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Author: William M. Kantor
Publisher:
ISBN:
Category : Architecture
Languages : en
Pages : 184
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Book Description
The theory of buildings was introduced by J. Tits in order to focus on geometric and combinatorial aspects of simple groups of Lie type. Since then, the theory has blossomed into an extremely active field of mathematical research having deep connections with topics as diverse as algebraic groups, arithmetic groups, finite simple groups, and finite geometries, as well as with graph theory and other aspects of combinatorics. This volume is intended to provide an up-to-date survey of the theory of buildings with special emphasis on its interaction with related geometries. Experts in their respective fields provide coverage of such topics as the classification and construction of buildings, finite groups associated with building-like geometries, graphs and associated schemes, and more.
Author: William M. Kantor
Publisher:
ISBN:
Category : Architecture
Languages : en
Pages : 184
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Book Description
The theory of buildings was introduced by J. Tits in order to focus on geometric and combinatorial aspects of simple groups of Lie type. Since then, the theory has blossomed into an extremely active field of mathematical research having deep connections with topics as diverse as algebraic groups, arithmetic groups, finite simple groups, and finite geometries, as well as with graph theory and other aspects of combinatorics. This volume is intended to provide an up-to-date survey of the theory of buildings with special emphasis on its interaction with related geometries. Experts in their respective fields provide coverage of such topics as the classification and construction of buildings, finite groups associated with building-like geometries, graphs and associated schemes, and more.
Author: William M. Kantor
Publisher:
ISBN: 9781383025118
Category : Geometry
Languages : en
Pages : 0
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Book Description
This volume is intended to provide an up-to-date survey of the theory of buildings with special emphasis on its interaction with related geometries. It will be of benefit as a guide for all those whose research touches on these themes.
Author: N.S. Narasimha Sastry
Publisher: Springer Science & Business Media
ISBN: 1461407095
Category : Mathematics
Languages : en
Pages : 348
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Book Description
This is the Proceedings of the ICM 2010 Satellite Conference on “Buildings, Finite Geometries and Groups” organized at the Indian Statistical Institute, Bangalore, during August 29 – 31, 2010. This is a collection of articles by some of the currently very active research workers in several areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lie theory, etc. These articles reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups. The unique perspective the authors bring in their articles on the current developments and the major problems in their area is expected to be very useful to research mathematicians, graduate students and potential new entrants to these areas.
Author: F. Kárteszi
Publisher: Elsevier
ISBN: 148327814X
Category : Mathematics
Languages : en
Pages : 281
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Book Description
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.
Author: Aart Blokhuis
Publisher: Springer Science & Business Media
ISBN: 1461302838
Category : Computers
Languages : en
Pages : 366
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Book Description
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.
Author: Gyorgy Kiss
Publisher: CRC Press
ISBN: 1498721664
Category : Mathematics
Languages : en
Pages : 338
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Book Description
Finite Geometries stands out from recent textbooks about the subject of finite geometries by having a broader scope. The authors thoroughly explain how the subject of finite geometries is a central part of discrete mathematics. The text is suitable for undergraduate and graduate courses. Additionally, it can be used as reference material on recent works. The authors examine how finite geometries’ applicable nature led to solutions of open problems in different fields, such as design theory, cryptography and extremal combinatorics. Other areas covered include proof techniques using polynomials in case of Desarguesian planes, and applications in extremal combinatorics, plus, recent material and developments. Features: Includes exercise sets for possible use in a graduate course Discusses applications to graph theory and extremal combinatorics Covers coding theory and cryptography Translated and revised text from the Hungarian published version
Author: Alexander Hulpke
Publisher: Walter de Gruyter
ISBN: 3110199742
Category : Mathematics
Languages : en
Pages : 287
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Book Description
This volume is the proceedings of a conference on Finite Geometries, Groups, and Computation that took place on September 4-9, 2004, at Pingree Park, Colorado (a campus of Colorado State University). Not accidentally, the conference coincided with the 60th birthday of William Kantor, and the topics relate to his major research areas. Participants were encouraged to explore the deeper interplay between these fields. The survey papers by Kantor, O'Brien, and Penttila should serve to introduce both students and the broader mathematical community to these important topics and some of their connections while the volume as a whole gives an overview of current developments in these fields.
Author:
Publisher:
ISBN: 9781461407102
Category :
Languages : en
Pages : 356
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Book Description
Author: Gyorgy Kiss
Publisher: CRC Press
ISBN: 1351646389
Category : Mathematics
Languages : en
Pages : 274
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Book Description
Finite Geometries stands out from recent textbooks about the subject of finite geometries by having a broader scope. The authors thoroughly explain how the subject of finite geometries is a central part of discrete mathematics. The text is suitable for undergraduate and graduate courses. Additionally, it can be used as reference material on recent works. The authors examine how finite geometries’ applicable nature led to solutions of open problems in different fields, such as design theory, cryptography and extremal combinatorics. Other areas covered include proof techniques using polynomials in case of Desarguesian planes, and applications in extremal combinatorics, plus, recent material and developments. Features: Includes exercise sets for possible use in a graduate course Discusses applications to graph theory and extremal combinatorics Covers coding theory and cryptography Translated and revised text from the Hungarian published version
Author: James Hirschfeld
Publisher: Springer
ISBN: 1447167902
Category : Mathematics
Languages : en
Pages : 422
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Book Description
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.
