Discrete Mathematics And Symmetry
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Discrete Mathematics And Symmetry
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Author : Angel Garrido
language : en
Publisher: MDPI
Release Date : 2020-03-05
Discrete Mathematics And Symmetry written by Angel Garrido and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-05 with Mathematics categories.
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.
Discrete Mathematics And Symmetry
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Author : Angel Garrido
language : en
Publisher:
Release Date : 2020
Discrete Mathematics And Symmetry written by Angel Garrido and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Mathematics categories.
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.
Applications Of Symmetry In Discrete Mathematics
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Author : Isla Harvey
language : en
Publisher: Murphy & Moore Publishing
Release Date : 2023-09-19
Applications Of Symmetry In Discrete Mathematics written by Isla Harvey and has been published by Murphy & Moore Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-19 with Mathematics categories.
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.
Rigidity And Symmetry
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Author : Robert Connelly
language : en
Publisher: Springer
Release Date : 2014-06-11
Rigidity And Symmetry written by Robert Connelly and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-11 with Mathematics categories.
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.
Symmetry Of Discrete Mathematical Structures And Their Symmetry Groups
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Author : Karl Heinrich Hofmann
language : de
Publisher:
Release Date : 1991
Symmetry Of Discrete Mathematical Structures And Their Symmetry Groups written by Karl Heinrich Hofmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Discrete groups categories.
Graph Symmetry
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Author : Gena Hahn
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Graph Symmetry written by Gena Hahn 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 2013-03-14 with Mathematics categories.
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.
Discrete Geometry And Symmetry
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Author : Marston D. E. Conder
language : en
Publisher: Springer
Release Date : 2018-06-11
Discrete Geometry And Symmetry written by Marston D. E. Conder and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-11 with Mathematics categories.
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.
Discrete Geometry And Symmetry
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Author : Isla Harvey
language : en
Publisher: States Academic Press
Release Date : 2023-09-19
Discrete Geometry And Symmetry written by Isla Harvey and has been published by States Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-19 with Mathematics categories.
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.
Symmetry In Graphs
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Author : Ted Dobson
language : en
Publisher: Cambridge University Press
Release Date : 2022-05-12
Symmetry In Graphs written by Ted Dobson 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 2022-05-12 with Language Arts & Disciplines categories.
The first full-length book on the theme of symmetry in graphs, a fast-growing topic in algebraic graph theory.
Continuous Symmetries And Integrability Of Discrete Equations
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Author : Decio Levi
language : en
Publisher: American Mathematical Society, Centre de Recherches Mathématiques
Release Date : 2023-01-23
Continuous Symmetries And Integrability Of Discrete Equations written by Decio Levi and has been published by American Mathematical Society, Centre de Recherches Mathématiques this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-23 with Mathematics categories.
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.