Description
Taylor & Francis Ltd Design Theory Second Edition 2008 Edition by Charles C. Lindner, Christopher A. Rodger
Design Theory, Second Edition presents some of the most important techniques used for constructing combinatorial designs. It augments the descriptions of the constructions with many figures to help students understand and enjoy this branch of mathematics.This edition now offers a thorough development of the embedding of Latin squares and combinatorial designs. It also presents some pure mathematical ideas, including connections between universal algebra and graph designs. The authors focus on several basic designs, including Steiner triple systems, Latin squares, and finite projective and affine planes. They produce these designs using flexible constructions and then add interesting properties that may be required, such as resolvability, embeddings, and orthogonality. The authors also construct more complicated structures, such as Steiner quadruple systems.By providing both classical and state-of-the-art construction techniques, this book enables students to produce many other types of designs. Steiner Triple SystemsThe Existence Problemv 3 (mod 6): The Bose Constructionv 1 (mod 6): The Skolem Constructionv 5 (mod 6): The 6n + 5 ConstructionQuasigroups with Holes and Steiner Triple SystemsThe Wilson ConstructionCyclic Steiner Triple SystemsThe 2n + 1 and 2n + 7 Constructions-Fold Triple SystemsTriple Systems of Index > 1The Existence of Indempotent Latin Squares2-fold Triple Systems= 3 and 6-Fold Triple Systems in GeneralQuasigroup Identities and Graph DecompositionsQuasigroup IdentitiesMendelsohn Triple Systems RevisitedSteiner Triple Systems RevisitedMaximum Packings and Minimum CoveringsThe General ProblemMaximum PackingsMinimum CoveringsKirkman Triple Systems A Recursive Construction Constructing Pairwise Balanced DesignsMutually Orthogonal Latin SquaresIntroductionThe Euler and MacNeish ConjecturesDisproof of the MacNeish ConjectureDisproof of the Euler ConjectureOrthogonal Latin Squares of Order n 2 (mod 4)Affine and Projective PlanesAffine PlanesProjective PlanesConnections between Affine and Projective Planes Connection between Affine Planes and Complete Sets of MOLSCoordinating the Affine PlaneIntersections of Steiner Triple SystemsTeirlinck's AlgorithmThe General Intersection ProblemEmbeddings Embedding Latin Rectangles-Necessary Conditions Edge-Coloring Bipartite Graphs Embedding Latin Rectangles: Ryser's Sufficient Conditions Embedding Idempotent Commutative Latin Squares: Cruse's Theorem Embedding Partial Steiner Triple SystemsSteiner Quadruple Systems IntroductionConstructions of Steiner Quadruple SystemsThe Stern and Lenz LemmaThe (3v - 2u)-ConstructionAppendix A: Cyclic Steiner Triple Systems Appendix B: Answers to Selected Exercises References Index