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Status:
Available5.0
34 reviews
ISBN-10 : 1315120070
ISBN-13 : 9781315120072
Author: Gyorgy Kiss, Tamas Szonyi
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
1. Definition of projective planes, examples
2. Basic properties of collineations and the Theorem of Baer
3. Coordinatization of projective planes
4. Projective spaces of higher dimensions
5. Higher dimensional representations
6. Arcs, ovals and blocking sets
7. (k; n)-arcs and multiple blocking sets
8. Algebraic curves and finite geometry
9. Arcs, caps, unitals and blocking sets in higher dimensional spaces
10. Generalized polygons, Möbius planes
11. Hyperovals
12. Some applications of finite geometry in combinatorics
13. Some applications of finite geometry in coding theory and cryptography
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Tags: Finite Geometries, Gyorgy Kiss, Tamas Szonyi, finite geometries
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