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
| Preface |
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vii | |
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1 Definition of projective planes, examples |
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1 | (28) |
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2 Basic properties of collineations and the Theorem of Baer |
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29 | (18) |
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3 Coordinatization of projective planes |
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47 | (28) |
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4 Projective spaces of higher dimensions |
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75 | (42) |
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5 Higher dimensional representations |
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117 | (16) |
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6 Arcs, ovals and blocking sets |
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133 | (28) |
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7 (k,n)-arcs and multiple blocking sets |
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161 | (16) |
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8 Algebraic curves and finite geometry |
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177 | (22) |
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9 Arcs, caps, unitals and blocking sets in higher dimensional spaces |
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199 | (30) |
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10 Generalized polygons, Mobius planes |
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229 | (26) |
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255 | (20) |
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12 Some applications of finite geometry in combinatorics |
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275 | (26) |
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13 Some applications of finite geometry in coding theory and cryptography |
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301 | (20) |
| Bibliography |
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321 | (12) |
| Index |
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333 | |
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 Sznyi 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.
