Combinatorial Designs: Constructions and Analysis

ISBN-13: 9781441930224 / Angielski / Miękka / 2011 / 300 str.

Douglas R. Stinson

Opis

Created to teach students many of the most important techniques used for constructing combinatorial designs, this is an ideal textbook for advanced undergraduate and graduate courses in combinatiorial design theory. The text features clear explanations of basic designs, such as Steiner and Kirkman triple systems, mutual orthogonal Latin squares, finite projective and affine planes, and Steiner quadruple systems. In these settings, the student will master various construction techniques, both classic and modern, and will be well-prepared to construct a vast array of combinatorial designs. Design theory offers a progressive approach to the subject, with carefully ordered results. It begins with simple constructions that gradually increase in complexity. Each design has a construction that contains new ideas or that reinforces and builds upon similar ideas previously introduced. A new text/reference covering all apsects of modern combinatorial design theory. Graduates and professionals in computer science, applied math, combinatorics, and applied statistics will find the book an essential resource.

Recenzje

From the reviews:

"This is the first rate textbook in combinatorial design theory, providing an elegant treatment ... . Topics have been chosen well ... . The language is clear and crisp. Proofs are carefully presented to convey the main insights, and examples are numerous. ... A strong feature of the book is the manner in which applications of designs are woven into the text ... . a valuable text for any course in combinatorial design theory, and will serve as an excellent reference ... ." (Charles J. Colbourn, Zentralblatt MATH, Vol. 1031, 2004)

"This book aims to thoroughly develop the most important techniques used for constructing combinatorial designs. The book provides a detailed and clear exposition of the classical core of combinatorial designs ... . Readers will master various construction techniques, both classic and modern, and will be well prepared to build a vast array of combinatorial designs. ... A variety of exercises enhance the book's utility as a course text." (L'Enseignment Mathematique, Vol. 50 (1-2), 2004)

"This excellent introductory textbook is the work of one of the top experts of the field. ... all of the material in this book is suitable for self-study by graduate students, who will find it provides helpful background information concerning research topics in design theory. Researchers may also find that some of the sections on advanced topics provide a useful reference for material that is not easily accessible in textbook form.' (Péter Hajnal, Acta Scientiarum Mathematicaram, Vol. 71, 2005)

"The book under review has eleven chapters. ... There are a dozen or so exercises ... at the end of each chapter. The book is very well written and well organized. ... This text should serve as a rich source of interesting research projects for advanced undergraduates. ... 'senior undergraduate or beginning graduate level' students are the intended audience ... ." (R. Gregory Taylor, SIGACT News, Vol. 39 (4), 2008)

Spis treści

* Introduction to BIBDs * Symmetric BIBDs * Difference sets and automorphisms * Hadamard matrices and designs * Resolvable BIBDs * Steiner triple systems * Mutually orthogonal Latin squares * Pairwise balanced designs * t-designs * Orthogonal arrays and codes * Index