An Algebraic Approach To Association Schemes PDF Download
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Author | : Paul-Hermann Zieschang |
Publisher | : Springer |
Total Pages | : 201 |
Release | : 2006-11-13 |
Genre | : Mathematics |
ISBN | : 3540685235 |
Download An Algebraic Approach to Association Schemes Book in PDF, ePub and Kindle
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.
Author | : P. Delsarte |
Publisher | : |
Total Pages | : 97 |
Release | : 1973 |
Genre | : Coding theory |
ISBN | : |
Download An Algebraic Approach to the Association Schemes of Coding Theory Book in PDF, ePub and Kindle
Author | : M. Hall Jr. |
Publisher | : Springer Science & Business Media |
Total Pages | : 480 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 940101826X |
Download Combinatorics Book in PDF, ePub and Kindle
Combinatorics has come of age. It had its beginnings in a number of puzzles which have still not lost their charm. Among these are EULER'S problem of the 36 officers and the KONIGSBERG bridge problem, BACHET's problem of the weights, and the Reverend T.P. KIRKMAN'S problem of the schoolgirls. Many of the topics treated in ROUSE BALL'S Recreational Mathe matics belong to combinatorial theory. All of this has now changed. The solution of the puzzles has led to a large and sophisticated theory with many complex ramifications. And it seems probable that the four color problem will only be solved in terms of as yet undiscovered deep results in graph theory. Combinatorics and the theory of numbers have much in common. In both theories there are many prob lems which are easy to state in terms understandable by the layman, but whose solution depends on complicated and abstruse methods. And there are now interconnections between these theories in terms of which each enriches the other. Combinatorics includes a diversity of topics which do however have interrelations in superficially unexpected ways. The instructional lectures included in these proceedings have been divided into six major areas: 1. Theory of designs; 2. Graph theory; 3. Combinatorial group theory; 4. Finite geometry; 5. Foundations, partitions and combinatorial geometry; 6. Coding theory. They are designed to give an overview of the classical foundations of the subjects treated and also some indication of the present frontiers of research.
Author | : Eiichi Bannai |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 303 |
Release | : 2021-02-22 |
Genre | : Mathematics |
ISBN | : 3110627736 |
Download Algebraic Combinatorics Book in PDF, ePub and Kindle
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.
Author | : Tzuong-tsieng Moh |
Publisher | : World Scientific |
Total Pages | : 266 |
Release | : 2022-02-18 |
Genre | : Mathematics |
ISBN | : 9811220980 |
Download Introduction To Algebraic Coding Theory Book in PDF, ePub and Kindle
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.
Author | : Christopher Godsil |
Publisher | : Cambridge University Press |
Total Pages | : 353 |
Release | : 2016 |
Genre | : Mathematics |
ISBN | : 1107128447 |
Download Erdos-Ko-Rado Theorems: Algebraic Approaches Book in PDF, ePub and Kindle
Graduate text focusing on algebraic methods that can be applied to prove the Erdős-Ko-Rado Theorem and its generalizations.
Author | : David Eisenbud |
Publisher | : Springer Science & Business Media |
Total Pages | : 265 |
Release | : 2006-04-06 |
Genre | : Mathematics |
ISBN | : 0387226397 |
Download The Geometry of Schemes Book in PDF, ePub and Kindle
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.
Author | : Chris Godsil |
Publisher | : Routledge |
Total Pages | : 382 |
Release | : 2017-10-19 |
Genre | : Mathematics |
ISBN | : 1351467506 |
Download Algebraic Combinatorics Book in PDF, ePub and Kindle
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.
Author | : Alexander Barg |
Publisher | : American Mathematical Soc. |
Total Pages | : 317 |
Release | : 2001 |
Genre | : Computers |
ISBN | : 0821820745 |
Download Codes and Association Schemes Book in PDF, ePub and Kindle
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.
Author | : Paul-Hermann Zieschang |
Publisher | : Springer Science & Business Media |
Total Pages | : 295 |
Release | : 2005-12-19 |
Genre | : Mathematics |
ISBN | : 3540305939 |
Download Theory of Association Schemes Book in PDF, ePub and Kindle
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.