Combinatorial Designs: Construction and AnalysisCreated 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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Contents
Contents | 1 |
Symmetric BIBDs | 23 |
Difference Sets and Automorphisms | 41 |
Hadamard Matrices and Designs 73 | 72 |
Resolvable BIBDs | 101 |
Latin Squares | 123 |
Pairwise Balanced Designs I 157 | 156 |
Pairwise Balanced Designs II | 179 |
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Common terms and phrases
A)-BIBD Abelian group affine plane affine resolvable algorithm apply Lemma authentication code automorphism bent function block contains Boolean Bruck-Ryser-Chowla Theorem codewords coefficients column Combinatorial Designs compute conference matrix construct Corollary D. R. STINSON define Definition denote design theory difference set entry equation Example exists finite field following result group G group-divisible design Hadamard matrix Hence idempotent incidence matrix integer isomorphic linear Mathematics matrix of order modulo MOLS MOLS(n nonzero number of blocks obtain occurs in exactly orbits orthogonal array orthogonal Latin squares pairwise balanced designs parallel classes parameters permutation plane of order polynomial positive integer prime power projective plane proof of Theorem prove q)-code QR(q quadratic residue quasigroup Reed-Muller codes regular Hadamard matrix resolvable BIBD SK(k squares of order strong starter subset subspace Suppose symmetric BIBD t-designs TD(k unique block vectors