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From the Publisher"The main difference between this edition and the first is the addition of ten new sections (six in Chapter 1 and four in Chapter 3)and more than 350 new exercises."
Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The material in Volume 1 was chosen to cover those parts of enumerative combinatorics of greatest applicability and with the most important connections with other areas of mathematics. The four chapters are devoted to an introduction to enumeration (suitable for advanced undergraduates), sieve methods, partially ordered sets, and rational generating functions. Much of the material is related to generating functions, a fundamental tool in enumerative combinatorics. In this new edition, the author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation, and differential posets.
This book is an introduction to enumerative combinatorics for graduate students and researchers. It concentrates on the theory and application of generating functions, a fundamental tool in enumerative combinatorics. The four chapters are devoted to enumeration, sieve methods (including the Principle of Inclusion-Exclusion), partially ordered sets, and rational generating functions. There are a large number of exercises, almost all with solutions, which greatly augment the text and provide entry into many areas not covered directly. The author stresses important connections with other areas of mathematics. This is a reissue of a book first published in 1986. The author has updated the references and included more problems. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.
1. What is enumerative combinatorics?; 2. Sieve methods; 3. Partially ordered sets; 4. Rational generating functions.