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Finite Geometries

Autor Gyorgy Kiss, Tamas Szonyi
en Limba Engleză Paperback – 21 ian 2023
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


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Specificații

ISBN-13: 9781032475387
ISBN-10: 1032475382
Pagini: 346
Ilustrații: 26
Dimensiuni: 156 x 234 x 23 mm
Greutate: 0.64 kg
Ediția:1
Editura: CRC Press
Colecția CRC Press

Cuprins

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

Notă biografică

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.

Descriere

Finite Geometries stands out from recent textbooks on the subject of finite geometries by having a broader scope. This textbook explains the recent proof techniques using polynomials in case of Desarguesian planes.