Geometry, Combinatorial Designs and Related Structures
1st Edition
Published on 29. March 2011
978-0-511-89340-7 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
25 Tables, unspecified; 28 Line drawings, unspecified
File size
52,28 MB
ISBN-13
978-0-511-89340-7 (9780511893407)
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Schweitzer Classification
Other editions
Additional editions
J. W. P. Hirschfeld | S. S. Magliveras | M. J. de Resmini
Geometry, Combinatorial Designs and Related Structures
Book
08/1997
Cambridge University Press
€79.20
Shipment within 15-20 days
Persons
Content
Preface; Introduction; 1. On maximum size anti-Pasch sets of triples; 2. Some simple 7-designs; 3. Inscribed bundles, Veronese surfaces and caps; 4. Embedding partial geometries in Steiner designs; 5. Finite geometry after Aschbacher's theorem: PGL(n,q) from a Kleinian viewpoint; 6. The Hermitian function field arising from a cyclic arc in a Galois plane; 7. Intercalates everywhere; 8. Difference sets: an update; 9. Computational results for the known biplanes of order 9; 10. A survey of small embeddings for partial cycle systems; 11. Rosa triple systems; 12. Searching for spreads and packings; 13. A note of Buekenhout-Metz unitals; 14. Elation generalized quadrangles of order (q^2, q); 15. Uniform parallelisms of PG(3,3); 16. Double-fives and partial spreads in PG(5,2); 17. Rank three geometries with simplicial residues; 18. Generalized quadrangles and the Axiom of Veblen; Talks; Participants.
