Ordering Block Designs: Gray Codes, Universal Cycles and Configuration Orderings
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.

1136505612
Ordering Block Designs: Gray Codes, Universal Cycles and Configuration Orderings
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.

69.95 In Stock
Ordering Block Designs: Gray Codes, Universal Cycles and Configuration Orderings

Ordering Block Designs: Gray Codes, Universal Cycles and Configuration Orderings

Ordering Block Designs: Gray Codes, Universal Cycles and Configuration Orderings
Add to Wishlist
Ordering Block Designs: Gray Codes, Universal Cycles and Configuration Orderings

Ordering Block Designs: Gray Codes, Universal Cycles and Configuration Orderings

Overview

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.

Product Details

ISBN-13: 9781461443247
Publisher: Springer New York
Publication date: 08/29/2012
Series: CMS Books in Mathematics
Edition description: 2012
Pages: 208
Product dimensions: 9.00(w) x 6.30(h) x 0.40(d)

About the Author

Megan Dewar is an Adjunct Professor at the School of Mathematics and Statistics, Carleton University.

Brett Stevens is a Professor at the School of Mathematics and Statistics, Carleton University.

Table of Contents

Abstract.- Acknowledgements.- Introduction.- Background.- Ordering the Blocks of Designs.- Gray Codes and Universal Cycles for Designs.- New Results in Configuration Ordering.- Conclusions and Future Work.- Bibliography.- Index.
From the B&N Reads Blog
Page 1 of

Related Subjects

Science & Technology
Mathematics
Computer Science & Combinatorics
Science & Technology
Mathematics
Computer Science & Combinatorics

Customer Reviews