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Catalan Numbers

$30.99 (P)

  • Date Published: March 2015
  • availability: In stock
  • format: Paperback
  • isbn: 9781107427747

$ 30.99 (P)
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About the Authors
  • Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book provides, for the first time, a comprehensive collection of their properties and applications in combinatorics, algebra, analysis, number theory, probability theory, geometry, topology, and other areas. After an introduction to the basic properties of Catalan numbers, the book presents 214 different kinds of objects which are counted using Catalan numbers, including of exercises with solutions. The reader can try solving the exercises or simply browse through them. 68 additional exercises with prescribed difficulty levels present various properties of Catalan numbers and related numbers, such as Fuss-Catalan numbers, Motzkin numbers, Schröder numbers, Narayana numbers, super Catalan numbers, q-Catalan numbers and (q,t)-Catalan numbers. The book concludes with a history of Catalan numbers by Igor Pak and a glossary of key terms. Whether your interest in mathematics is recreation or research, you will find plenty of fascinating and stimulating facts here.

    • Accessible to all levels of persons with an interest in mathematics
    • Author is a world expert in this area
    • The 214 combinatorial interpretations of Catalan numbers and the 68 additional problems in the form of exercises with solutions allow the reader to approach this material in numerous ways: browsing, studying the material, and attempting to solve the exercises
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    Product details

    • Date Published: March 2015
    • format: Paperback
    • isbn: 9781107427747
    • length: 222 pages
    • dimensions: 230 x 153 x 13 mm
    • weight: 0.29kg
    • contains: 150 b/w illus. 282 exercises
    • availability: In stock
  • Table of Contents

    1. Basic properties
    2. Bijective exercises
    3. Bijective solutions
    4. Additional problems
    5. Solutions to additional problems.

  • 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. He won the AMS 2001 Leroy P. Steele Prize for Mathematical Exposition for his books Enumerative Combinatorics, Volumes 1 and 2, which contain material that form the basis for much of the present book.

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