An Algebraic Approach to Association Schemes

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Publisher : Springer
ISBN 13 : 3540685235
Total Pages : 201 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis An Algebraic Approach to Association Schemes by : Paul-Hermann Zieschang

Download or read book An Algebraic Approach to Association Schemes written by Paul-Hermann Zieschang and published by Springer. This book was released on 2006-11-13 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary object of the lecture notes is to develop a treatment of association schemes analogous to that which has been so successful in the theory of finite groups. The main chapters are decomposition theory, representation theory, and the theory of generators. Tits buildings come into play when the theory of generators is developed. Here, the buildings play the role which, in group theory, is played by the Coxeter groups. - The text is intended for students as well as for researchers in algebra, in particular in algebraic combinatorics.

An Algebraic Approach to the Association Schemes of Coding Theory

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Publisher :
ISBN 13 :
Total Pages : 97 pages
Book Rating : 4.:/5 (145 download)

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Book Synopsis An Algebraic Approach to the Association Schemes of Coding Theory by : P. Delsarte

Download or read book An Algebraic Approach to the Association Schemes of Coding Theory written by P. Delsarte and published by . This book was released on 1973 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Combinatorics

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Publisher : Taylor & Francis
ISBN 13 : 9789027705938
Total Pages : 500 pages
Book Rating : 4.7/5 (59 download)

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Book Synopsis Combinatorics by : Marshall Hall

Download or read book Combinatorics written by Marshall Hall and published by Taylor & Francis. This book was released on 1975-04-30 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, Breukelen, The Netherlands, July 8-30, 1974

Algebraic Combinatorics

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110627736
Total Pages : 303 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Algebraic Combinatorics by : Eiichi Bannai

Download or read book Algebraic Combinatorics written by Eiichi Bannai and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-02-22 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series is devoted to the publication of high-level monographs which cover the whole spectrum of current discrete mathematics and its applications in various fields. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of discrete mathematics. Contributions which are on the borderline of discrete mathematics and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.

Introduction To Algebraic Coding Theory

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Publisher : World Scientific
ISBN 13 : 9811220980
Total Pages : 266 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Introduction To Algebraic Coding Theory by : Tzuong-tsieng Moh

Download or read book Introduction To Algebraic Coding Theory written by Tzuong-tsieng Moh and published by World Scientific. This book was released on 2022-02-18 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this age of technology where messages are transmitted in sequences of 0's and 1's through space, errors can occur due to noisy channels. Thus, self-correcting code is vital to eradicate these errors when the number of errors is small. It is widely used in industry for a variety of applications including e-mail, telephone, and remote sensing (for example, photographs of Mars).An expert in algebra and algebraic geometry, Tzuong-Tsieng Moh covers many essential aspects of algebraic coding theory in this book, such as elementary algebraic coding theories, the mathematical theory of vector spaces and linear algebras behind them, various rings and associated coding theories, a fast decoding method, useful parts of algebraic geometry and geometric coding theories.This book is accessible to advanced undergraduate students, graduate students, coding theorists and algebraic geometers.

Erdos-Ko-Rado Theorems: Algebraic Approaches

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Publisher : Cambridge University Press
ISBN 13 : 1107128447
Total Pages : 353 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Erdos-Ko-Rado Theorems: Algebraic Approaches by : Christopher Godsil

Download or read book Erdos-Ko-Rado Theorems: Algebraic Approaches written by Christopher Godsil and published by Cambridge University Press. This book was released on 2016 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate text focusing on algebraic methods that can be applied to prove the Erdős-Ko-Rado Theorem and its generalizations.

Linear Associative Algebras Corresponding to Association Schemes of Partially Balanced Designs

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Publisher :
ISBN 13 :
Total Pages : 62 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Linear Associative Algebras Corresponding to Association Schemes of Partially Balanced Designs by : Raj Chandra Bose

Download or read book Linear Associative Algebras Corresponding to Association Schemes of Partially Balanced Designs written by Raj Chandra Bose and published by . This book was released on 1958 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraic Combinatorics

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Publisher : Routledge
ISBN 13 : 1351467506
Total Pages : 382 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Algebraic Combinatorics by : Chris Godsil

Download or read book Algebraic Combinatorics written by Chris Godsil and published by Routledge. This book was released on 2017-10-19 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate level text is distinguished both by the range of topics and the novelty of the material it treats--more than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It is instructive to consider these polynomials together because they have a number of properties in common. The matchings polynomial has links with a number of problems in combinatorial enumeration, particularly some of the current work on the combinatorics of orthogonal polynomials. This connection is discussed at some length, and is also in part the stimulus for the inclusion of chapters on orthogonal polynomials and formal power series. Many of the properties of orthogonal polynomials are derived from properties of characteristic polynomials. The second half of the book introduces the theory of polynomial spaces, which provide easy access to a number of important results in design theory, coding theory and the theory of association schemes. This book should be of interest to second year graduate text/reference in mathematics.

The Geometry of Schemes

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Publisher : Springer Science & Business Media
ISBN 13 : 0387226397
Total Pages : 265 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis The Geometry of Schemes by : David Eisenbud

Download or read book The Geometry of Schemes written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Codes and Association Schemes

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Publisher : American Mathematical Soc.
ISBN 13 : 0821820745
Total Pages : 317 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Codes and Association Schemes by : Alexander Barg

Download or read book Codes and Association Schemes written by Alexander Barg and published by American Mathematical Soc.. This book was released on 2001 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents papers related to the DIMACS workshop, "Codes and Association Schemes". The articles are devoted to the following topics: applications of association schemes and of the polynomial method to properties of codes, structural results for codes, structural results for association schemes, and properties of orthogonal polynomials and their applications in combinatorics. Papers on coding theory are related to classical topics, such as perfect codes, bounds on codes, codes and combinatorial arrays, weight enumerators, and spherical designs. Papers on orthogonal polynomials provide new results on zeros and symptotic properties of standard families of polynomials encountered in coding theory. The theme of association schemes is represented by new classification results and new classes of schemes related to posets. This volume collects up-to-date applications of the theory of association schemes to coding and presents new properties of both polynomial and general association schemes. It offers a solid representation of results in problems in areas of current interest.

Theory of Association Schemes

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Publisher : Springer Science & Business Media
ISBN 13 : 3540305939
Total Pages : 295 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Theory of Association Schemes by : Paul-Hermann Zieschang

Download or read book Theory of Association Schemes written by Paul-Hermann Zieschang and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a concept-oriented treatment of the structure theory of association schemes. The generalization of Sylow’s group theoretic theorems to scheme theory arises as a consequence of arithmetical considerations about quotient schemes. The theory of Coxeter schemes (equivalent to the theory of buildings) emerges naturally and yields a purely algebraic proof of Tits’ main theorem on buildings of spherical type.

Semidefinite Optimization and Convex Algebraic Geometry

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Publisher : SIAM
ISBN 13 : 1611972280
Total Pages : 487 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Semidefinite Optimization and Convex Algebraic Geometry by : Grigoriy Blekherman

Download or read book Semidefinite Optimization and Convex Algebraic Geometry written by Grigoriy Blekherman and published by SIAM. This book was released on 2013-03-21 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.

Graph Algorithms in the Language of Linear Algebra

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Publisher : SIAM
ISBN 13 : 9780898719918
Total Pages : 388 pages
Book Rating : 4.7/5 (199 download)

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Book Synopsis Graph Algorithms in the Language of Linear Algebra by : Jeremy Kepner

Download or read book Graph Algorithms in the Language of Linear Algebra written by Jeremy Kepner and published by SIAM. This book was released on 2011-01-01 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The current exponential growth in graph data has forced a shift to parallel computing for executing graph algorithms. Implementing parallel graph algorithms and achieving good parallel performance have proven difficult. This book addresses these challenges by exploiting the well-known duality between a canonical representation of graphs as abstract collections of vertices and edges and a sparse adjacency matrix representation. This linear algebraic approach is widely accessible to scientists and engineers who may not be formally trained in computer science. The authors show how to leverage existing parallel matrix computation techniques and the large amount of software infrastructure that exists for these computations to implement efficient and scalable parallel graph algorithms. The benefits of this approach are reduced algorithmic complexity, ease of implementation, and improved performance.

Introduction to Algebraic Geometry

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Publisher : American Mathematical Soc.
ISBN 13 : 1470435187
Total Pages : 498 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Introduction to Algebraic Geometry by : Steven Dale Cutkosky

Download or read book Introduction to Algebraic Geometry written by Steven Dale Cutkosky and published by American Mathematical Soc.. This book was released on 2018-06-01 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski's main theorem, and Bertini's theorems for general linear systems are presented, with proofs, in the final chapters. With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.

Algorithmic Algebra

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Publisher : Springer Science & Business Media
ISBN 13 : 1461243440
Total Pages : 427 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Algorithmic Algebra by : Bhubaneswar Mishra

Download or read book Algorithmic Algebra written by Bhubaneswar Mishra and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithmic Algebra studies some of the main algorithmic tools of computer algebra, covering such topics as Gröbner bases, characteristic sets, resultants and semialgebraic sets. The main purpose of the book is to acquaint advanced undergraduate and graduate students in computer science, engineering and mathematics with the algorithmic ideas in computer algebra so that they could do research in computational algebra or understand the algorithms underlying many popular symbolic computational systems: Mathematica, Maple or Axiom, for instance. Also, researchers in robotics, solid modeling, computational geometry and automated theorem proving community may find it useful as symbolic algebraic techniques have begun to play an important role in these areas. The book, while being self-contained, is written at an advanced level and deals with the subject at an appropriate depth. The book is accessible to computer science students with no previous algebraic training. Some mathematical readers, on the other hand, may find it interesting to see how algorithmic constructions have been used to provide fresh proofs for some classical theorems. The book also contains a large number of exercises with solutions to selected exercises, thus making it ideal as a textbook or for self-study.

Distance-Regular Graphs

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Publisher : Springer Science & Business Media
ISBN 13 : 3642743412
Total Pages : 513 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Distance-Regular Graphs by : Andries E. Brouwer

Download or read book Distance-Regular Graphs written by Andries E. Brouwer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since the discovery of the five platonic solids in ancient times, the study of symmetry and regularity has been one of the most fascinating aspects of mathematics. Quite often the arithmetical regularity properties of an object imply its uniqueness and the existence of many symmetries. This interplay between regularity and symmetry properties of graphs is the theme of this book. Starting from very elementary regularity properties, the concept of a distance-regular graph arises naturally as a common setting for regular graphs which are extremal in one sense or another. Several other important regular combinatorial structures are then shown to be equivalent to special families of distance-regular graphs. Other subjects of more general interest, such as regularity and extremal properties in graphs, association schemes, representations of graphs in euclidean space, groups and geometries of Lie type, groups acting on graphs, and codes are covered independently. Many new results and proofs and more than 750 references increase the encyclopaedic value of this book.

Association Schemes

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Publisher : Cambridge University Press
ISBN 13 : 9781139449939
Total Pages : 410 pages
Book Rating : 4.4/5 (499 download)

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Book Synopsis Association Schemes by : R. A. Bailey

Download or read book Association Schemes written by R. A. Bailey and published by Cambridge University Press. This book was released on 2004-02-26 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Association schemes are of interest to both mathematicians and statisticians and this book was written with both audiences in mind. For statisticians, it shows how to construct designs for experiments in blocks, how to compare such designs, and how to analyse data from them. The reader is only assumed to know very basic abstract algebra. For pure mathematicians, it tells why association schemes are important and develops the theory to the level of advanced research. This book arose from a course successfully taught by the author and as such the material is thoroughly class-tested. There are a great number of examples and exercises that will increase the book's appeal to both graduate students and their instructors. It is ideal for those coming either from pure mathematics or statistics backgrounds who wish to develop their understanding of association schemes.