Cambridge University Press eBooks· 2015
Catalan Numbers
- 277citations
- 2015year
Short summary
This book offers the first comprehensive collection of Catalan numbers, detailing their properties and applications across diverse mathematical fields like combinatorics, algebra, and probability.
AI-generated from the title and abstract; the full text is not read.
Key points
- Catalan numbers are a highly prevalent sequence in mathematics.
- The book compiles properties and applications across 10+ mathematical fields.
- It features 214 exercises on objects counted by Catalan numbers.
- 68 additional exercises cover related sequences like Fuss-Catalan and Motzkin numbers.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. Cambridge University Press eBooks, 2015 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics