Combinatorial Theory

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.

Spis treści:
Permutations and Combinations.
Inversion Formulae.
Generating Functions and Recursions.
Partitions.
Distinct Representatives.
Ramsey′s Theorem.
Some Extremal Problems.
Convex Spaces and Linear Programming.
Graphical Methods, Debruijn Sequences.
Block Designs.
Difference Sets.
Finite Geometries.
Orthogonal Latin Squares.
Hadamard Matrices.
General Constructions of Block Designs.
Theorems on Completion and Embedding.
Coding Theory and Block Designs.
Appendices.
Bibliography.
Index.