Discrete Mathematics And Symmetry

Author : Angel Garrido
Publisher : MDPI
Page : 458 pages
File Size : 54,6 Mb
Release : 2020-03-05
Category : Mathematics
ISBN : 9783039281909

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Discrete Mathematics and Symmetry by Angel Garrido Pdf

Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group.

Author : Angel Garrido
Publisher : Unknown
Page : 458 pages
File Size : 52,7 Mb
Release : 2020
Category : Mathematics
ISBN : 3039281917

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Discrete Mathematics and Symmetry by Angel Garrido Pdf

Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group.

Author : Isla Harvey
Publisher : Murphy & Moore Publishing
Page : 0 pages
File Size : 52,9 Mb
Release : 2023-09-19
Category : Mathematics
ISBN : 1639877460

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Applications of Symmetry in Discrete Mathematics by Isla Harvey Pdf

Discrete mathematics refers to the study of mathematical structures that are countable or otherwise separable or unique. Logical statements, combinations and graphs are examples of discrete structures. Symmetry is a proportionate and balanced resemblance between two halves of an object. It implies that one half is the mirror image of the other. Discrete symmetry in mathematics is a symmetry that explains non-continuous changes in a system. Symmetry is frequently used in discrete mathematics to show relationships between two or more elements of a set, where the first element relates to the second element and vice-versa. This book explores all the important aspects of discrete mathematics and symmetry in the present day scenario. It presents researches and studies performed by experts across the globe. This book, with its detailed analyses and data, will prove immensely beneficial to professionals and students involved in this area of mathematics at various levels.

Author : Karl Heinrich Hofmann,Rudolf Wille
Publisher : Unknown
Page : 188 pages
File Size : 50,5 Mb
Release : 1991
Category : Discrete groups
ISBN : STANFORD:36105031375558

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Symmetry of Discrete Mathematical Structures and Their Symmetry Groups by Karl Heinrich Hofmann,Rudolf Wille Pdf

Author : Robert Connelly,Asia Ivić Weiss,Walter Whiteley
Publisher : Springer
Page : 374 pages
File Size : 41,7 Mb
Release : 2014-06-11
Category : Mathematics
ISBN : 9781493907816

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Rigidity and Symmetry by Robert Connelly,Asia Ivić Weiss,Walter Whiteley Pdf

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.

Author : Gena Hahn,Gert Sabidussi
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 46,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401589376

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Graph Symmetry by Gena Hahn,Gert Sabidussi Pdf

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.

Author : Richard Johnsonbaugh
Publisher : Prentice Hall
Page : 785 pages
File Size : 51,6 Mb
Release : 2009
Category : Computer science
ISBN : 9780131593183

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Discrete Mathematics by Richard Johnsonbaugh Pdf

For a one- or two-term introductory course in discrete mathematics. Focused on helping students understand and construct proofs and expanding their mathematical maturity, this best-selling text is an accessible introduction to discrete mathematics. Johnsonbaugh's algorithmic approach emphasizes problem-solving techniques. The Seventh Edition reflects user and reviewer feedback on both content and organization.

Author : Marston D. E. Conder,Antoine Deza,Asia Ivić Weiss
Publisher : Springer
Page : 333 pages
File Size : 54,9 Mb
Release : 2018-06-11
Category : Mathematics
ISBN : 9783319784342

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Discrete Geometry and Symmetry by Marston D. E. Conder,Antoine Deza,Asia Ivić Weiss Pdf

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.

Author : Isla Harvey
Publisher : States Academic Press
Page : 0 pages
File Size : 45,8 Mb
Release : 2023-09-19
Category : Mathematics
ISBN : 1639897437

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Discrete Geometry and Symmetry by Isla Harvey Pdf

Discrete geometry refers to a subfield of geometry that examines discrete and highly symmetric structures in geometry and how discrete geometric objects might be constructed. It is closely connected to computational geometry as well as other mathematical subjects including combinatorial geometry and topology, combinatorial optimization, geometric graph theory, and finite geometry. Discrete geometry focuses on the problems that aim to characterize specific discrete arrangements of geometric objects having high symmetry. Many of the techniques used to investigate discrete arrangements are based on a wide range of symetrizations. Discrete geometry is used in numerous theoretical disciplines including algebraic geometry and topology, geometry of numbers, mathematical physics, functional analysis, geometric measure theory, calculus of variations, and group theory. This book is compiled in such a manner, that it will provide an in-depth knowledge about the theory and applications of discrete geometry and symmetry. It is a resource guide for experts as well as students.

Author : Ted Dobson,Aleksander Malnič,Dragan Marušič
Publisher : Cambridge University Press
Page : 527 pages
File Size : 52,9 Mb
Release : 2022-05-12
Category : Language Arts & Disciplines
ISBN : 9781108429061

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Symmetry in Graphs by Ted Dobson,Aleksander Malnič,Dragan Marušič Pdf

The first full-length book on the theme of symmetry in graphs, a fast-growing topic in algebraic graph theory.

Author : Peter Gritzmann,Bernd Sturmfels,Victor Klee
Publisher : American Mathematical Soc.
Page : 660 pages
File Size : 47,5 Mb
Release : 1991
Category : Mathematics
ISBN : 0821870831

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Applied Geometry and Discrete Mathematics by Peter Gritzmann,Bernd Sturmfels,Victor Klee Pdf

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.

Author : Guillaume Aubrun,Adam Skalski,Roland Speicher
Publisher : Springer
Page : 119 pages
File Size : 45,6 Mb
Release : 2017-10-11
Category : Mathematics
ISBN : 9783319632063

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Quantum Symmetries by Guillaume Aubrun,Adam Skalski,Roland Speicher Pdf

Providing an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems. A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantum groups, and in quantum physics. The first lecture presents the close connection between distributional symmetries and independence properties. The second introduces many structures (graphs, C*-algebras, discrete groups) whose quantum symmetries are much richer than their classical symmetry groups, and describes the associated quantum symmetry groups. The last lecture shows how functional analytic and geometric ideas can be used to detect and to quantify entanglement in high dimensions. The book will allow graduate students and young researchers to gain a better understanding of free probability, the theory of compact quantum groups, and applications of the theory of Banach spaces to quantum information. The latter applications will also be of interest to theoretical and mathematical physicists working in quantum theory.

Author : K. D. Joshi
Publisher : New Age International
Page : 768 pages
File Size : 53,5 Mb
Release : 1989
Category : Mathematics
ISBN : 8122401201

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Foundations of Discrete Mathematics by K. D. Joshi Pdf

This Book Is Meant To Be More Than Just A Text In Discrete Mathematics. It Is A Forerunner Of Another Book Applied Discrete Structures By The Same Author. The Ultimate Goal Of The Two Books Are To Make A Strong Case For The Inclusion Of Discrete Mathematics In The Undergraduate Curricula Of Mathematics By Creating A Sequence Of Courses In Discrete Mathematics Parallel To The Traditional Sequence Of Calculus-Based Courses.The Present Book Covers The Foundations Of Discrete Mathematics In Seven Chapters. It Lays A Heavy Emphasis On Motivation And Attempts Clarity Without Sacrificing Rigour. A List Of Typical Problems Is Given In The First Chapter. These Problems Are Used Throughout The Book To Motivate Various Concepts. A Review Of Logic Is Included To Gear The Reader Into A Proper Frame Of Mind. The Basic Counting Techniques Are Covered In Chapters 2 And 7. Those In Chapter 2 Are Elementary. But They Are Intentionally Covered In A Formal Manner So As To Acquaint The Reader With The Traditional Definition-Theorem-Proof Pattern Of Mathematics. Chapters 3 Introduces Abstraction And Shows How The Focal Point Of Todays Mathematics Is Not Numbers But Sets Carrying Suitable Structures. Chapter 4 Deals With Boolean Algebras And Their Applications. Chapters 5 And 6 Deal With More Traditional Topics In Algebra, Viz., Groups, Rings, Fields, Vector Spaces And Matrices.The Presentation Is Elementary And Presupposes No Mathematical Maturity On The Part Of The Reader. Instead, Comments Are Inserted Liberally To Increase His Maturity. Each Chapter Has Four Sections. Each Section Is Followed By Exercises (Of Various Degrees Of Difficulty) And By Notes And Guide To Literature. Answers To The Exercises Are Provided At The End Of The Book.

Author : Sergei Kurgalin,Sergei Borzunov
Publisher : Springer Nature
Page : 507 pages
File Size : 41,6 Mb
Release : 2020-08-12
Category : Computers
ISBN : 9783030422219

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The Discrete Math Workbook by Sergei Kurgalin,Sergei Borzunov Pdf

This practically-focused study guide introduces the fundamentals of discrete mathematics through an extensive set of classroom-tested problems. Each chapter presents a concise introduction to the relevant theory, followed by a detailed account of common challenges and methods for overcoming these. The reader is then encouraged to practice solving such problems for themselves, by tackling a varied selection of questions and assignments of different levels of complexity. This updated second edition now covers the design and analysis of algorithms using Python, and features more than 50 new problems, complete with solutions. Topics and features: provides a substantial collection of problems and examples of varying levels of difficulty, suitable for both laboratory practical training and self-study; offers detailed solutions to each problem, applying commonly-used methods and computational schemes; introduces the fundamentals of mathematical logic, the theory of algorithms, Boolean algebra, graph theory, sets, relations, functions, and combinatorics; presents more advanced material on the design and analysis of algorithms, including Turing machines, asymptotic analysis, and parallel algorithms; includes reference lists of trigonometric and finite summation formulae in an appendix, together with basic rules for differential and integral calculus. This hands-on workbook is an invaluable resource for undergraduate students of computer science, informatics, and electronic engineering. Suitable for use in a one- or two-semester course on discrete mathematics, the text emphasizes the skills required to develop and implement an algorithm in a specific programming language.

Author : Decio Levi,Pavel Winternitz,Ravil I. Yamilov
Publisher : American Mathematical Society, Centre de Recherches Mathématiques
Page : 520 pages
File Size : 49,7 Mb
Release : 2023-01-23
Category : Mathematics
ISBN : 9780821843543

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Continuous Symmetries and Integrability of Discrete Equations by Decio Levi,Pavel Winternitz,Ravil I. Yamilov Pdf

This book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices, and in finding numerical approximations for differential equations preserving their symmetries. The book contains three chapters and five appendices. The first chapter is an introduction to the general ideas about symmetries, lattices, differential difference and partial difference equations and Lie point symmetries defined on them. Chapter 2 deals with integrable and linearizable systems in two dimensions. The authors start from the prototype of integrable and linearizable partial differential equations, the Korteweg de Vries and the Burgers equations. Then they consider the best known integrable differential difference and partial difference equations. Chapter 3 considers generalized symmetries and conserved densities as integrability criteria. The appendices provide details which may help the readers' understanding of the subjects presented in Chapters 2 and 3. This book is written for PhD students and early researchers, both in theoretical physics and in applied mathematics, who are interested in the study of symmetries and integrability of difference equations.