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Informationen zum Autor W.D. Wallis Klappentext This new edition presents a comprehensive look at combinatorial designs. It covers classical designs such as Latin squares! balanced incomplete block designs! and finite projective and affine planes as well as more contemporary designs that include one-factorizations! Room squares! tournament designs! and nested designs. The book features applications in cryptography! computer science! experimental design! communications theory! and more. With every topic! it includes instructive examples and theorems. The text also provides exercises in each section! select answers in the back of the book! and more complete solutions on the author's website. Zusammenfassung 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 Inhaltsverzeichnis Basic Concepts. Balanced Designs. Finite Geometries. Some Properties of Finite Geometries. Difference Sets and Difference Methods. More about Block Designs. The Main Existence Theorem. Latin Squares. More about Orthogonality. One-Factorizations. Applications of One-Factorizations. Steiner Triple Systems. Kirkman Triple Systems and Generalizations. Hadamard Matrices. Room Squares. Further Applications of Design Theory. References. Answers and Solutions. Index....
Summary
Offers an introduction to the areas of design theory as well as to more contemporary designs based on applications in a variety of fields. This work also introduces balanced designs and finite geometries. It then delves into balanced incomplete block designs, covering difference methods, residual and derived designs, and resolvability.
