Finite Geometry and Combinatorial Applications

Simeon Ball (Universitat Politècnica de Catalunya, Barcelona)

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English

Cambridge University Press
02 July 2015

Discrete mathematics; Geometry; Combinatorics & graph theory

Series: London Mathematical Society Student Texts

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.

By: Simeon Ball (Universitat Politècnica de Catalunya Barcelona)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 82
Dimensions: Height: 239mm, Width: 15mm, Spine: 43mm
Weight: 570g
ISBN: 9781107107991
ISBN 10: 1107107997
Series: London Mathematical Society Student Texts
Pages: 298
Publication Date: 02 July 2015
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

Simeon Ball is a senior lecturer in the Department of Applied Mathematics IV at Universitat Politècnica 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.