Catalan Numbers Generating Function
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Analytic Combinatorics
Author: Philippe Flajolet
language: en
Publisher: Cambridge University Press
Release Date: 2009-01-15
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
generatingfunctionology
Generating functions, one of the most important tools in enumerative combinatorics, are a bridge between discrete mathematics and continuous analysis. Generating functions have numerous applications in mathematics, especially in - Combinatorics - Probability Theory - Statistics - Theory of Markov Chains - Number Theory One of the most important and relevant recent applications of combinatorics lies in the development of Internet search engines whose incredible capabilities dazzle even the mathematically trained user.
Catalan Numbers with Applications
This book presents a clear and comprehensive introduction to one of the truly fascinating topics in mathematics: Catalan numbers. They crop up in chess, computer programming and even train tracks. In addition to lucid descriptions of the mathematics and history behind Catalan numbers, Koshy includes short biographies of the prominent mathematicians who have worked with the numbers.