Generatingfunctionology : Third Edition

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. Front Cover Contents 1. Introductory Ideas and Examples 2. Series 3. Cards, Decks, and Hands: The Exponential Formula 4. Applications of Generating Functions 5. Analytic and Asymptotic Methods Back Cover A generating function is a clothesline on which we hang up a sequence of numbers for display.