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Lectures on Generating Functions
By Sergei K. Lando
Lectures on Generating Functions
By Sergei K. Lando
Published by AMS Bookstore, 2003
ISBN 0821834819, 9780821834817
148 pages
This book, based on the course given by the author at the College of Mathematics of the Independent University of Moscow, introduces the reader to the language of generating functions, which is nowadays the main language of enumerative combinatorics. It 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 theexclusion-inclusion principle. In the final chapter, the author describes applications of generating functions to enumeration of trees, plane graphs, and graphs embedded in two-dimensional surfaces. Throughout the book, the reader is motivated by interesting examples rather than by general theories. It alsocontains a lot of exercises to help the reader master the material. Little beyond the standard calculus course is necessary to understand the book. It can serve as a text for a one-semester undergraduate course in combinatorics.
By Sergei K. Lando
Lectures on Generating Functions
By Sergei K. Lando
Published by AMS Bookstore, 2003
ISBN 0821834819, 9780821834817
148 pages
This book, based on the course given by the author at the College of Mathematics of the Independent University of Moscow, introduces the reader to the language of generating functions, which is nowadays the main language of enumerative combinatorics. It 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 theexclusion-inclusion principle. In the final chapter, the author describes applications of generating functions to enumeration of trees, plane graphs, and graphs embedded in two-dimensional surfaces. Throughout the book, the reader is motivated by interesting examples rather than by general theories. It alsocontains a lot of exercises to help the reader master the material. Little beyond the standard calculus course is necessary to understand the book. It can serve as a text for a one-semester undergraduate course in combinatorics.
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