Handbook Of Incidence Geometry
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Handbook Of Incidence Geometry
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Author : Francis Buekenhout
language : en
Publisher: North-Holland
Release Date : 1995
Handbook Of Incidence Geometry written by Francis Buekenhout and has been published by North-Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
Hardbound. This Handbook deals with the foundations of incidence geometry, in relationship with division rings, rings, algebras, lattices, groups, topology, graphs, logic and its autonomous development from various viewpoints. Projective and affine geometry are covered in various ways. Major classes of rank 2 geometries such as generalized polygons and partial geometries are surveyed extensively.More than half of the book is devoted to buildings at various levels of generality, including a detailed and original introduction to the subject, a broad study of characterizations in terms of points and lines, applications to algebraic groups, extensions to topological geometry, a survey of results on diagram geometries and nearby generalizations such as matroids.
An Introduction To Incidence Geometry
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Author : Bart De Bruyn
language : en
Publisher: Birkhäuser
Release Date : 2016-11-09
An Introduction To Incidence Geometry written by Bart De Bruyn and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-09 with Mathematics categories.
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
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Author : Ernest E. Shult
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-13
Points And Lines written by Ernest E. Shult and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-13 with Mathematics categories.
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.
Groups And Geometries
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Author : Lino Di Martino
language : en
Publisher: Birkhäuser
Release Date : 2013-12-01
Groups And Geometries written by Lino Di Martino and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of finite characteristic, 3. buildings, and the geometry of projective and polar spaces, and 4. geometries of sporadic simple groups. We are grateful to the authors for their efforts in providing us with manuscripts in LaTeX. Barbara Priwitzer and Thomas Hintermann, Mathematics Editors of Birkhauser, have been very helpful and supportive throughout the preparation of this volume.
General Galois Geometries
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Author : James Hirschfeld
language : en
Publisher: Springer
Release Date : 2016-02-03
General Galois Geometries written by James Hirschfeld and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-03 with Mathematics categories.
This book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries. This volume completes the trilogy comprised of plane case (first volume) and three dimensions (second volume). This revised edition includes much updating and new material. It is a mostly self-contained study of classical varieties over a finite field, related incidence structures and particular point sets in finite n-dimensional projective spaces. General Galois Geometries is suitable for PhD students and researchers in combinatorics and geometry. The separate chapters can be used for courses at postgraduate level.
Projective Geometry
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Author : Albrecht Beutelspacher
language : en
Publisher: Cambridge University Press
Release Date : 1998-01-29
Projective Geometry written by Albrecht Beutelspacher and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-29 with Mathematics categories.
Projective geometry is not only a jewel of mathematics, but has also many applications in modern information and communication science. This book presents the foundations of classical projective and affine geometry as well as its important applications in coding theory and cryptography. It also could serve as a first acquaintance with diagram geometry. Written in clear and contemporary language with an entertaining style and around 200 exercises, examples and hints, this book is ideally suited to be used as a textbook for study in the classroom or on its own.
Geometry Combinatorial Designs And Related Structures
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Author : J. W. P. Hirschfeld
language : en
Publisher: Cambridge University Press
Release Date : 1997-08-14
Geometry Combinatorial Designs And Related Structures written by J. W. P. Hirschfeld and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-14 with Mathematics categories.
This volume examines state of the art research in finite geometries and designs.
Finite Geometries
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Author : Aart Blokhuis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Finite Geometries written by Aart Blokhuis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Computers categories.
When? These are the proceedings of Finite Geometries, the Fourth Isle of Thorns Conference, which took place from Sunday 16 to Friday 21 July, 2000. It was organised by the editors of this volume. The Third Conference in 1990 was published as Advances in Finite Geometries and Designs by Oxford University Press and the Second Conference in 1980 was published as Finite Geometries and Designs by Cambridge University Press. The main speakers were A. R. Calderbank, P. J. Cameron, C. E. Praeger, B. Schmidt, H. Van Maldeghem. There were 64 participants and 42 contributions, all listed at the end of the volume. Conference web site http://www. maths. susx. ac. uk/Staff/JWPH/ Why? This collection of 21 articles describes the latest research and current state of the art in the following inter-linked areas: • combinatorial structures in finite projective and affine spaces, also known as Galois geometries, in which combinatorial objects such as blocking sets, spreads and partial spreads, ovoids, arcs and caps, as well as curves and hypersurfaces, are all of interest; • geometric and algebraic coding theory; • finite groups and incidence geometries, as in polar spaces, gener alized polygons and diagram geometries; • algebraic and geometric design theory, in particular designs which have interesting symmetric properties and difference sets, which play an important role, because of their close connections to both Galois geometry and coding theory.
Finite Geometry And Combinatorial Applications
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Author : Simeon Ball
language : en
Publisher: Cambridge University Press
Release Date : 2015-07-02
Finite Geometry And Combinatorial Applications written by Simeon Ball and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-02 with Mathematics categories.
A graduate-level introduction to finite geometry and its applications to other areas of combinatorics.
Geometries On Surfaces
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Author : Burkard Polster
language : en
Publisher: Cambridge University Press
Release Date : 2001-10-03
Geometries On Surfaces written by Burkard Polster and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10-03 with Mathematics categories.
The projective, Möbius, Laguerre, and Minkowski planes over the real numbers are just a few examples of a host of fundamental classical topological geometries on surfaces. This book summarizes all known major results and open problems related to these classical point-line geometries and their close (nonclassical) relatives. Topics covered include: classical geometries; methods for constructing nonclassical geometries; classifications and characterizations of geometries. This work is related to many other fields including interpolation theory, convexity, the theory of pseudoline arrangements, topology, the theory of Lie groups, and many more. The authors detail these connections, some of which are well-known, but many much less so. Acting both as a reference for experts and as an accessible introduction for graduate students, this book will interest anyone wishing to know more about point-line geometries and the way they interact.