Enumerative Combinatorics - Volume 1

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.

Enumerative combinatorics deals with the basic problem of counting how many objects have a given property. Since this problem arises in many areas of mathematics and science the subject is of great applicability. This book provides an introduction to the subject at a level suitable for graduate students and research mathematicians. The author has made a special effort, by providing extensive exercises with solutions, to show the broad applicability of enumerative combinatorics to other areas of mathematics.