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 combinatorial 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 mathematics, combinatorics, and applied statistics will find the book an essential resource. Combinatorial Designs 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, Treating The Material Progressively From Simple To More Complex. Readers Will Master Various Construction Techniques, Both Classic And Modern, And Will Be Well Prepared To Build A Vast Array Of Combinatorial Designs. The Main Prerequisites Are Familiarity With Basic Abstract Algebra, Linear Algebra And Some Number Theory Fundamentals.--jacket. Introduction To Balanced Incomplete Block Designs -- Symmetric Bibds -- Difference Sets And Automorphisms -- Hadamard Matrices And Designs -- Resolvable Bibds -- Latin Squares -- Pairwise Balanced Designs I -- Pairwise Balanced Designs Ii -- T-designs And T-wise Balanced Designs -- Orthogonal Arrays And Codes -- Applications Of Combinatorial Designs. Douglas R. Stinson. Includes Bibliographical References (p. [287]-293) And Index. Front Matter....Pages I-XVI Introduction to Balanced Incomplete Block Designs....Pages 1-21 Symmetric BIBDs....Pages 23-40 Difference Sets and Automorphisms of Designs....Pages 41-71 Hadamard Matrices and Designs....Pages 73-100 Resolvable BIBDs....Pages 101-121 Latin Squares....Pages 123-155 Pairwise Balanced Designs I: Designs with Specified Block Sizes....Pages 157-178 Pairwise Balanced Designs II: Minimal Designs....Pages 179-199 t -Designs and t -wise Balanced Designs....Pages 201-223 Orthogonal Arrays and Codes....Pages 225-255 Selected Applications of Combinatorial Designs....Pages 257-277 Back Matter....Pages 279-300 Combinatorial design theory concerns questions about whether it is possible to arrange elements of a finite set into subsets so that certain "balance" properties are satisfied.
