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Lectures on Generating Functions

S. K. Lando Independent University of Moscow, Moscow, Russia
Available Formats:
Softcover ISBN: 978-0-8218-3481-7
Product Code: STML/23
List Price: $37.00 Individual Price:$29.60
Electronic ISBN: 978-1-4704-1819-9
Product Code: STML/23.E
List Price: $34.00 Individual Price:$27.20
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List Price: $55.50 Click above image for expanded view Lectures on Generating Functions S. K. Lando Independent University of Moscow, Moscow, Russia Available Formats:  Softcover ISBN: 978-0-8218-3481-7 Product Code: STML/23  List Price:$37.00 Individual Price: $29.60  Electronic ISBN: 978-1-4704-1819-9 Product Code: STML/23.E  List Price:$34.00 Individual Price: $27.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$55.50
• Book Details

Student Mathematical Library
Volume: 232003; 148 pp
MSC: 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 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.

• Chapters
• Chapter 1. Formal power series and generating functions. Operations with formal power series. Elementary generating functions
• Chapter 2. Generating functions for well-known 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 inclusion-exclusion 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 232003; 148 pp
MSC: 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 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.

• Chapters
• Chapter 1. Formal power series and generating functions. Operations with formal power series. Elementary generating functions
• Chapter 2. Generating functions for well-known 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 inclusion-exclusion 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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.