Lectures on generating functions
著者
書誌事項
Lectures on generating functions
（Student mathematical library, v. 23）
American Mathematical Society, c2003
- タイトル別名
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Лекции о производящих функциях
Lekt︠s︡ii o proizvodi︠a︡shchikh funkt︠s︡ii︠a︡kh
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注記
Includes bibliographical references (p. 145-146) and index
Original Russian ed. published: [Russia] : МЦНМО, c2002
内容説明・目次
内容説明
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.
目次
Formal power series and generating functions. Operations with formal power series. Elementary generating functions Generating functions for well-known sequences Unambiguous formal grammars. The Lagrange theorem Analytic properties of functions represented as power series and their asymptotics of their coefficients Generating functions of several variables Partitions and decompositions Dirichlet generating functions and the inclusion-exclusion principle Enumeration of embedded graphs Final and bibliographical remarks Bibliography Index.
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