Introduction to Combinatorial Designs (Hardcover, 2)

Basic Concepts Combinatorial Designs Some Examples of Designs Block Designs Systems of Distinct Representatives Balanced Designs Pairwise Balanced Designs Balanced Incomplete Block Designs Another Proof of Fisher’s Inequality t-Designs Finite Geometries Finite Affine Planes Finite Fields Construction of Finite Affine Geometries Finite Projective Geometries Some Properties of Finite Geometries Ovals in Projective Planes The Desargues Configuration Difference Sets and Difference Methods Difference Sets Construction of Difference Sets Properties of Difference Sets General Difference Methods Singer Difference Sets More about Block Designs Residual and Derived Designs Resolvability The Main Existence Theorem Sums of Squares The Bruck?Ryser?Chowla Theorem Another Proof Latin Squares Latin Squares and Subsquares Orthogonality Idempotent Latin Squares Transversal Designs More about Orthogonality Spouse-Avoiding Mixed Doubles Tournaments Three Orthogonal Latin Squares Bachelor Squares One-Factorizations Basic Ideas The Variability of One-Factorizations Starters Applications of One-Factorizations An Application to Finite Projective Planes Tournament Applications of One-Factorizations Tournaments Balanced for Carryover Steiner Triple Systems Construction of Triple Systems Subsystems Simple Triple Systems Cyclic Triple Systems Large Sets and Related Designs Kirkman Triple Systems and Generalizations Kirkman Triple Systems Kirkman Packings and Coverings Hadamard Matrices Basic Ideas Hadamard Matrices and Block Designs Further Hadamard Matrix Constructions Regular Hadamard Matrices Equivalence Room Squares Definitions Starter Constructions Subsquare Constructions The Existence Theorem Howell Rotations Further Applications of Design Theory Statistical Applications Information and Cryptography Golf Designs References ANSWERS AND SOLUTIONS INDEX