Introduction to Combinatorial Designs, Second Edition

W.D. Wallis

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May 17, 2007 by Chapman and Hall/CRC
Textbook - 328 Pages - 42 B/W Illustrations
ISBN 9781584888383 - CAT# C8385
Series: Discrete Mathematics and Its Applications

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Features

  • Covers classical designs such as Latin squares, balanced incomplete block designs, and finite projective and affine planes
  • Introduces modern extensions of design theory, including one-factorizations, Room squares, tournament designs, and nested designs
  • Features applications in several areas, including cryptography, computer science, experimental design, and communications theory
  • Includes instructive examples and theorems with every topic
  • Provides exercises in each section, select answers in the back of the book, and more complete solutions on the author’s website
  • Contains references to classical literature to put results in a historical perspective
  • Summary

    Combinatorial theory is one of the fastest growing areas of modern mathematics. Focusing on a major part of this subject, Introduction to Combinatorial Designs, Second Edition provides a solid foundation in the classical areas of design theory as well as in more contemporary designs based on applications in a variety of fields.

    After an overview of basic concepts, the text introduces balanced designs and finite geometries. The author then delves into balanced incomplete block designs, covering difference methods, residual and derived designs, and resolvability. Following a chapter on the existence theorem of Bruck, Ryser, and Chowla, the book discusses Latin squares, one-factorizations, triple systems, Hadamard matrices, and Room squares. It concludes with a number of statistical applications of designs.

    Reflecting recent results in design theory and outlining several applications, this new edition of a standard text presents a comprehensive look at the combinatorial theory of experimental design. Suitable for a one-semester course or for self-study, it will prepare readers for further exploration in the field.

    To access supplemental materials for this volume, visit the author’s website at http://www.math.siu.edu/Wallis/designs