Combinatorics is the study of how discrete sets are arranged, counted, and constructed. This book details several general theories: the Ramsey theory, the Plya theory of counting, and the probabilistic method. It provides a basic framework in which to introduce fundamental results, discuss interconnections and problem solving techniques, and collect open problems.
Table of Contents
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.
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.