Finite Geometry and Combinatorial Applications
Published on 26. August 2015
978-1-316-31106-6 (ISBN)
Description
The projective and polar geometries that arise from a vector space over a finite field are particularly useful in the construction of combinatorial objects, such as latin squares, designs, codes and graphs. This book provides an introduction to these geometries and their many applications to other areas of combinatorics. Coverage includes a detailed treatment of the forbidden subgraph problem from a geometrical point of view, and a chapter on maximum distance separable codes, which includes a proof that such codes over prime fields are short. The author also provides more than 100 exercises (complete with detailed solutions), which show the diversity of applications of finite fields and their geometries. Finite Geometry and Combinatorial Applications is ideal for anyone, from a third-year undergraduate to a researcher, who wishes to familiarise themselves with and gain an appreciation of finite geometry.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 35 Line drawings, unspecified
File size
2,91 MB
ISBN-13
978-1-316-31106-6 (9781316311066)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Simeon Ball
Finite Geometry and Combinatorial Applications
Book
07/2015
Cambridge University Press
€171.20
Shipment within 15-20 days
Simeon Ball
Finite Geometry and Combinatorial Applications
Book
06/2015
Cambridge University Press
€60.00
Shipment within 15-20 days
Person
Simeon Ball is a senior lecturer in the Department of Applied Mathematics IV at Universitat Politecnica de Catalunya, Barcelona. He has published over 50 articles and been awarded various prestigious grants, including the Advanced Research Fellowship from EPSRC in the UK and the Ramon y Cajal grant in Spain. In 2012 he proved the MDS conjecture for prime fields, which conjectures that all linear codes over prime fields that meet the Singleton bound are short. This is one of the oldest conjectures in the theory of error-correcting codes.
Content
1. Fields; 2. Vector spaces; 3. Forms; 4. Geometries; 5. Combinatorial applications; 6. The forbidden subgraph problem; 7. MDS codes; Appendix A. Solutions to the exercises; Appendix B. Additional proofs; Appendix C. Notes and references; References; Index.
