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基本説明
THis new edition adds material on embedding designs, algorithms for producing disjoint designs, and more.
Full Description
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.
Contents
Steiner Triple Systems. λ-Fold Triple Systems. Quasigroup Identities and Graph Decompositions. Maximum Packings and Minimum Coverings. Kirkman Triple Systems. Mutually Orthogonal Latin Squares. Affine and Projective Planes. Intersections of Steiner Triple Systems. Embeddings. Steiner Quadruple Systems. Appendices. References. Index.
