Synopses & Reviews
This book, the first of a two-volume basic introduction to enumerative combinatorics, concentrates on the theory and application of generating functions, a fundamental tool in enumerative combinatorics. Richard Stanley covers those parts of enumerative combinatorics with the greatest applications to other areas of mathematics. The four chapters are devoted to an accessible introduction to enumeration, sieve methods--including the Principle of Inclusion-Exclusion, partially ordered sets, and rational generating functions. A large number of exercises, almost all with solutions, augment the text and provide entry into many areas not covered directly. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.
Review
"...sure to become a standard as an introductory graduate text in combinatorics." Bulletin of the AMS"Stanley's book is very readable and a mine of information." Journal of the LMS"...will engage from start to finish the attention of any mathematician who will open it at page one." Gian-Carlo Rota"...an excellent and valuable book." Mathematical Reviews
Synopsis
Enumerative combinatorics deals with the basic problem of counting how many objects have a given property, a subject of great applicability. This book provides an introduction at a level suitable for graduate students. Extensive exercises with solutions show connections to other areas of mathematics.
Table of Contents
1. What is enumerative combinatorics?; 2. Sieve methods; 3. Partially ordered sets; 4. Rational generating functions.