[PDF] Association Schemes eBook

Author : Paul-Hermann Zieschang
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 31,55 MB
Release : 2005-10-20
Category : Mathematics
ISBN : 9783540261360

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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.

Author : R. A. Bailey
Publisher : Cambridge University Press
Page : 410 pages
File Size : 14,35 MB
Release : 2004-02-26
Category : Mathematics
ISBN : 9781139449939

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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.

Author : Eiichi Bannai
Publisher : Walter de Gruyter GmbH & Co KG
Page : 303 pages
File Size : 10,25 MB
Release : 2021-02-22
Category : Mathematics
ISBN : 3110627736

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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 : Alexander Barg
Publisher : American Mathematical Soc.
Page : 317 pages
File Size : 13,15 MB
Release : 2001
Category : Computers
ISBN : 0821820745

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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
Page : 201 pages
File Size : 43,33 MB
Release : 2006-11-13
Category : Mathematics
ISBN : 3540685235

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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 : Rosemary Bailey
Publisher :
Page : 387 pages
File Size : 24,96 MB
Release : 2004
Category : Association schemes (Combinatorial analysis)
ISBN : 9780511185571

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Based on the author's graduate course on association schemes and the optimal design of scientific experiments, this book is accessible to both pure mathematicians and statisticians alike. It will appeal to researchers as an accessible reference work from which to learn about the statistical/combinatorial aspect of their work.

Author : R.L. Graham
Publisher : Elsevier
Page : 2404 pages
File Size : 21,44 MB
Release : 1995-12-11
Category : Computers
ISBN : 008093384X

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Handbook of Combinatorics

Author : David Eisenbud
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 24,24 MB
Release : 2006-04-06
Category : Mathematics
ISBN : 0387226397

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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 : M. Hall Jr.
Publisher : Springer Science & Business Media
Page : 480 pages
File Size : 13,63 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 940101826X

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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.