- Provides one of the few in the area of Incidence Geometry which discusses several families of point-line geometries at the same time
- Includes the graph theory necessary for the study of certain point-line geometries
- Shows the connections between these various point-line geometries
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- About this book
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This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs.
This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end of the book. This book is aimed at graduate students and researchers in the fields of combinatorics and incidence geometry.
- Reviews
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“This book grew out of lectures given by the author for students at the graduate level. … The book contains 80 exercises with complete solutions. It can be used as a textbook for a graduate course, but is also suitable for self-study.” (Norbert Knarr, zbMATH, 1376.51001, 2018)
- Table of contents (9 chapters)
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Introductory notions
Pages 1-10
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Some classes of point-line geometries
Pages 11-37
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Strongly regular and distance-regular graphs
Pages 39-60
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Projective spaces
Pages 61-88
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Generalized polygons
Pages 89-127
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Table of contents (9 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- An Introduction to Incidence Geometry
- Authors
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- Bart De Bruyn
- Series Title
- Frontiers in Mathematics
- Copyright
- 2016
- Publisher
- Birkhäuser Basel
- Copyright Holder
- Springer International Publishing Switzerland
- eBook ISBN
- 978-3-319-43811-5
- DOI
- 10.1007/978-3-319-43811-5
- Softcover ISBN
- 978-3-319-43810-8
- Series ISSN
- 1660-8046
- Edition Number
- 1
- Number of Pages
- XII, 372
- Topics
