Ordering Block Designs

Gray Codes, Universal Cycles and Configuration Orderings

  • Megan Dewar
  • Brett Stevens

Part of the CMS Books in Mathematics book series (CMSBM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Megan Dewar, Brett Stevens
    Pages 1-11
  3. Megan Dewar, Brett Stevens
    Pages 13-62
  4. Megan Dewar, Brett Stevens
    Pages 63-76
  5. Megan Dewar, Brett Stevens
    Pages 77-112
  6. Megan Dewar, Brett Stevens
    Pages 113-172
  7. Megan Dewar, Brett Stevens
    Pages 173-202
  8. Back Matter
    Pages 203-207

About this book

Introduction

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.

Keywords

combinatorial ordering de Bruijn cycles design theory

Authors and affiliations

  • Megan Dewar
    • 1
  • Brett Stevens
    • 2
  1. 1.OttawaCanada
  2. 2.School of Mathematics & StatisticsCarleton UniversityOttawaCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-4325-4
  • Copyright Information Springer Science+Business Media New York 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-4324-7
  • Online ISBN 978-1-4614-4325-4
  • Series Print ISSN 1613-5237
  • About this book