Near Polygons - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Near Polygons write by Bart de Bruyn. This book was released on 2010-04-11. Near Polygons available in PDF, EPUB and Kindle. 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.
An Introduction to Incidence Geometry
An Introduction to Incidence Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Incidence Geometry write by Bart De Bruyn. This book was released on 2016-11-09. An Introduction to Incidence Geometry available in PDF, EPUB and Kindle. 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.
Points and Lines
Points and Lines - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Points and Lines write by Ernest E. Shult. This book was released on 2010-12-13. Points and Lines available in PDF, EPUB and Kindle. The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type. Virtually all of these geometries (or homomorphic images of them) are characterized in this book by simple local axioms on points and lines. Simple point-line characterizations of Lie incidence geometries allow one to recognize Lie incidence geometries and their automorphism groups. These tools could be useful in shortening the enormously lengthy classification of finite simple groups. Similarly, recognizing ruled manifolds by axioms on light trajectories offers a way for a physicist to recognize the action of a Lie group in a context where it is not clear what Hamiltonians or Casimir operators are involved. The presentation is self-contained in the sense that proofs proceed step-by-step from elementary first principals without further appeal to outside results. Several chapters have new heretofore unpublished research results. On the other hand, certain groups of chapters would make good graduate courses. All but one chapter provide exercises for either use in such a course, or to elicit new research directions.
Generalized Polygons
Generalized Polygons - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Generalized Polygons write by Hendrik Van Maldeghem. This book was released on 2012-01-05. Generalized Polygons available in PDF, EPUB and Kindle. Generalized Polygons is the first book to cover, in a coherent manner, the theory of polygons from scratch. In particular, it fills elementary gaps in the literature and gives an up-to-date account of current research in this area, including most proofs, which are often unified and streamlined in comparison to the versions generally known. Generalized Polygons will be welcomed both by the student seeking an introduction to the subject as well as the researcher who will value the work as a reference. In particular, it will be of great value for specialists working in the field of generalized polygons (which are, incidentally, the rank 2 Tits-buildings) or in fields directly related to Tits-buildings, incidence geometry and finite geometry. The approach taken in the book is of geometric nature, but algebraic results are included and proven (in a geometric way!). A noteworthy feature is that the book unifies and generalizes notions, definitions and results that exist for quadrangles, hexagons, octagons - in the literature very often considered separately - to polygons. Many alternative viewpoints given in the book heighten the sense of beauty of the subject and help to provide further insight into the matter.
Groups of Exceptional Type, Coxeter Groups and Related Geometries
Groups of Exceptional Type, Coxeter Groups and Related Geometries - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Groups of Exceptional Type, Coxeter Groups and Related Geometries write by N.S. Narasimha Sastry. This book was released on 2014-04-02. Groups of Exceptional Type, Coxeter Groups and Related Geometries available in PDF, EPUB and Kindle. The book deals with fundamental structural aspects of algebraic and simple groups, Coxeter groups and the related geometries and buildings. All contributing authors are very active researchers in the topics related to the theme of the book. Some of the articles provide the latest developments in the subject; some provide an overview of the current status of some important problems in this area; some survey an area highlighting the current developments; and some provide an exposition of an area to collect problems and conjectures. It is hoped that these articles would be helpful to a beginner to start independent research on any of these topics, as well as to an expert to know some of the latest developments or to consider some problems for investigation.
