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This book is concerned with the relations between graphs, error-correcting codes and designs, in particular how techniques of graph theory and coding theory can give information about designs. A major revision and expansion of a previous volume in this series, this account includes many examples and new results as well as improved treatments of older material. So that non-specialists will find the treatment accessible the authors have included short introductions to the three main topics. This book will be welcomed by graduate students and research mathematicians and be valuable for advanced courses in finite combinatorics.
This book stresses the connection between, and the applications of, design theory to graphs and codes. Beginning with a brief introduction to design theory and the necessary background, the book also provides relevant topics for discussion from the theory of graphs and codes.
These are notes deriving from lecture courses on the theory of t-designs and graph theory given by the authors in 1973 at Westfield College, London.
A self-contained account suited for a wide audience describing coding theory, combinatorial designs and their relations.
This monograph on strongly regular graphs is an invaluable reference for anybody working in algebraic combinatorics.
Graphs have become a fixture of everyday life, used in scientific and business publications, in magazines and newspapers, on television, on billboards, and even on cereal boxes. Nonetheless, surprisingly few graphs communicate effectively, and most graphs fail because they do not take into account the goals, needs, and abilities of the viewers. In raph Design for Eye and Mind, Stephen Kosslyn addresses these problems by presenting eight psychological principles for constructing effective graphs. Each principle is solidly rooted both in the scientific literature on how we perceive and comprehend graphs and in general facts about how our eyes and brains process visual information. Kosslyn then uses these eight psychological principles as the basis for hundreds of specific recommendations that serve as a concrete, step-by-step guide to deciding whether a graph is an appropriate display to use, choosing the correct type of graph for a specific type of data and message, and then constructing graphs that will be understood at a glance. Kosslyn also includes a complete review of the scientific literature on graph perception and comprehension, and appendices that provide a quick tutorial on basic statistics and a checklist for evaluating computer-graphics programs. Graph Design for Eye and Mind is an invaluable reference for anyone who uses visual displays to convey information in the sciences, humanities, and businesses such as finance, marketing, and advertising.
Fundamentals of Codes, Graphs, and Iterative Decoding is an explanation of how to introduce local connectivity, and how to exploit simple structural descriptions. Chapter 1 provides an overview of Shannon theory and the basic tools of complexity theory, communication theory, and bounds on code construction. Chapters 2 - 4 provide an overview of "classical" error control coding, with an introduction to abstract algebra, and block and convolutional codes. Chapters 5 - 9 then proceed to systematically develop the key research results of the 1990s and early 2000s with an introduction to graph theory, followed by chapters on algorithms on graphs, turbo error control, low density parity check codes, and low density generator codes.
This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.
Revised throughout Includes new chapters on the network simplex algorithm and a section on the five color theorem Recent developments are discussed
Design theory is a branch of combinatorics with applications in number theory, coding theory and geometry. In this book the authors discuss the generalization of results and applications to quasi-symmetric designs. The coverage is comprehensive and will be useful for researchers and graduate students. An attractive feature is the discussion of unsolved problems.