Enumerative Combinatorics: Volume 1 / Edition 1

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Overview

This second volume of a two-volume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, D-finite generating functions, noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course on combinatorics, and includes the important Robinson-Schensted-Knuth algorithm. An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory including jeu de taquin and the Littlewood-Richardson rule. There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.

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.

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Editorial Reviews

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"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."
-Mathematical reviews
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Product Details

Meet 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.
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Table of Contents

Notation
Ch. 1 What Is Enumerative Combinatorics? 1
Ch. 2 Sieve Methods 64
Ch. 3 Partially Ordered Sets 96
Ch. 4 Rational Generating Functions 202
App Graph Theory Terminology 293
Index 296
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