Catalan Numbers

Richard P. Stanley (Massachusetts Institute of Technology)

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English

Cambridge University Press
30 March 2015

Discrete mathematics; Combinatorics & graph theory

Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book gives for the first time a comprehensive collection of their properties and applications to combinatorics, algebra, analysis, number theory, probability theory, geometry, topology, and other areas. Following an introduction to the basic properties of Catalan numbers, the book presents 214 different kinds of objects counted by them in the form of exercises with solutions. The reader can try solving the exercises or simply browse through them. Some 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 ends 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.

By: Richard P. Stanley (Massachusetts Institute of Technology)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 230mm, Width: 153mm, Spine: 13mm
Weight: 320g
ISBN: 9781107427747
ISBN 10: 1107427746
Pages: 222
Publication Date: 30 March 2015
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active

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.