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Overview
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.
This new edition includes several new areas of application, including the cycle index of the symmetric group, permutations, and square roots, counting polyminoes, and exact covering sequences. An appendix on using Maple and Mathematica to generate applications is also included. Includes exercises and solutions at the end of each chapter.
Synopsis
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.
Booknews
Generating functions are a "bridge" between discrete mathematics on the one hand, and continuous analysis and complex variable theory on the other. This book is about generating functions and some of their uses in discrete mathematics. A textbook for use in advanced undergraduate level courses in discrete mathematics. Annotation c. Book News, Inc., Portland, OR (booknews.com)