Lectures on Generating Functions

This book introduces readers to the language of generating functions, which nowadays, is the main language of enumerative combinatorics. The book starts with definitions, simple properties, and numerous examples of generating functions. It then discusses topics such as formal grammars, generating functions in several variables, partitions and decompositions, and the exclusion-inclusion principle. In the final chapter, the author describes applications to enumeration of trees, plane graphs, and graphs embedded in two-dimensional surfaces. Throughout the book, the author motivates readers by giving interesting examples rather than general theories. It contains numerous exercises to help students master the material. The only prerequisite is a standard calculus course. The book is an excellent text for a one-semester undergraduate course in combinatorics.

ISBN	0821834819	Pages	148
ISBN13	9780821834817 (What's this?)	Volumes	001
Publisher	American Mathematical Society	Weight (grammes)	202
Imprint	American Mathematical Society	Published in	Providence
Format	Paperback	Series title	Student Mathematical Library
Publication date	15 Oct 2003	Height (mm)	210
Library of Congress	QA164.8.L3	Width (mm)	140
DEWEY	511.6	Academic level	Professional / Scholarly
DEWEY edition	DC22

	Preface to the English Edition
	Preface
Ch. 1	Formal Power Series and Generating Functions. Operations with Formal Power Series, Elementary Generating Functions	1
Ch. 2	Generating Functions for Well-Known Sequences	17
Ch. 3	Unambiguous Formal Grammars. The Lagrange Theorem	35
Ch. 4	Analytic Properties of Functions Represented as Power Series and the Asymptotics of their Coefficients	47
Ch. 5	Generating Functions of Several Variables	59
Ch. 6	Partitions and Decompositions	87
Ch. 7	Dirichlet Generating Functions and the Inclusion-Exclusion Principle	101
Ch. 8	Enumeration of Embedded Graphs	113
	Final and Bibliographical Remarks	143
	Bibliography	145
	Index	147

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