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.
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Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book provides some basic background and then presents more than 250 exercises and solutions on properties and applications of these numbers, with difficulty levels ranging from recreational to research.About 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. 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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Buchbeschreibung Cambridge University Press Mrz 2015, 2015. Taschenbuch. Buchzustand: Neu. Neuware - More than 250 exercises and solutions on properties and applications of Catalan numbers, at levels ranging from recreational to research. 222 pp. Englisch. Artikel-Nr. 9781107427747