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Enumerative combinatorics. Vol. 1. (English) Zbl 0889.05001
Cambridge Studies in Advanced Mathematics. 49. Cambridge: Cambridge University Press. xi, 325 p. (1997).
[See Zbl 0608.05001 for the first edition published by Wadsworth.]

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 \(\dots\). The second intended audience consists of professional combinatorialists, for whom this book could serve as a general reference \(\dots\). 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.

05-02 Research exposition (monographs, survey articles) pertaining to combinatorics
05A15 Exact enumeration problems, generating functions
05A16 Asymptotic enumeration
06A07 Combinatorics of partially ordered sets