Finite Geometry and Combinatorial Applications

A graduate-level introduction to finite geometry and its applications to other areas of combinatorics.

Simeon Ball (Author)

9781107107991, Cambridge University Press

Hardback, published 2 July 2015

298 pages, 35 b/w illus. 105 exercises
23.9 x 1.5 x 4.3 cm, 0.57 kg

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.

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.

Subject Areas: Combinatorics & graph theory [PBV], Geometry [PBM], Discrete mathematics [PBD], Mathematics [PB]