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Zusatztext ?it is remarkable how quickly the book propels the reader from the basics to the frontiers of design theory ? Combined! these features make the book an excellent candidate for a design theory text. At the same time! even the seasoned researcher of triple systems will find this a useful resource.-Peter James Dukes (3-VCTR-MS; Victoria! BC)! Mathematical Reviews! 2010 Informationen zum Autor Charles C. Lindner, Christopher A. Rodger Klappentext Now updated! this edition 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. Zusammenfassung Presents some of the techniques used for constructing combinatorial designs. This work contains material on embeddings, directed designs, universal algebraic representations of designs and intersection properties of designs. It also includes important results in combinatorial designs. Inhaltsverzeichnis 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 ...
