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Enumerative Combinatorics

Volume 1

2nd Edition

$57.00 (P)

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: December 2011
  • availability: Available
  • format: Paperback
  • isbn: 9781107602625

$ 57.00 (P)
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About the Authors
  • 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.

    • Includes hundreds of exercises, most with solutions that augment the text and present new results
    • Offers many connections with other areas of mathematics, such as finite fields, algebraic topology and polytopes
    • Discusses many topics not found in other texts, such as the cd-index, combinatorial properties of GL(n,q), promotion and evacuation, and P-partitions
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    Reviews & endorsements

    "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

    • Edition: 2nd Edition
    • Date Published: December 2011
    • format: Paperback
    • isbn: 9781107602625
    • length: 642 pages
    • dimensions: 226 x 153 x 34 mm
    • weight: 0.85kg
    • contains: 165 b/w illus. 536 exercises
    • availability: Available
  • Table of Contents

    1. What is enumerative combinatorics?
    2. Sieve methods
    3. Partially ordered sets
    4. Rational generating functions.

  • Instructors have used or reviewed this title for the following courses

    • Enumerative combinatorics
    • Intro to combinatorics
  • Author

    Richard P. Stanley, Massachusetts Institute of Technology
    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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