New generatingfunctionology

This is the Second Edition of the introduction to the use of generating functions and series in combinatorial mathematics. This new edition includes several new areas of application, including the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences. Generatingfunctionology provides information pertinent to generating functions and some of their uses in discrete mathematics. This book presents the power of the method by giving a number of examples of problems that can be profitably thought about from the point of view of generating functions. Organized into five chapters, this book begins with an overview of the basic concepts of a generating function. This text then discusses the different kinds of series that are widely used as generating functions. Other chapters explain how to make much more precise estimates of the sizes of the coefficients of power series based on the analyticity of the function that is represented by the series. This book discusses as well the applications of the theory of generating functions to counting problems. The final chapter deals with the formal aspects of the theory of generating functions. This book is a valuable resource for mathematicians and students. Content: Front Matter, Page iii Copyright, Page iv Preface, Page v Chapter 1 - Introductory Ideas and Examples, Pages 1-26 Chapter 2 - Series, Pages 27-63 Chapter 3 - Cards, Decks, and Hands: The Exponential Formula, Pages 64-97 Chapter 4 - Applications of Generating Functions, Pages 98-137 Chapter 5 - Analytic and Asymptotic Methods, Pages 138-162 Solutions, Pages 163-180 References, Pages 181-182 Index, Pages 183-184 A generating function is a clothesline on which we hang up a sequence of numbers for display. Herbert S. Wilf. Includes Bibliographical References (p. 181-182) And Index.