Graph Theory, Coding Theory and Block Designs
Title | Graph Theory, Coding Theory and Block Designs PDF eBook |
Author | P. J. Cameron |
Publisher | Cambridge University Press |
Pages | 125 |
Release | 1975-09-18 |
Genre | Mathematics |
ISBN | 0521207428 |
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.
Graph Theory, Coding Theory and Block Designs
Title | Graph Theory, Coding Theory and Block Designs PDF eBook |
Author | P. J. Cameron |
Publisher | |
Pages | 124 |
Release | 1975 |
Genre | |
ISBN | 9781107093287 |
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.
Graph Theory, Coding Theory, and Block Designs
Title | Graph Theory, Coding Theory, and Block Designs PDF eBook |
Author | Peter Jephson Cameron |
Publisher | |
Pages | 114 |
Release | 1975 |
Genre | Block designs |
ISBN | 9781107090125 |
These are notes deriving from lecture courses given by the authors in 1973 at Westfield College, London. The lectures described the connection between the theory of t-designs on the one hand, and graph theory on the other. A feature of this book is the discussion of then-recent construction of t-designs from codes. Topics from a wide range of finite combinatorics are covered and the book will interest all scholars of combinatorial theory.
Ordering Block Designs
Title | Ordering Block Designs PDF eBook |
Author | Megan Dewar |
Publisher | Springer Science & Business Media |
Pages | 219 |
Release | 2012-08-30 |
Genre | Mathematics |
ISBN | 1461443253 |
The study of combinatorial block designs is a vibrant area of combinatorial mathematics with connections to finite geometries, graph theory, coding theory and statistics. The practice of ordering combinatorial objects can trace its roots to bell ringing which originated in 17th century England, but only emerged as a significant modern research area with the work of F. Gray and N. de Bruijn. These two fascinating areas of mathematics are brought together for the first time in this book. It presents new terminology and concepts which unify existing and recent results from a wide variety of sources. In order to provide a complete introduction and survey, the book begins with background material on combinatorial block designs and combinatorial orderings, including Gray codes -- the most common and well-studied combinatorial ordering concept -- and universal cycles. The central chapter discusses how ordering concepts can be applied to block designs, with definitions from existing (configuration orderings) and new (Gray codes and universal cycles for designs) research. Two chapters are devoted to a survey of results in the field, including illustrative proofs and examples. The book concludes with a discussion of connections to a broad range of applications in computer science, engineering and statistics. This book will appeal to both graduate students and researchers. Each chapter contains worked examples and proofs, complete reference lists, exercises and a list of conjectures and open problems. Practitioners will also find the book appealing for its accessible, self-contained introduction to the mathematics behind the applications.
Ordering Block Designs
Title | Ordering Block Designs PDF eBook |
Author | Springer |
Publisher | |
Pages | 220 |
Release | 2012-08-30 |
Genre | |
ISBN | 9781461443261 |
Graphs, Codes and Designs
Title | Graphs, Codes and Designs PDF eBook |
Author | P. J. Cameron |
Publisher | Cambridge University Press |
Pages | 164 |
Release | 1980-07-31 |
Genre | Mathematics |
ISBN | 9780521231411 |
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.
Coding Theory and Design Theory
Title | Coding Theory and Design Theory PDF eBook |
Author | Dijen Ray-Chaudhuri |
Publisher | Springer Science & Business Media |
Pages | 252 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461389941 |
This IMA Volume in Mathematics and its Applications Coding Theory and Design Theory Part I: Coding Theory is based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on APPLIED COMBINATORICS. We are grateful to the Scientific Committee: Victor Klee (Chairman), Daniel Kleitman, Dijen Ray-Chaudhuri and Dennis Stanton for planning and implementing an exciting and stimulating year long program. We especially thank the Workshop Organizer, Dijen Ray-Chaudhuri, for organizing a workshop which brought together many of the major figures in a variety of research fields in which coding theory and design theory are used. A vner Friedman Willard Miller, Jr. PREFACE Coding Theory and Design Theory are areas of Combinatorics which found rich applications of algebraic structures. Combinatorial designs are generalizations of finite geometries. Probably, the history of Design Theory begins with the 1847 pa per of Reverand T. P. Kirkman "On a problem of Combinatorics", Cambridge and Dublin Math. Journal. The great Statistician R. A. Fisher reinvented the concept of combinatorial 2-design in the twentieth century. Extensive application of alge braic structures for construction of 2-designs (balanced incomplete block designs) can be found in R. C. Bose's 1939 Annals of Eugenics paper, "On the construction of balanced incomplete block designs". Coding Theory and Design Theory are closely interconnected. Hamming codes can be found (in disguise) in R. C. Bose's 1947 Sankhya paper "Mathematical theory of the symmetrical factorial designs".