## 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

Foreword | |

Applications of Combinatorial Designs | |

Symmetric BIBDs | |

Hadamard Matrices and Designs | |

Resolvable BIBDs | |

Latin Squares | |

Pairwise Balanced Designs I | |

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### Common terms and phrases

A)-BIBD A)-design Abelian group affine plane affine resolvable apply Lemma automorphism bent function block contains Bruck-Ryser-Chowla Theorem codewords coefficients Combinatorial Designs compute conference matrix consider Corollary 4.7 define Definition delete denote design theory Dev(D difference family difference set easy elements entries equation Example finite field Fisher's Inequality following result group G group-divisible design Hadamard matrix Hence incidence matrix induction integer isomorphic l)-difference Lemma linear matrix of order modulo MOLS(n Multiplier Theorem multiset nonzero occurs in exactly orbits orthogonal array orthogonal Latin squares pair of points pairwise balanced designs parallel class permutation plane of order points occurs polynomial positive integer prime power projective plane proof of Theorem quadratic residue quasigroup resolvable BIBD sharply transitive squares of order stab(A strong starter subgroup subset subspace Suppose d,e,f Suppose that X,A symmetric BIBD symmetric v,k transversal design unique block vectors verify