CMS Books in Mathematics

Ordering Block Designs

Gray Codes, Universal Cycles and Configuration Orderings

Authors: Dewar, Megan, Stevens, brett

  • This book provides the first comprehensive introduction to the problem of ordering blocks of designs
  • Includes a large introductory section on relevant design theory and literature on Gray codes and Universal cycles
  • Expands the definition of configuration orderings and uses new language to unify existing material
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eBook $54.99
price for USA (gross)
  • ISBN 978-1-4614-4325-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.95
price for USA
  • ISBN 978-1-4614-4324-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $69.95
price for USA
  • ISBN 978-1-4939-0165-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
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About this Textbook

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. 

About the authors

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.

Reviews

From the reviews:

“This book offers a comprehensive survey of order structures on the blocks of combinatorial designs. … I found the book to be a very pleasant read. … Throughout, there are plenty of nice examples and diagrams to bring the subject to life. References are listed at the end of each chapter, rather than at the end of the book. This structure works well here. … This is obviously very welcome for students and other researchers … .” (Peter James Dukes, Mathematical Reviews, May, 2013)

“This monograph focuses on ordered blocks where the difference between adjacent blocks is minimal. … the book is only of interest to mathematical researchers in the field of combinatorial design theory. Each chapter includes some problem exercises … and a list of references. The authors have taken great care in explaining the mathematical formulae, using figures where applicable.” (Klaus Galensa, Computing Reviews, January, 2013)


Table of contents (6 chapters)

  • Introduction

    Dewar, Megan (et al.)

    Pages 1-11

  • Background

    Dewar, Megan (et al.)

    Pages 13-62

  • Ordering the Blocks of Designs

    Dewar, Megan (et al.)

    Pages 63-76

  • Results in Configuration Ordering

    Dewar, Megan (et al.)

    Pages 77-112

  • Results in Gray Codes and Universal Cycles for Designs

    Dewar, Megan (et al.)

    Pages 113-172

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-1-4614-4325-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.95
price for USA
  • ISBN 978-1-4614-4324-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $69.95
price for USA
  • ISBN 978-1-4939-0165-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Ordering Block Designs
Book Subtitle
Gray Codes, Universal Cycles and Configuration Orderings
Authors
Series Title
CMS Books in Mathematics
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-4325-4
DOI
10.1007/978-1-4614-4325-4
Hardcover ISBN
978-1-4614-4324-7
Softcover ISBN
978-1-4939-0165-4
Series ISSN
1613-5237
Edition Number
1
Number of Pages
XII, 208
Topics