Cambridge Studies in Advanced Mathematics. 49. Cambridge: Cambridge University Press. xi, 325 p. £40.00; $ 59.95 (1997).
[See Zbl 0608.05001 for the first edition of the book.]
As the author explains in his introduction: “This book has three intended audiences and serves three different purposes. First, it may be used as a graduate-level introduction to a fascinating area of mathematics . The second intended audience consists of professional combinatorialists, for whom this book could serve as a general reference . Finally, this book may be used by mathematicians outside combinatorics whose work requires them to solve a combinatorial problem.”
The book serves all of these audiences well. The first chapter is a basic introduction to combinatorics and includes the fundamental counting formulas organized as counting functions under various conditions. The second chapter is devoted to a discussion of sieve methods. The remainder of the book consists of two long chapters: Partially ordered sets and Rational generating functions.
The book contains many careful examples and includes a large variety of exercises. The exercises are rated as to difficulty and a complete set of solutions is included. In addition each chapter contains a collection of historical notes and an extensive set of references.