Geometry, Combinatorial Designs and Related Structures

J. W. P. Hirschfeld, S. S. Magliveras, M. J. de Resmini

• Publisher: Cambridge University Press
• Year: 1997
• Print ISBN:
  9780521595384
• eBook ISBN:
  9780511893407
• Topic: Mathematics
• Subtopic: Discrete Mathematics
• Index: Mathematics

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.

Table of contents

• Cover
• Half-title
• Title
• Copyright
• Contents
• Preface
• Introduction
• S. Akbari, G.B. Khosrovshahi, C. Maysoori, and S. Shariari On maximum size anti-Pasch sets of triples
• A. Betten, R. Laue, and A. Wassermann Some simple 7—designs
• A. Bonisoli and A. Cossidente Inscribed bundles, Veronese surfaces and caps
• A.E. Brouwer, W.H. Haemers, and V.D. Tonchev Embedding partial geometries in Steiner designs
• P.J. Cameron Finite geometry after Aschbacher's theorem: PGL(n, q) from a Kleinian viewpoint
• A. Cossidente and G. Korchmaros The Hermitian function field arising from a cyclic arc in a GaloiC vlane
• P. Danziger and E. Mendelsohn Intercalates everywhere
• D. Jungnickel and B. Schmidt Difference sets: an update
• J.D. Key and V.D. Tonchev Computational results for the known biplanes of order 9
• C.C. Lindner A survey of small embeddings for partial cycle systems
• A.C.H. Ling and C.J. Colbourn Rosa triple systems
• R. Mathon Searching for spreads and packings
• K. Metsch A note on Buekenhout-Metz unitals
• CM. O'Keefe and T. Penttila Elation generalized quadrangles of order (q2,q)
• A.R. Prince Uniform parallelisms of PG(3,3)
• R. Shaw Double-fives and partial spreads in PG(5,2)
• E.E. Shult Rank three geometries with simplicial residues
• J.A. Thas and H. Van Maldeghem Generalized quadrangles and the Axiom of Veblen
• Talks
• Participants