Softcover ISBN:  9780821834817 
Product Code:  STML/23 
List Price:  $37.00 
Individual Price:  $29.60 
Electronic ISBN:  9781470418199 
Product Code:  STML/23.E 
List Price:  $34.00 
Individual Price:  $27.20 

Book DetailsStudent Mathematical LibraryVolume: 23; 2003; 148 ppMSC: Primary 05;
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 exclusioninclusion principle. In the final chapter, the author describes applications to enumeration of trees, plane graphs, and graphs embedded in twodimensional 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 onesemester undergraduate course in combinatorics.ReadershipAdvanced undergraduates, graduate students, and research mathematicians interested in modern methods of combinatorics.

Table of Contents

Chapters

Chapter 1. Formal power series and generating functions. Operations with formal power series. Elementary generating functions

Chapter 2. Generating functions for wellknown sequences

Chapter 3. Unambiguous formal grammars. The Lagrange theorem

Chapter 4. Analytic properties of functions represented as power series and their asymptotics of their coefficients

Chapter 5. Generating functions of several variables

Chapter 6. Partitions and decompositions

Chapter 7. Dirichlet generating functions and the inclusionexclusion principle

Chapter 8. Enumeration of embedded graphs

Final and bibliographical remarks


Reviews

A crisp and sophisticated text … More examples than general theory. Covers standard material, but digs deeper … An enjoyable read for professionals.
MAA Monthly 
(This book) is driven by very, very interesting problems and examples.
MAA Reviews


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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 exclusioninclusion principle. In the final chapter, the author describes applications to enumeration of trees, plane graphs, and graphs embedded in twodimensional 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 onesemester undergraduate course in combinatorics.
Advanced undergraduates, graduate students, and research mathematicians interested in modern methods of combinatorics.

Chapters

Chapter 1. Formal power series and generating functions. Operations with formal power series. Elementary generating functions

Chapter 2. Generating functions for wellknown sequences

Chapter 3. Unambiguous formal grammars. The Lagrange theorem

Chapter 4. Analytic properties of functions represented as power series and their asymptotics of their coefficients

Chapter 5. Generating functions of several variables

Chapter 6. Partitions and decompositions

Chapter 7. Dirichlet generating functions and the inclusionexclusion principle

Chapter 8. Enumeration of embedded graphs

Final and bibliographical remarks

A crisp and sophisticated text … More examples than general theory. Covers standard material, but digs deeper … An enjoyable read for professionals.
MAA Monthly 
(This book) is driven by very, very interesting problems and examples.
MAA Reviews