Combinatorics of Finite Geometries

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Cambridge University Press, May 28, 1997 - Mathematics - 193 pages
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Combinatorics of Finite Geometries is an introductory text on the combinatorial theory of finite geometry. Assuming only a basic knowledge of set theory and analysis, it provides a thorough review of the topic and leads the student to results at the frontiers of research. This book begins with an elementary combinatorial approach to finite geometries based on finite sets of points and lines, and moves into the classical work on affine and projective planes. Later, it addresses polar spaces, partial geometries, and generalized quadrangles. The revised edition contains an entirely new chapter on blocking sets in linear spaces, which highlights some of the most important applications of blocking sets--from the initial game-theoretic setting to their very recent use in cryptography. Extensive exercises at the end of each chapter insure the usefulness of this book for senior undergraduate and beginning graduate students.
 

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Contents

Preface
xi
Preface to the first edition
xiii
1 Nearlinear spaces
1
2 Linear spaces
23
3 Projective spaces
41
4 Affine spaces
67
5 Polar spaces
89
6 Generalized quadrangles
112
7 Partial geometries
138
8 Blocking sets
158
Bibliography
176
Index of notation
190
Subject index
191
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