Finite geometries
著者
書誌事項
Finite geometries
CRC Press, c2020
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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
目次
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
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