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Ordering Block Designs

Gray Codes, Universal Cycles and Configuration Orderings

Springer New York,
Buch
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This book opens with basic material on combinatorial block designs and combinatorial orderings, goes on to show how ordering concepts can be applied to block designs, and connects these concepts to applications in computer science, engineering and statistics.

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Titel: Ordering Block Designs
Autoren/Herausgeber: Megan Dewar, brett Stevens
Aus der Reihe: CMS Books in Mathematics
Ausgabe: 2012

ISBN/EAN: 9781493901654

Seitenzahl: 208
Format: 23,5 x 15,5 cm
Produktform: Taschenbuch/Softcover
Gewicht: 343 g
Sprache: Englisch

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.

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. 

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