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Finite Geometry and Combinatorial Applications - Simeon Ball

Finite Geometry and Combinatorial Applications

(Autor)

Buch | Hardcover
298 Seiten
2015
Cambridge University Press (Verlag)
978-1-107-10799-1 (ISBN)
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For students and researchers interested in algebraic combinatorics, this book not only provides an introduction to the geometries arising from vector spaces over finite fields but also shows how these geometries can be applied to various combinatorial objects. More than 100 exercises and solutions are provided.
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.

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.

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.

Erscheint lt. Verlag 2.7.2015
Reihe/Serie London Mathematical Society Student Texts
Zusatzinfo Worked examples or Exercises; 35 Line drawings, unspecified
Verlagsort Cambridge
Sprache englisch
Maße 15 x 239 mm
Gewicht 570 g
Themenwelt Mathematik / Informatik Mathematik Geometrie / Topologie
Mathematik / Informatik Mathematik Graphentheorie
ISBN-10 1-107-10799-7 / 1107107997
ISBN-13 978-1-107-10799-1 / 9781107107991
Zustand Neuware
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