The projective and polar geometries that arise from a vector space over a finite field are particularly useful within the construction of combinatorial objects, such as latin squares, designs, codes and graphs. This book provides an introduction to those geometries and their many applications to other areas of combinatorics. Coverage features a detailed remedy of the forbidden subgraph problem from a geometrical standpoint, and a chapter on maximum distance separable codes, which incorporates a proof that such codes over prime fields are short. The creator also provides more than 100 exercises (complete with detailed solutions), which show the range of applications of finite fields and their geometries. Finite Geometry and Combinatorial Applications is perfect for any person, from a third-year undergraduate to a researcher, who wishes to familiarise themselves with and gain an appreciation of finite geometry.
Finite Geometry and Combinatorial Applications (London Mathematical Society Student Texts)