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.

Zusammenfassung

Dedicated to the Russian mathematician Albert Shiryaev on his 70th birthday, this is a collection of papers written by his former students, co-authors and colleagues. The book represents the state-of-the-art of a quickly maturing theory and will be an essential source for researchers in this area. The diversity of topics and comprehensive style of the papers make the book attractive for Ph.D. students and young researchers.

Inhalt
Dense near polygons.- Regular near polygons.- Glued near polygons.- Valuations.- The known slim dense near polygons.- Slim dense near hexagons.- Slim dense near polygons with a nice chain of convex subpolygons.- Slim dense near octagons.- Nondense slim near hexagons.