Symmetries in Graphs, Maps, and Polytopes

5th SIGMAP Workshop, West Malvern, UK, July 2014

Author: Jozef Širáň,Robert Jajcay

Publisher: Springer

ISBN: 3319304518

Category: Mathematics

Page: 332

View: 5017

This volume contains seventeen of the best papers delivered at the SIGMAP Workshop 2014, representing the most recent advances in the field of symmetries of discrete objects and structures, with a particular emphasis on connections between maps, Riemann surfaces and dessins d’enfant.Providing the global community of researchers in the field with the opportunity to gather, converse and present their newest findings and advances, the Symmetries In Graphs, Maps, and Polytopes Workshop 2014 was the fifth in a series of workshops. The initial workshop, organized by Steve Wilson in Flagstaff, Arizona, in 1998, was followed in 2002 and 2006 by two meetings held in Aveiro, Portugal, organized by Antonio Breda d’Azevedo, and a fourth workshop held in Oaxaca, Mexico, organized by Isabel Hubard in 2010.This book should appeal to both specialists and those seeking a broad overview of what is happening in the area of symmetries of discrete objects and structures.iv>

Applications of Group Theory to Combinatorics

Author: Jack Koolen,Jin Ho Kwak,Ming-Yao Xu

Publisher: CRC Press

ISBN: 9780203885765

Category: Mathematics

Page: 188

View: 9190

Applications of Group Theory to Combinatorics contains 11 survey papers from international experts in combinatorics, group theory and combinatorial topology. The contributions cover topics from quite a diverse spectrum, such as design theory, Belyi functions, group theory, transitive graphs, regular maps, and Hurwitz problems, and present the state-of-the-art in these areas. Applications of Group Theory to Combinatorics will be useful in the study of graphs, maps and polytopes having maximal symmetry, and is aimed at researchers in the areas of group theory and combinatorics, graduate students in mathematics, and other specialists who use group theory and combinatorics. Jack Koolen teaches at the Department of Mathematics at Pohang University of Science and Technology, Korea. His main research interests include the interaction of geometry, linear algebra and combinatorics, on which he published 60 papers. Jin Ho Kwak is Professor at the Department of Mathematics at Pohang University of Science and Technology, Korea, where he is director of the Combinatorial and Computational Mathematics Center (Com2MaC). He works on combinatorial topology, mainly on covering enumeration related to Hurwitz problems and regular maps on surfaces, and published more than 100 papers in these areas. Ming-Yao Xu is Professor in Department of Mathematics at Peking University, China. The focus in his research is in finite group theory and algebraic graph theory. Ming-Yao Xu published over 80 papers on these topics.

Discrete Geometry and Symmetry

Dedicated to Károly Bezdek and Egon Schulte on the Occasion of Their 60th Birthdays

Author: Marston D. E. Conder,Antoine Deza,Asia Ivić Weiss

Publisher: Springer

ISBN: 331978434X

Category: Mathematics

Page: 333

View: 9214

This book consists of contributions from experts, presenting a fruitful interplay between different approaches to discrete geometry. Most of the chapters were collected at the conference “Geometry and Symmetry” in Veszprém, Hungary from 29 June to 3 July 2015. The conference was dedicated to Károly Bezdek and Egon Schulte on the occasion of their 60th birthdays, acknowledging their highly regarded contributions in these fields. While the classical problems of discrete geometry have a strong connection to geometric analysis, coding theory, symmetry groups, and number theory, their connection to combinatorics and optimization has become of particular importance. The last decades have seen a revival of interest in discrete geometric structures and their symmetry. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory and geometry, combinatorial group theory, and hyperbolic geometry and topology. This book contains papers on new developments in these areas, including convex and abstract polytopes and their recent generalizations, tiling and packing, zonotopes, isoperimetric inequalities, and on the geometric and combinatorial aspects of linear optimization. The book is a valuable resource for researchers, both junior and senior, in the field of discrete geometry, combinatorics, or discrete optimization. Graduate students find state-of-the-art surveys and an open problem collection.

Rigidity and Symmetry

Author: Robert Connelly,Asia Ivić Weiss,Walter Whiteley

Publisher: Springer

ISBN: 1493907816

Category: Mathematics

Page: 374

View: 6621

This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures and to explore the interaction of geometry, algebra and combinatorics. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory, classical geometry, hyperbolic geometry and topology. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. The volume will be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and graduate levels, as well as post docs, structural engineers and chemists.

Graph Symmetry

Algebraic Methods and Applications

Author: Gena Hahn,Gert Sabidussi

Publisher: Springer Science & Business Media

ISBN: 9401589372

Category: Mathematics

Page: 418

View: 2923

The last decade has seen two parallel developments, one in computer science, the other in mathematics, both dealing with the same kind of combinatorial structures: networks with strong symmetry properties or, in graph-theoretical language, vertex-transitive graphs, in particular their prototypical examples, Cayley graphs. In the design of large interconnection networks it was realised that many of the most fre quently used models for such networks are Cayley graphs of various well-known groups. This has spawned a considerable amount of activity in the study of the combinatorial properties of such graphs. A number of symposia and congresses (such as the bi-annual IWIN, starting in 1991) bear witness to the interest of the computer science community in this subject. On the mathematical side, and independently of any interest in applications, progress in group theory has made it possible to make a realistic attempt at a complete description of vertex-transitive graphs. The classification of the finite simple groups has played an important role in this respect.

Convexity and Graph Theory

Author: M. Rosenfeld,J. Zaks

Publisher: Elsevier

ISBN: 9780080871981

Category: Mathematics

Page: 338

View: 706

Among the participants discussing recent trends in their respective fields and in areas of common interest in these proceedings are such world-famous geometers as H.S.M. Coxeter, L. Danzer, D.G. Larman and J.M. Wills, and equally famous graph-theorists B. Bollobás, P. Erdös and F. Harary. In addition to new results in both geometry and graph theory, this work includes articles involving both of these two fields, for instance ``Convexity, Graph Theory and Non-Negative Matrices'', ``Weakly Saturated Graphs are Rigid'', and many more. The volume covers a broad spectrum of topics in graph theory, geometry, convexity, and combinatorics. The book closes with a number of abstracts and a collection of open problems raised during the conference.

Integer Programming and Combinatorial Optimization

14th International Conference, IPCO 2010, Lausanne, Switzerland, June 9-11, 2010, Proceedings

Author: Friedrich Eisenbrand,Bruce Shepherd

Publisher: Springer Science & Business Media

ISBN: 3642130356

Category: Computers

Page: 466

View: 7710

The LNCS series reports state-of-the-art results in computer science research, development, and education, at a high level and in both printed and electronic form. Enjoying tight cooperation with the R&D community, with numerous individuals, as well as with prestigious organizations and societies, LNCS has grown into the most comprehensive computer science research forum available. The scope of LNCS, including its subseries LNAI and I.NBI, spans the whole range of computer science and information technology including interdisciplinary topics in a variety of application fields. The type of material published traditionally includes ûproceedings (published in time for the respective conference) ûpost-proceedings (consisting of thoroughly revised final full papers) ûresearch monographs (which may be based on outstanding PhD work, research projects, technical reports, etc.) More recently, several color-cover sublines have been added featuring, beyond a collection of papers, various added-value components; these sublines include -tutorials (textbook-like monographs or collections of lectures given at advanced courses) -state-of-the-art surveys (offering complete and mediated coverage of a topic) -hot topics (introducing emergent topics to the broader community)

Regular Polytopes

Author: H. S. M. Coxeter

Publisher: Courier Corporation

ISBN: 0486141586

Category: Mathematics

Page: 368

View: 5175

Foremost book available on polytopes, incorporating ancient Greek and most modern work. Discusses polygons, polyhedrons, and multi-dimensional polytopes. Definitions of symbols. Includes 8 tables plus many diagrams and examples. 1963 edition.

Abstract Regular Polytopes

Author: Peter McMullen,Egon Schulte

Publisher: Cambridge University Press

ISBN: 9780521814966

Category: Mathematics

Page: 551

View: 5865

A modern, comprehensive review of abstract regular polytopes.

Geometry and Its Applications

Author: Walter A. Meyer

Publisher: Elsevier

ISBN: 9780080478036

Category: Mathematics

Page: 560

View: 5157

Meyer's Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry's usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers. Realistic applications integrated throughout the text, including (but not limited to): Symmetries of artistic patterns Physics Robotics Computer vision Computer graphics Stability of architectural structures Molecular biology Medicine Pattern recognition Historical notes included in many chapters

Knots 90

Proceedings of the International Conference on Knot Theory and Related Topics Held in Osaka (Japan), August 15-19, 1990

Author: Akio Kawauchi

Publisher: Walter de Gruyter

ISBN: 9783110126235

Category: Mathematics

Page: 641

View: 6634

From Groups to Geometry and Back

Author: Vaughn Climenhaga,Anatole Katok

Publisher: American Mathematical Soc.

ISBN: 1470434792

Category: Geometry

Page: 420

View: 8768

Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering spaces and deck transformations. In the other direction, Cayley graphs, planar models, and fundamental domains appear as geometric objects associated to groups. The final chapter discusses groups themselves as geometric objects, including a gentle introduction to Gromov's theorem on polynomial growth and Grigorchuk's example of intermediate growth. The book is accessible to undergraduate students (and anyone else) with a background in calculus, linear algebra, and basic real analysis, including topological notions of convergence and connectedness. This book is a result of the MASS course in algebra at Penn State University in the fall semester of 2009.

Handbook of Discrete and Computational Geometry, Second Edition

Author: Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman

Publisher: CRC Press

ISBN: 9781420035315

Category: Mathematics

Page: 1560

View: 1969

While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discrete and Computational Geometry, which in its first edition, quickly became the definitive reference work in its field. But with the rapid growth of the discipline and the many advances made over the past seven years, it's time to bring this standard-setting reference up to date. Editors Jacob E. Goodman and Joseph O'Rourke reassembled their stellar panel of contributors, added manymore, and together thoroughly revised their work to make the most important results and methods, both classic and cutting-edge, accessible in one convenient volume. Now over more then 1500 pages, the Handbook of Discrete and Computational Geometry, Second Edition once again provides unparalleled, authoritative coverage of theory, methods, and applications. Highlights of the Second Edition: Thirteen new chapters: Five on applications and others on collision detection, nearest neighbors in high-dimensional spaces, curve and surface reconstruction, embeddings of finite metric spaces, polygonal linkages, the discrepancy method, and geometric graph theory Thorough revisions of all remaining chapters Extended coverage of computational geometry software, now comprising two chapters: one on the LEDA and CGAL libraries, the other on additional software Two indices: An Index of Defined Terms and an Index of Cited Authors Greatly expanded bibliographies

Applied Geometry and Discrete Mathematics

The Victor Klee Festschrift

Author: Peter Gritzmann,Bernd Sturmfels,Victor Klee

Publisher: American Mathematical Soc.

ISBN: 9780821870839

Category: Mathematics

Page: 608

View: 579

This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's 65th birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics, education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honour of Klee's achievements, this volume presents more than 40 papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, this book shows how different branches of mathematics interact. It is a fitting tribute to one of the leading figures in discrete mathematics.

A Course in Convexity

Author: Alexander Barvinok

Publisher: American Mathematical Soc.

ISBN: 0821829688

Category: Mathematics

Page: 366

View: 4894

Convexity is a simple idea that manifests itself in a surprising variety of places. This fertile field has an immensely rich structure and numerous applications. Barvinok demonstrates that simplicity, intuitive appeal, and the universality of applications make teaching (and learning) convexity a gratifying experience. The book will benefit both teacher and student: It is easy to understand, entertaining to the reader, and includes many exercises that vary in degree of difficulty. Overall, the author demonstrates the power of a few simple unifying principles in a variety of pure and applied problems. The prerequisites are minimal amounts of linear algebra, analysis, and elementary topology, plus basic computational skills. Portions of the book could be used by advanced undergraduates. As a whole, it is designed for graduate students interested in mathematical methods, computer science, electrical engineering, and operations research. The book will also be of interest to research mathematicians, who will find some results that are recent, some that are new, and many known results that are discussed from a new perspective.

Geometric Structure of Chemistry-Relevant Graphs

Zigzags and Central Circuits

Author: Michel-Marie Deza,Mathieu Dutour Sikirić,Mikhail Ivanovitch Shtogrin

Publisher: Springer

ISBN: 8132224493

Category: Mathematics

Page: 211

View: 1059

The central theme of the present book is zigzags and central-circuits of three- or four-regular plane graphs, which allow a double covering or covering of the edgeset to be obtained. The book presents zigzag and central circuit structures of geometric fullerenes and several other classes of graph of interest in the fields of chemistry and mathematics. It also discusses the symmetries, parameterization and the Goldberg–Coxeter construction for those graphs. It is the first book on this subject, presenting full structure theory of such graphs. While many previous publications only addressed particular questions about selected graphs, this book is based on numerous computations and presents extensive data (tables and figures), as well as algorithmic and computational information. It will be of interest to researchers and students of discrete geometry, mathematical chemistry and combinatorics, as well as to lay mathematicians.