Geometry, Combinatorial Designs and Related Structures

doi:10.1017/CBO9780511526114

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Edited by J. W. P. Hirschfeld, University of Sussex, S. S. Magliveras, University of Nebraska, Lincoln, M. J. de Resmini, Università degli Studi di Roma 'La Sapienza', Italy

Publisher:: Cambridge University Press
Online publication date:: November 2009
Print publication year:: 1997
Online ISBN:: 9780511526114
DOI:: https://doi.org/10.1017/CBO9780511526114

Subjects:: Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding, Geometry and Topology
Series:: London Mathematical Society Lecture Note Series (245)

54.99 (GBP)

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This volume presents up-to-date research on finite geometries and designs, a key area in modern applicable mathematics. An introductory chapter discusses topics presented in each of the main chapters, and is followed by articles from leading international figures in this field. These include a discussion of the current state of finite geometry from a group-theoretical viewpoint, and surveys of difference sets and of small embeddings of partial cycle systems into Steiner triple systems. Also presented are successful searches for spreads and packing of designs, rank three geometries with simplicial residues and generalized quadrangles satisfying Veblen's Axiom. In addition, there are articles on new 7-designs, biplanes, various aspects of triple systems, and many other topics. This book will be a useful reference for researchers working in finite geometries, design theory or combinatorics in general.

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Geometry, Combinatorial Designs and Related Structures

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

Introduction
pp 1-6

On maximum size anti-Pasch sets of triples
pp 7-14

Some simple 7–designs
pp 15-26

Inscribed bundles, Veronese surfaces and caps
pp 27-32

Embedding partial geometries in Steiner designs
pp 33-42

Finite geometry after Aschbacher's Theorem: PGL(n, q) from a Kleinian viewpoint
pp 43-62

The Hermitian function field arising from a cyclic arc in a Galois plane
pp 63-68

Intercalates everywhere
pp 69-88

Difference sets: an update
pp 89-112

Computational results for the known biplanes of order 9
pp 113-122

A survey of small embeddings for partial cycle systems
pp 123-148

Rosa triple systems
pp 149-160

Searching for spreads and packings
pp 161-176

A note on Buekenhout-Metz unitals
pp 177-180

Elation generalized quadrangles of order (q2, q)
pp 181-192

Uniform parallelisms of PG(3, 3)
pp 193-200

Double-fives and partial spreads in PG(5, 2)
pp 201-216

Rank three geometries with simplicial residues
pp 217-240

Generalized quadrangles and the Axiom of Veblen
pp 241-254

Talks
pp 255-256

Participants
pp 257-258

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Geometry, Combinatorial Designs and Related Structures

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