Introductory Combinatorics

Focusing on the core material of value to students in a wide variety of fields, this book presents a broad comprehensive survey of modern combinatorics at an introductory level. The author begins with an introduction of concepts fundamental to all branches of combinatorics in the context of combinatorial enumeration. Chapter 2 is devoted to enumeration problems that involve counting the number of equivalence classes of an equivalence relation. Chapter 3 discusses somewhat less direct methods of enumeration, the principle of inclusion and exclusion and generating functions. The remainder of the book is devoted to a study of combinatorial structures. Cover......Page bogart_cover.djvu Front Matter......Page _004.djvu Preface......Page _005.djvu Contents......Page _013.djvu 1 An Introduction to Enumeration ......Page 001.djvu 2 Equivalence Relations, Partitions, and Multisets ......Page 069.djvu 3 Algebraic Counting Techniques ......Page 119.djvu 4 Graph Theory ......Page 200.djvu 5 Matching and Optimization......Page 291.djvu 6 Combinatorial Designs ......Page 359.djvu 7 Ordered Sets ......Page 442.djvu 8 Enumeration under Group Action ......Page 532.djvu Answers to Exercises ......Page 581.djvu Index ......Page 642.djvu Applications for discrete mathematics and specifically combinatorial mathematics in computer science, operations research, statistics, and the social and physical sciences have increased the growth in the field of combinatorics. Bogart (mathematics, Dartmouth College) addresses this new interest with his survey of topics such as enumeration, graph and algorithmic graph theory, and ordered sets, including interval orders, lattices, and Boolean algebras. This work is designed for introductory courses in combinatorics, or more generally, discrete mathematics. The author has chosen core material of value to students in a wide variety of disciplines: mathematics, computer science, operations research, physical sciences, and behavioural sciences. 1