Stanley, Richard P. [Rota, Gian-Carlo] Enumerative combinatorics. Vol. 1. With a foreword by Gian-Carlo Rota. Corrected reprint of the 1986 hardback edition. (English) Zbl 0945.05006 Cambridge Studies in Advanced Mathematics. 49. Cambridge: Cambridge University Press. xi, 326 p. (1999). 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.”These audiences are now well served by this very affordable paperback edition!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 carefully chosen 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.See the reviews of the originals in [Zbl 0608.05001; Zbl 0889.05001]. Reviewer: J.E.Graver (Syracuse) Cited in 7 ReviewsCited in 32 Documents MSC: 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 Keywords:enumerative combinatorics; partially ordered sets; counting formulas; counting functions; sieve methods; generating functions Citations:Zbl 0608.05001; Zbl 0889.05001 PDFBibTeX XMLCite \textit{R. P. Stanley}, Enumerative combinatorics. Vol. 1. With a foreword by Gian-Carlo Rota. Corrected reprint of the 1986 hardback edition. Cambridge: Cambridge University Press (1999; Zbl 0945.05006)