the "Lemma of Tangents".A generalized oval of PG(3n -1, q) … In 1954 Segre proved that every oval of PG(2, q), with q odd, is a nonsingular conic.The proof relies on the "Lemma of Tangents".A generalized oval of PG(3n -1, q) is a set of q n + 1 (n -1)-dimensional subspaces of PG(3n -1, q), every three of them generate PG(3n -1, q); a generalized oval with n = 1 is an oval.The only known generalized ovals are essentially ovals of PG(2, q n ) interpreted over GF(q).If the oval of PG(2, q n ) is a conic, then we call the corresponding generalized oval classical.Now assume q odd.In the paper we prove several properties of classical generalized ovals.Further we obtain a strong characterization of classical generalized ovals in PG(3n -1, q) and an interesting theorem on generalized ovals in PG(5, q), developing a theory in the spirit of Segre's approach.So for example a "Lemma of Tangents" for generalized ovals is obtained.We hope such an approach will lead to a classification of all generalized ovals in PG(3n -1, q), with q odd.

View PDF Chat

Collineations and dualities of partial geometries

2010-04-15

Beukje Temmermans , J. A. Thas , Hendrik Van Maldeghem

André embeddings of affine planes

2010-01-01

J. A. Thas , Hendrik Van Maldeghem

An Andre embedding is a representation of a point-line geometry S with approximately s(2) points on a line in a planar space with approximately s points per line, but such … An Andre embedding is a representation of a point-line geometry S with approximately s(2) points on a line in a planar space with approximately s points per line, but such that the lines of S are contained in planes of the planar space. An example is the Andre representation (also sometimes called the Bose-Bruck representation) of an affine translation plane of order q(2) (with kernel of order at least q) in 4-dimensional affine space AG(4, q), using a line spread at infinity. In this paper, we classify all Andre embeddings of affine planes of order q(2) in PG(4, q), q > 2, and obtain, besides the natural extension to PG(4, q) of the above example, two other related constructions. We also consider Andre embeddings of affine planes of order q(2) in PG(d, q), with d > 4 and q > 2.

Bounds on partial ovoids and spreads in classical generalized quadrangles

2010-01-01

Stefaan De Winter , J. A. Thas

We present an improvement on a recent bound for small maximal partial ovoids of W(q 3 ).We also classify maximal partial ovoids of size (q 2 -1) of Q(4, q) … We present an improvement on a recent bound for small maximal partial ovoids of W(q 3 ).We also classify maximal partial ovoids of size (q 2 -1) of Q(4, q) which allow a certain large automorphism group, and discuss examples for small q.

View PDF Chat

A characterization of the Grassmann embedding of H(q), with q even

2009-10-21

A. De Wispelaere , J. A. Thas , Hendrik Van Maldeghem

On collineations and dualities of finite generalized polygons

2009-09-01

Beukje Temmermans , J. A. Thas , Hendrik Van Maldeghem

View PDF Chat

Finite Translation Generalized Quadrangles

2009-07-01

J. A. Thas

My talk is a survey on finite translation generalized quadrangles. To each translation generalized quadrangle of order (s, t), with s not equal 1 not equal t, there corresponds a … My talk is a survey on finite translation generalized quadrangles. To each translation generalized quadrangle of order (s, t), with s not equal 1 not equal t, there corresponds a set O(n, m, q) of q(m) + 1 (n - 1)-dimensional subspaces of the projective space PG(2n+m-1, q) satisfying (i) every three subspaces generate a PG (3n - 1, q) and (ii) for every such subspace pi there is a subspace PG(n + m - 1, q) containing pi and having empty intersection with the other elements of O(n, m, q). Conversely, every such O(n, m, q) defines a finite translation generalized quadrangle. For each known example of O(n, m, q) we have m is an element of {n, 2n}, and for q even there are no other examples. Many papers were written on the case m = 2n. Here emphasis is on the case m = n, and besides interesting and useful old results several new theorems are stated.

Finite Generalized Quadrangles

2009-04-08

Stanley E. Payne , J. A. Thas

Subquadrangles of order s of generalized quadrangles of order (s,s2)

2009-01-01

Koen Thas , J. A. Thas

In this paper we consider the subquadrangles of order s for all known classes of generalized quadrangles of order (s, s 2 ). In this paper we consider the subquadrangles of order s for all known classes of generalized quadrangles of order (s, s 2 ).

View PDF Chat

Finite BN-pairs of rank 2, I

2009-01-01

J. A. Thas

One of the fundamental problems in Incidence Geometry is the classification of finite BN-pairs of rank 2 (most notably those of type B 2 ), without the use of the … One of the fundamental problems in Incidence Geometry is the classification of finite BN-pairs of rank 2 (most notably those of type B 2 ), without the use of the classification theorem for finite simple groups.In this paper, which is the first in a series, we classify finite BN-pairs of rank 2 (and the buildings that arise) for which the associated parameters (s, t) are powers of 2, and such that the associated polygon has no proper thick ideal or full subpolygons.As a corollary, we obtain the complete classification of generalized octagons of order (s, t) with st a power of 2, admitting a BN-pair.(For quadrangles and hexagons, this result will be obtained in part II.)

View PDF Chat

Characterizations of Hermitian varieties by intersection numbers

2008-05-27

Jeroen Schillewaert , J. A. Thas

Finite geometries

2008-02-14

A. Blokhuis , J. W. P. Hirschfeld , Dieter Jungnickel +1 more

Generalized hexagons and Singer geometries

2007-12-13

J. A. Thas , Hendrik Van Maldeghem

A characterization of the natural embedding of the split Cayley hexagon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mstyle mathvariant="sans-serif"><mml:mi>H</mml:mi></mml:mstyle><mml:mrow><mml:mo>(</mml:mo><mml:mi>q</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" display="inline" overflow="scroll"><mml:mstyle mathvariant="sans-serif"><mml:mi>PG</…

2007-08-15

J. A. Thas , Hendrik Van Maldeghem

The uniqueness of 1-systems of W 5(q) satisfying the BLT-property, with q odd

2007-02-22

J. A. Thas

Coauthor	Papers Together
Hendrik Van Maldeghem	42
J. W. P. Hirschfeld	16
Koen Thas	12
Frank De Clerck	11
Sam Payne	8
Deirdre Luyckx	7
Leo Storme	6
Beukje Temmermans	4
Stefaan De Winter	4
Ernest E. Shult	4
Hans Gevaert	3
Leen Brouns	3
Marijke De Soete	3
Matthew R. Brown	3
Stanley E. Payne	2
Aiden A. Bruen	2
Christine M. O’Keefe	2
Ingrid Debroey	2
N. De Feyter	2
Dieter Jungnickel	2
J. Chris Fisher	2
Bruce N. Cooperstein	2
Jeroen Schillewaert	2
Maxime Willems	1
A. De Wispelaere	1
S. K. J. Vereecke	1
R. Kaya	1
Dina Ghinelli	1
S. E. Payne	1
Chris Herssens	1
S. Ekmekçi	1
D. Jungnickel	1
Guglielmo Lunardon	1
D. R. Hughes	1
Peter J‎. Cameron	1
Ziya AKÇA	1
Nicola Durante	1
I. Bloemen	1
G. Hanssens	1
A. Bayar	1
Nicholas Hamilton	1
José Felipe Voloch	1
Paul De Winne	1
Van Maldeghem	1
Laura Bader	1
S. E. Payne	1
Aart Blokhuis	1
R. H. Dye	1
A. Blokhuis	1

Finite Generalized Quadrangles

2009-04-08

Stanley E. Payne , J. A. Thas

General Galois Geometries

2016-01-01

J. W. P. Hirschfeld , J. A. Thas

Projective Geometries over Finite Fields

1998-01-08

J. W. P. Hirschfeld

Abstract This book is an account of the combinatorics of projective spaces over a finite field, with special emphasis on one and two dimensions. With its successor volumes, Finite projective … Abstract This book is an account of the combinatorics of projective spaces over a finite field, with special emphasis on one and two dimensions. With its successor volumes, Finite projective spaces over three dimensions (1985), which is devoted to three dimensions, and General Galois geometries (1991), on a general dimension, it provides a comprehensive treatise of this area of mathematics. The area is interesting in itself, but is important for its applications to coding theory and statistics, and its use of group theory, algebraic geometry, and number theory. This edition is a complete reworking of the first edition. The chapters bear almost the same titles as the first edition, but every chapter has been changed. The most significant changes are to Chapters 2, 10, 12, 13, which respectively describe generalities, the geometry of arcs in ovals, the geometry of arcs of higher degree, and blocking sets. The book is divided into three parts. The first part comprises two chapters, the first of which is a survey of finite fields; the second outlines the fundamental properties of projective spaces and their automorphisms, as well as properties of algebraic varieties and curves, in particular, that are used in the rest of the book and the accompanying two volumes. Parts II and III are entirely self-contained; all proofs of results are given. The second part comprises Chapters 3 to 5. They cover, in an arbitrary dimension, the properties of subspaces such as their number and characterization, of partitions into both subspaces and subgeometries, and of quadrics and Hermitian varieties, as well as polarities. Part III is a detailed account of the line and the plane. In the plane, fundamental properties are first revisited without much resort to the generalities of Parts I and II. Then, the structure of arcs and their relation to curves is described; this includes arcs both of degree two and higher degrees. There are further chapters on blocking sets and on small planes, which means of orders up to thirteen. A comprehensive bibliography of more than 3000 items is provided. At the end of each chapter is a section, Notes and References, which attributes proofs, includes further comments, and lists every relevant reference from the bibliography.

General Galois Geometries

1993-03-01

Francis Buekenhout

By J. W. P. Hirschfeld and J. A. Thas: 407 pp., £55.00, ISBN 0 19 853537 6 (Clarendon Press, 1991). By J. W. P. Hirschfeld and J. A. Thas: 407 pp., £55.00, ISBN 0 19 853537 6 (Clarendon Press, 1991).

Generalized Quadrangles and Flocks of Cones

1987-10-01

J. A. Thas

An essay on skew translation generalized quadrangles

1989-10-01

Stanley E. Payne

Some generalized quadrangles with parametersq 2,q

1986-03-01

William M. Kantor

Generalized quadrangles in projective spaces

1974-12-01

Francis Buekenhout , Claude Lef�vre

Strongly regular graphs, partial geometries and partially balanced designs

1963-06-01

R. C. Bose

View PDF Chat

Flocks inPG(3,q)

1979-02-01

J. Chris Fisher , J. A. Thas

Generalized quadrangles associated with G2(q)

1980-09-01

William M. Kantor

Semi-partial geometries and spreads of classical polar spaces

1983-07-01

J. A. Thas

Ovoids and spreads of finite classical polar spaces

1981-01-01

J. A. Thas

Spreads and ovoids in finite generalized quadrangles

1994-10-01

J. A. Thas , S. E. Payne

Polar spaces, generalized hexagons and perfect codes

1980-07-01

J. A. Thas

Derivation of Flocks of Quadratic Cones

1990-01-01

Laura Bader , Guglielmo Lunardon , J. A. Thas

Generalized Quadrangles of Order (s, s2), II

1997-08-01

J. A. Thas

A class of translation planes

1976-07-01

Michael J. Walker

m-systems of polar spaces

1994-10-01

Ernest E. Shult , J. A. Thas

Caratterizzazione delle quadriche di uno spazio (tridimensionale) lineare sopra un corpo finito.

1955-01-01

Gianfranco Panella

Ovoids and Translation Planes

1982-10-01

William M. Kantor

An ovoid in an orthogonal vector space V of type Ω + (2 n , q ) or Ω(2 n – 1, q ) is a set Ω of q … An ovoid in an orthogonal vector space V of type Ω + (2 n , q ) or Ω(2 n – 1, q ) is a set Ω of q n –1 + 1 pairwise non-perpendicular singular points. Ovoids probably do not exist when n > 4 (cf. [ 12 ], [ 6 ]) and seem to be rare when n = 4. On the other hand, when n = 3 they correspond to affine translation planes of order q 2 , via the Klein correspondence between PG (3, q ) and the Ω + (6, q ) quadric. In this paper we will describe examples having n = 3 or 4. Those with n = 4 arise from PG (2, q 3 ), AG (2, q 3 ), or the Ree groups. Since each example with n = 4 produces at least one with n = 3, we are led to new translation planes of order q 2 .

View PDF Chat

Embedded Thick Finite Generalized Hexagons in Projective Space

1996-12-01

J. A. Thas , Hendrik Van Maldeghem

The nonexistence of certain generalized polygons

1964-07-01

Walter Feit , Graham Higman

Generalized quadrangles of orrder (s, s2), I

1994-08-01

J. A. Thas

On semipartial geometries

1978-11-01

Ingrid Debroey , J. A. Thas

Projective Geometry over a Finite Field

1995-01-01

J. A. Thas

Some maximal arcs in finite projective planes

1969-04-01

R. H. F. Denniston

Generalized Quadrangles of Order (s, s2), III

1999-08-01

J. A. Thas

Finite Geometries

1968-01-01

Peter F. Dembowski

Ovoßdes et Groupes de Suzuki

1962-12-01

Jacques Tits

Complete arcs and algebraic curves in PG(2, q)

1987-04-01

J. A. Thas

On 4-gonal configurations with parameters r=q 2+1 and k=q+1

1974-11-01

J. A. Thas

Ovals In a Finite Projective Plane

1955-01-01

Beniamino Segre

1. Let be a finite projective plane (8, §17), i.e. a projective space of dimension 2 over a Galois field γ. We suppose that γ has characteristic p ≠ 2, … 1. Let be a finite projective plane (8, §17), i.e. a projective space of dimension 2 over a Galois field γ. We suppose that γ has characteristic p ≠ 2, hence order q = p n , where p is an odd prime and h is a positive integer. It is well known that every straight line and every non-singular conic of then contains q + 1 points exactly.

View PDF Chat

A geometric construction of generalized quadrangles from polar spaces of rank three

1992-05-01

Norbert Knarr

Partitions and their stabilizers for line complexes and quadrics

1977-12-01

R. H. Dye

Conical flocks, partial flocks, derivation, and generalized quadrangles

1991-05-01

Sam Payne , J. A. Thas

Ovoids ofPG(3, 16) are elliptic quadrics, II

1992-07-01

Christine M. O’Keefe , Tim Penttila

PROJECTIVE GEOMETRIES OVER FINITE FIELDS

1999-11-01

Ray Hill

By J. W. P. Hirschfeld: 555 pp., £65.00, isbn 0 19 850295 8 (Clarendon Press, 1998). By J. W. P. Hirschfeld: 555 pp., £65.00, isbn 0 19 850295 8 (Clarendon Press, 1998).

Flat Lax and Weak Lax Embeddings of Finite Generalized Hexagons

1998-08-01

J. A. Thas , Hendrik Van Maldeghem

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

1969-11-01

R. W. Ahrens , G Szekeres

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 … 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 exactly κ other vertices), and every pair of vertices is adjacent to exactly λ others? Two vertices are said to be adjacent if they are connected by an edge. We call a graph with the above properties a symmetric (ν, κ, λ) graph and refer to the last of the properties as the A-condition. The complete graph of order v is a trivial example of a symmetric (ν, ν— 1, ν — 2) graph, but we are of course only interested in non-trivial constructions.

View PDF Chat

Polarities of generalized hexagons and perfect codes

1976-11-01

Peter J‎. Cameron , J. A. Thas , Sam Payne

The equivalence of certain generalized quadrangles

1971-05-01

Stanley E. Payne

Flocks of quadratic cones, generalized quadrangles and translation planes

1988-09-01

Hans Gevaert , NormanL. Johnson

Caps and codes

1978-01-01

Raymond A. Hill

k-arcs and partial flocks

1995-09-01

Leo Storme , J. A. Thas

TRANSLATION GENERALIZED QUADRANGLES FOR WHICH THE TRANSLATION DUAL ARISES FROM A FLOCK

2003-09-01

Koen Thas

It is shown that each finite translation generalized quadrangle (TGQ) , subtended ovoids in generalized quadrangles, and the understanding of automorphism groups of certain generalized quadrangles. Several problems on these … It is shown that each finite translation generalized quadrangle (TGQ) , subtended ovoids in generalized quadrangles, and the understanding of automorphism groups of certain generalized quadrangles. Several problems on these topics will be solved completely.

View PDF Chat