- 280 pages
- English
- PDF
- Only available on web
Introduction to Finite Geometries
About This Book
North-Holland Texts in Advanced Mathematics: Introduction to Finite Geometries focuses on the advancements in finite geometries, including mapping and combinatorics. The manuscript first offers information on the basic concepts on finite geometries and Galois geometries. Discussions focus on linear mapping of a given quadrangle onto another given quadrangle; point configurations of order 2 on a Galois plane of even order; canonical equation of curves of the second order on the Galois planes of even order; and set of collineations mapping a Galois plane onto itself. The text then ponders on geometrical configurations and nets, as well as pentagon theorem and the Desarguesian configuration, two pentagons inscribed into each other, and the concept of geometrical nets. The publication takes a look at combinatorial applications of finite geometries and combinatorics and finite geometries. Topics include generalizations of the Petersen graph, combinatorial extremal problem, and theorem of closure of the hyperbolic space. The book is a valuable source of data for readers interested in finite geometries.
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Table of contents
- Front Cover
- Introduction to Finite Geometries
- Copyright Page
- Table of Contents
- Dedication
- PREFACE
- COMMON NOTATION
- CHAPTER 1. BASIC CONCEPTS CONCERNING FINITE GEOMETRIES
- CHAPTER 2. GALOIS GEOMETRIES
- CHAPTER 3. GEOMETRICAL CONFIGURATIONS AND NETS
- CHAPTER 4. SOME COMBINATORIAL APPLICATIONS OF FINITE GEOMETRIES
- CHAPTER 5. COMBINATORICS AND FINITE GEOMETRIES
- CHAPTER 6. SOME ADDITIONAL THEMES IN THE THEORY OF FINITE GEOMETRIES
- CHAPTER 7. APPENDIX
- BIBLIOGRAPHICAL NOTES
- INDEX