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Near Polygons
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This book intends to give an extensive treatment of the basic theory of general near polygons. Near polygons have been introduced about 25 years ago and have been studied intensively in the 1980s. In recent years the subject of near polygons has regained interest. This book discusses old and new results on this subject. In the first part of the book, we develop the basic theory of near polygons. We discuss three important classes of near polygons (dense, regular and glued near polygons) and develop the theory of valuations which is very important for classification purposes. In the second part of the book, we discuss recent results on the classification of dense near polygons with three points on each line.
Near polygons were introduced about 25 years ago and studied intensively in the 1980s. In recent years the subject has regained interest. This monograph gives an extensive overview of the basic theory of general near polygons.
The first part of the book includes a discussion of the classes of dense near polygons, regular near polygons, and glued near polygons. Also valuations, one of the most important tools for classifying dense near polygons, are treated in detail. The second part of the book discusses the classification of dense near polygons with three points per line.
The book is self-contained and almost all theorems are accompanied with proofs. Several new results are presented. Many known results occur in a more general form and the proofs are often more streamlined than their original versions. The volume is aimed at advanced graduate students and researchers in the fields of combinatorics and finite geometry.
The first part of the book includes a discussion of the classes of dense near polygons, regular near polygons, and glued near polygons. Also valuations, one of the most important tools for classifying dense near polygons, are treated in detail. The second part of the book discusses the classification of dense near polygons with three points per line.
The book is self-contained and almost all theorems are accompanied with proofs. Several new results are presented. Many known results occur in a more general form and the proofs are often more streamlined than their original versions. The volume is aimed at advanced graduate students and researchers in the fields of combinatorics and finite geometry.