Ebook: Combinatorial Designs: Constructions and Analysis

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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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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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.
Content:
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

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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.
Content:
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
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