Introduction to Combinatorics

This gradual, systematic introduction to the main concepts of combinatorics is the ideal text for advanced undergraduate and early graduate courses in this subject. Each of the book's three sections--Existence, Enumeration, and Construction--begins with a simply stated first principle, which is then developed step by step until it leads to one of the three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, Polya's graph enumeration formula, and Leech's 24-dimensional lattice.

Along the way, Professor Martin J. Erickson introduces fundamental results, discusses interconnection and problem-solving techniques, and collects and disseminates open problems that raise new and innovative questions and observations. His carefully chosen end-of-chapter exercises demonstrate the applicability of combinatorial methods to a wide variety of problems, including many drawn from the William Lowell Putnam Mathematical Competition. Many important combinatorial methods are revisited several times in the course of the text--in exercises and examples as well as theorems and proofs. This repetition enables students to build confidence and reinforce their understanding of complex material.

Mathematicians, statisticians, and computer scientists profit greatly from a solid foundation in combinatorics. Introduction to Combinatorics builds that foundation in an orderly, methodical, and highly accessible manner.

MARTIN J. ERICKSON, PhD, is Associate Professor at Truman State University, Kirksville, Missouri. His research interests include combinatorics, graph theory, and coding theory. Professor Erickson has received numerous national awards and is the author of several previous publications.

Preliminaries: Set Theory, Algebra, and Number Theory.

EXISTENCE.

The Pigeonhole Principle.

Sequences and Partial Orders.

Ramsey Theory.

ENUMERATION.

The Fundamental Counting Problem.

Recurrence Relations and Explicit Formulas.

Permutations and Tableaux.

The Polya Theory of Counting.

CONSTRUCTION.

Codes.

Designs.

Big Designs.

Bibliography.

Index.