## Introduction to combinatorial designsCombinatorial theory is one of the fastest growing areas of modern mathematics. Focusing on a major part of this subject, Introduction to Combinatorial Designs, Second Edition provides a solid foundation in the classical areas of design theory as well as in more contemporary designs based on applications in a variety of fields. After an overview of basic concepts, the text introduces balanced designs and finite geometries. The author then delves into balanced incomplete block designs, covering difference methods, residual and derived designs, and resolvability. Following a chapter on the existence theorem of Bruck, Ryser, and Chowla, the book discusses Latin squares, one-factorizations, triple systems, Hadamard matrices, and Room squares. It concludes with a number of statistical applications of designs. Reflecting recent results in design theory and outlining several applications, this new edition of a standard text presents a comprehensive look at the combinatorial theory of experimental design. Suitable for a one-semester course or for self-study, it will prepare readers for further exploration in the field. To access supplemental materials for this volume, visit the authorżs website at http://www.math.siu.edu/Wallis/designs |

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### Contents

Balanced Designs | 15 |

Finite Geometries | 35 |

Difference Sets and Difference Methods | 63 |

Copyright | |

14 other sections not shown

### Common terms and phrases

array balanced incomplete block called cell Combinatorial combinatorial design conference matrix congruent consider construct COROLLARY define denoted design with parameters diag diagonal difference set disjoint edges entries equation equivalent example Exercises exists factors Figure finite field geometry graph Hadamard matrix idempotent Latin square incidence matrix incomplete block design initial blocks integer irreducible polynomial isomorphism Kirkman triple system large set LEMMA Math matrix of side modulo multiple mutually orthogonal Latin number of blocks occurs one-factorization ordered pairs orthogonal Latin squares pairwise balanced design parallel class PB(v permutation points polynomial positive integer precisely once prime power Proof Prove result Room square round row and column Section Smith normal form square of side starter Steiner triple system subset Suppose symbols symmetric balanced incomplete TD(k teams THEOREM tournament transversal treatments type II oval unique unordered pairs vector Verify write