The Isomorphism Problem In Coxeter Groups

Author : C. Patrick Bahls
Publisher : World Scientific
Page : 194 pages
File Size : 43,5 Mb
Release : 2005
Category : Mathematics
ISBN : 9781860945540

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The Isomorphism Problem in Coxeter Groups by C. Patrick Bahls Pdf

The book is the first to give a comprehensive overview of the techniques and tools currently being used in the study of combinatorial problems in Coxeter groups. It is self-contained, and accessible even to advanced undergraduate students of mathematics.The primary purpose of the book is to highlight approximations to the difficult isomorphism problem in Coxeter groups. A number of theorems relating to this problem are stated and proven. Most of the results addressed here concern conditions which can be seen as varying degrees of uniqueness of representations of Coxeter groups. Throughout the investigation, the readers are introduced to a large number of tools in the theory of Coxeter groups, drawn from dozens of recent articles by prominent researchers in geometric and combinatorial group theory, among other fields. As the central problem of the book may in fact be solved soon, the book aims to go further, providing the readers with many techniques that can be used to answer more general questions. The readers are challenged to practice those techniques by solving exercises, a list of which concludes each chapter.

Author : N.S. Narasimha Sastry
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 55,8 Mb
Release : 2014-04-02
Category : Mathematics
ISBN : 9788132218142

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Groups of Exceptional Type, Coxeter Groups and Related Geometries by N.S. Narasimha Sastry Pdf

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.

Author : Harold Scott Macdonald Coxeter,Chandler Davis,Erich W. Ellers
Publisher : American Mathematical Soc.
Page : 344 pages
File Size : 47,7 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821887602

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The Coxeter Legacy by Harold Scott Macdonald Coxeter,Chandler Davis,Erich W. Ellers Pdf

This collection of essays on the legacy of mathematican Donald Coxeter is a mixture of surveys, updates, history, storytelling and personal memories covering both applied and abstract maths. Subjects include: polytopes, Coxeter groups, equivelar polyhedra, Ceva's theorum, and Coxeter and the artists.

Author : Michael Davis
Publisher : Princeton University Press
Page : 600 pages
File Size : 46,5 Mb
Release : 2012-11-26
Category : Mathematics
ISBN : 9781400845941

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The Geometry and Topology of Coxeter Groups. (LMS-32) by Michael Davis Pdf

The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures.

Author : Benjamin Fine,Gerhard Rosenberger,Dennis Spellman
Publisher : World Scientific
Page : 253 pages
File Size : 51,8 Mb
Release : 2008-10-23
Category : Mathematics
ISBN : 9789814471671

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Aspects Of Infinite Groups: A Festschrift In Honor Of Anthony Gaglione by Benjamin Fine,Gerhard Rosenberger,Dennis Spellman Pdf

This book is a festschrift in honor of Professor Anthony Gaglione's sixtieth birthday. This volume presents an excellent mix of research and expository articles on various aspects of infinite group theory. The papers give a broad overview of present research in infinite group theory in general, and combinatorial group theory and non-Abelian group-based cryptography in particular. They also pinpoint the interactions between combinatorial group theory and mathematical logic, especially model theory.

Author : Ann C. Kim,Bernhard H. Neumann
Publisher : Springer
Page : 194 pages
File Size : 55,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540467564

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Groups - Korea 1988 by Ann C. Kim,Bernhard H. Neumann Pdf

These proceedings include selected and refereed original papers; most are research papers, a few are comprehensive survey articles.

Author : Michael Davis
Publisher : Princeton University Press
Page : 601 pages
File Size : 53,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9780691131382

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The Geometry and Topology of Coxeter Groups by Michael Davis Pdf

The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures.

Author : Anders Bjorner,Francesco Brenti
Publisher : Springer Science & Business Media
Page : 371 pages
File Size : 43,9 Mb
Release : 2006-02-25
Category : Mathematics
ISBN : 9783540275961

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Combinatorics of Coxeter Groups by Anders Bjorner,Francesco Brenti Pdf

Includes a rich variety of exercises to accompany the exposition of Coxeter groups Coxeter groups have already been exposited from algebraic and geometric perspectives, but this book will be presenting the combinatorial aspects of Coxeter groups

Author : Anonim
Publisher : Unknown
Page : 932 pages
File Size : 41,5 Mb
Release : 2008
Category : Mathematics
ISBN : UOM:39015078588798

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Mathematical Reviews by Anonim Pdf

Author : David Fernández-Baca
Publisher : Springer Science & Business Media
Page : 685 pages
File Size : 48,8 Mb
Release : 2012-03-30
Category : Computers
ISBN : 9783642293436

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LATIN 2012: Theoretical Informatics by David Fernández-Baca Pdf

This book constitutes the proceedings of the 10th Latin American Symposium on Theoretical Informatics, LATIN 2012, held in Arequipa, Peru, in April 2012. The 55 papers presented in this volume were carefully reviewed and selected from 153 submissions. The papers address a variety of topics in theoretical computer science with a certain focus on algorithms, automata theory and formal languages, coding theory and data compression, algorithmic graph theory and combinatorics, complexity theory, computational algebra, computational biology, computational geometry, computational number theory, cryptography, theoretical aspects of databases and information retrieval, data structures, networks, logic in computer science, machine learning, mathematical programming, parallel and distributed computing, pattern matching, quantum computing and random structures.

Author : Benjamin Fine,Delaram Kahrobaei,Gerhard Rosenberger
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 49,9 Mb
Release : 2012
Category : Computers
ISBN : 9780821875636

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Computational and Combinatorial Group Theory and Cryptography by Benjamin Fine,Delaram Kahrobaei,Gerhard Rosenberger Pdf

This volume contains the proceedings of the AMS Special Session on Computational Algebra, Groups, and Applications, held April 30-May 1, 2011, at the University of Nevada, Las Vegas, Nevada, and the AMS Special Session on the Mathematical Aspects of Cryptography and Cyber Security, held September 10-11, 2011, at Cornell University, Ithaca, New York. Over the past twenty years combinatorial and infinite group theory has been energized by three developments: the emergence of geometric and asymptotic group theory, the development of algebraic geometry over groups leading to the solution of the Tarski problems, and the development of group-based cryptography. These three areas in turn have had an impact on computational algebra and complexity theory. The papers in this volume, both survey and research, exhibit the tremendous vitality that is at the heart of group theory in the beginning of the twenty-first century as well as the diversity of interests in the field.

Author : Anonim
Publisher : Unknown
Page : 614 pages
File Size : 46,5 Mb
Release : 2007
Category : Algebraic topology
ISBN : UCSD:31822036042224

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Algebraic & Geometric Topology by Anonim Pdf

Author : Markus Lohrey
Publisher : Springer Science & Business Media
Page : 193 pages
File Size : 50,8 Mb
Release : 2014-04-04
Category : Mathematics
ISBN : 9781493907489

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The Compressed Word Problem for Groups by Markus Lohrey Pdf

The Compressed Word Problem for Groups provides a detailed exposition of known results on the compressed word problem, emphasizing efficient algorithms for the compressed word problem in various groups. The author presents the necessary background along with the most recent results on the compressed word problem to create a cohesive self-contained book accessible to computer scientists as well as mathematicians. Readers will quickly reach the frontier of current research which makes the book especially appealing for students looking for a currently active research topic at the intersection of group theory and computer science. The word problem introduced in 1910 by Max Dehn is one of the most important decision problems in group theory. For many groups, highly efficient algorithms for the word problem exist. In recent years, a new technique based on data compression for providing more efficient algorithms for word problems, has been developed, by representing long words over group generators in a compressed form using a straight-line program. Algorithmic techniques used for manipulating compressed words has shown that the compressed word problem can be solved in polynomial time for a large class of groups such as free groups, graph groups and nilpotent groups. These results have important implications for algorithmic questions related to automorphism groups.

Author : Anonim
Publisher : Unknown
Page : 500 pages
File Size : 42,9 Mb
Release : 2013
Category : Mathematics
ISBN : OSU:32435087103040

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Hokkaido Mathematical Journal by Anonim Pdf

Author : American Mathematical Society
Publisher : Unknown
Page : 754 pages
File Size : 44,9 Mb
Release : 2007
Category : Mathematics
ISBN : CORNELL:31924099691275

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Abstracts of Papers Presented to the American Mathematical Society by American Mathematical Society Pdf