Synopses & Reviews
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.
Review
Advance praise: '... sure to become a standard as an introductory graduate text in combinatorics.' Bulletin of the American Mathematical Society
Review
'... will engage from start to finish the attention of any mathematician who will open it at page one.' Gian-Carlo Rota
Synopsis
This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises.
Synopsis
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 more than 300 new exercises, many with solutions, updated and expanded chapter bibliographies, substantial new material on permutation statistics, coverage of additional topic such as hyperplan arrangements and the cd-index, and a rearranged and generalized treatment of P-partitions.
About the Author
Richard P. Stanley is a Professor of Applied Mathematics at the Massachusetts Institute of Technology. He is universally recognized as a leading expert in the field of combinatorics and its applications to a variety of other mathematical disciplines. In addition to the seminal two-volume book Enumerative Combinatorics, he is the author of Combinatorics and Commutative Algebra (1983) as well as more than 100 research articles in mathematics. Among Stanley's many distinctions are membership in the National Academy of Sciences (elected in 1995), the 2001 Leroy P. Steele Prize for mathematical exposition and the 2003 Schock Prize.
Table of Contents
1. What is enumerative combinatorics?; 2. Sieve methods; 3. Partially ordered sets; 4. Rational generating functions.