@book {IOPORT.01033382, author = {Stanley, Richard P.}, title = {Enumerative combinatorics. Vol. 1. 2nd ed.}, year = {1997}, isbn = {0-521-55309-1}, edition = {2nd ed.}, pages = {xi, 325~p.}, publisher = {Cambridge: Cambridge University Press}, abstract = {[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 $\dots$. 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.}, reviewer = {J.E.Graver (Syracuse)}, identifier = {01033382}, }