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Books > Science & Mathematics > Mathematics > Combinatorics & graph theory
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Ordering Block Designs - Gray Codes, Universal Cycles and Configuration Orderings (Hardcover, 2012 ed.)
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Ordering Block Designs - Gray Codes, Universal Cycles and Configuration Orderings (Hardcover, 2012 ed.)
Series: CMS Books in Mathematics
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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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