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Catalan Numbers

Autor Richard P. Stanley
en Limba Engleză Paperback – 25 mar 2015
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.
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Specificații

ISBN-13: 9781107427747
ISBN-10: 1107427746
Pagini: 222
Ilustrații: 150 b/w illus. 282 exercises
Dimensiuni: 153 x 230 x 13 mm
Greutate: 0.3 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Locul publicării:New York, United States

Cuprins

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

Notă biografică


Descriere

More than 250 exercises and solutions on properties and applications of Catalan numbers, at levels ranging from recreational to research.