Finite Geometries

by Isle of Thorns Conference 2000 (University of Sussex); Hirschfeld, J. W. P.; Jungnickel, D.; Thas, J. A.

• ISBN13: 9780792369943
• ISBN10: 0792369947
• Format: Hardcover
• Copyright: 2001-08-01
• Publisher: Kluwer Academic Pub

Summary

This is a graduate-level book aimed at experienced researchers as well as beginning graduate students in finite geometry, incidence geometry, design theory, coding theory and combinatorics. The 21 articles arise from the Fourth Isle of Thorns Conference on Finite Geometries, held in July 2000. The book contains new high-level results at the forefront of the field as well as authoritative surveys. The articles are written so that beginning graduate students can appreciate them. Among the surveys by the invited speakers are P.J. Cameron 'Fixed Points and cycles', C.E. Praeger 'Implications of line-transitivity for designs', B. Schmidt, 'Exponent bounds', which explains recent results on difference sets, and several papers with H. Van Maideghem as co-author on generalized polygons. The editors also contribute: A. Blokhuis, D. Jungnickel, and B. Schmidt 'On a class of symmetric divisible designs which are almost projective planes', and D. Luyckx and J.A. Thas discuss the geometry of the quadric in six dimensions. There is also a lengthy and complete survey by J.W.P. Hirschfeld and L. Storme 'The packing problem in statistics, coding theory and finite projective spaces: update 2001'. Audience: Researchers as well as beginning graduate students in the areas of finite geometry, incidence geometry, design theory, coding theory and combinatorics will appreciate the surveys and original papers by leaders in these fields.

Table of Contents

Preface	vii
Point-line geometries with a generating set that depends on the underlying field	1	(26)
R.J. Blok
A. Pasini
On a class of symmetric divisible designs which are almost projective planes	27	(8)
Aart Blokhuis
Dieter Jungnickel
Bernhard Schmidt
Generalized elliptic cubic curves, Part 1	35	(14)
Francis Buekenhout
Fixed points and cycles	49	(12)
Peter J. Cameron
RWPRI geometries for the alternating group A8	61	(38)
Philippe Cara
A characterization of truncated Dn-buildings as flag-transitive PG.PG*-geometries	99	(22)
I. Cardinali
A. Pasini
Group-theoretic characterizations of classical ovoids	121	(12)
A. Cossidente
O.H. King
A general framework for subexponential discrete logarithm algorithms in groups of unknown order	133	(14)
Andreas Enge
Generalized quadrangles and pencils of quadrics	147	(12)
Dina Ghinelli
Stefan Lowe
The Desarguesian plane of order thirteen	159	(12)
M. Giulietti
J.W.P. Hirschfeld
G. Korchmaros
Two characterizations of the Hermitian spread in the split Cayley hexagon	171	(6)
Eline Govaert
Hendrik Van Maldeghem
Epimorphisms of generalized polygons, Part 2: some existence and non-existence results	177	(24)
Ralf Gramlich
Hendrik Van Maldeghem
The packing problem in statistics, coding theory and finite projective spaces: update 2001	201	(46)
J.W.P. Hirschfeld
L. Storme
The geometric approach to linear codes	247	(10)
I.N. Landjev
Flocks and locally hermitian 1-systems of Q(6,q)	257	(20)
D. Luyckx
J. A. Thas
Diagrams for embeddings of polygons	277	(18)
B. Muhlherr
H. Van Maldeghem
The Law-Penttila q-clan geometries	295	(10)
Stanley E. Payne
Implications of line-transitivity for designs	305	(14)
Cheryl E. Praeger
Exponent bounds	319	(14)
Bernhard Schmidt
On symmetries and translation generalized quadrangles	333	(14)
Koen Thas
Complete caps in projective space which are disjoint from a subspace of codimension two	347	(16)
David L. Wehlau
Participants	363	(2)
Talks	365