Combinatorial Designs: Construction and Analysis

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Springer Science & Business Media, 2004 - Computers - 300 pages
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.

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Applications of Combinatorial Designs
Symmetric BIBDs
Hadamard Matrices and Designs
Resolvable BIBDs
Latin Squares
Pairwise Balanced Designs I
Pairwise Balanced Designs II
fDesigns and twise Balanced Designs
Orthogonal Arrays and Codes
A Small Symmetric BIBDs and Abelian Difference Sets

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