Finite Geometries

Finite Geometries stands out from recent textbooks about the subject of finite geometries by having a broader scope. The authors thoroughly explain how the subject of finite geometries is a central part of discrete mathematics. The text is suitable for undergraduate and graduate courses. Additionally, it can be used as reference material on recent works.

The authors examine how finite geometries? applicable nature led to solutions of open problems in different fields, such as design theory, cryptography and extremal combinatorics. Other areas covered include proof techniques using polynomials in case of Desarguesian planes, and applications in extremal combinatorics, plus, recent material and developments.

Features:

• Includes exercise sets for possible use in a graduate course





• Discusses applications to graph theory and extremal combinatorics





• Covers coding theory and cryptography





• Translated and revised text from the Hungarian published version

Definition of projective planes, examples

Basic properties of collineations and the Theorem of Baer

Coordination of projective planes

Projective spaces of higher dimensions

Higher dimensional representations

Arcs, ovals and blocking sets

(k, n)-arcs and multiple blocking sets

Algebraic curves and finite geometries

Arcs, caps, unitals and blocking sets in higher dimensional spaces

Generalized polygons, Mobius planes

Hyperovals

Some applications of finite geometry in combinatorics

Some applications of finite geometry in coding theory and cryptography

György Kiss is an associate professor of Mathematics at Eötvös Loránd University (ELTE), Budapest, Hungary, and also at the University of Primorska, Koper, Slovenia. He is a senior researcher of the MTA-ELTE Geometric and Algebraic Combinatorics Research group. His research interests are in finite and combinatorial geometry.

Tamás Szőnyi is a Professor at the Department of Computer Science in Eötvös Loránd University, Budapest, Hungary, and also at the University of Primorska, Koper, Slovenia. He is the head of the MTA-ELTE Geometric and Algebraic Combinatorics Research Group. His primary research interests include finite geometry, combinatorics, coding theory and block designs.