Enumerative Combinatorics, Volume 1

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Overview

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.

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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Product Details

  • ISBN-13: 9780521663519
  • Publisher: Cambridge University Press
  • Publication date: 2/28/2000
  • Series: Cambridge Studies in Advanced Mathematics Series , #49
  • Edition description: Older Edition
  • Pages: 340
  • Product dimensions: 5.98 (w) x 8.98 (h) x 0.75 (d)

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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  • Anonymous

    Posted June 15, 2001

    A Masterpiece of Mathematical Writing

    It was only after having been prodded by Eratosthenes, then Librarian of Alexandria, that Archimedes was induced to write 'The Method.' Fermat is notorious for having written in the margins of Diophantus's 'Arithmetica', where there was never enough room for methods. Newton took an extra year writing 'Principia Mathematica' in order to conceal his methods. (Only after Leibniz began publishing did Newton talk openly about calculus.) Abel said about Gauss that 'he is like the fox, who effaces his tracks with his tail.' Fortunately, mathematicians of the first rank no longer deliberately hide their methods. Unfortunately, few of them seem both willing and able to write lucidly enough for nonspecialists to appreciate subtleties of approach. Richard Stanley is a refreshing exception. His two volume 'Enumerative Combinatorics' is already a classic, both for its depth and for its clarity. Reading these books, one achieves a sense, not only of 'what', but of 'why' and 'how'. Technique is generously illustrated, not only in the exposition, but in the explicit solutions of numerous well chosen exercises. These volumes comprise a masterpiece of mathematical writing.

    1 out of 1 people found this review helpful.

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