Combinatorial Theory: Hall/Combinatorial

Content: Chapter 1 Permutations and Combinations (pages 1–7): Chapter 2 Inversion Formulae (pages 8–19): Chapter 3 Generating Functions and Recursions (pages 20–30): Chapter 4 Partitions (pages 31–47): Chapter 5 Distinct Representatives (pages 48–72): Chapter 6 Ramsey's Theorem (pages 73–76): Chapter 7 Some Extremal Problems (pages 77–84): Chapter 8 Convex Spaces and Linear Programming (pages 85–109): Chapter 9 Graphical Methods. Debruijn Sequences (pages 110–125): Chapter 10 Block Designs (pages 126–146): Chapter 11 Difference Sets (pages 147–198): Chapter 12 Finite Geometries (pages 199–221): Chapter 13 Orthogonal Latin Squares (pages 222–237): Chapter 14 Hadamard Matrices (pages 238–263): Chapter 15 General Constructions of Block Designs (pages 264–335): Chapter 16 Theorems on Completion and Embedding (pages 336–375): Chapter 17 Coding Theory and Block Designs (pages 376–404):

Includes proof of van der Waerden's 1926 conjecture on permanents, Wilson's theorem on asymptotic existence, and other developments in combinatorics since 1967. Also covers coding theory and its important connection with designs, problems of enumeration, and partition. Presents fundamentals in addition to latest advances, with illustrative problems at the end of each chapter. Enlarged appendixes include a longer list of block designs.

This introductory textbook examines the theory of combinatorics. It includes proof of Van der Waerden's 1926 conjecture on permanents, Wilson's theorem on asymptotic existence, and covers coding theory and its important connection with designs, problems of enumeration, and partition. Included in this book is proof of van der Waeroen's 1926 conjecture on permanents, Wilson's theorem on asymptotic existence, and other developments in combinatorics since 1967.