*(English)*Zbl 0889.05001

[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 $\cdots $. The second intended audience consists of professional combinatorialists, for whom this book could serve as a general reference $\cdots $. 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.

##### MSC:

05-02 | Research monographs (combinatorics) |

05A15 | Exact enumeration problems, generating functions |

05A16 | Asymptotic enumeration |

06A07 | Combinatorics of partially ordered sets |