Description
Book SynopsisIntroduces readers to the language of generating functions, which is the main language of enumerative combinatorics. This book starts with definitions, simple properties, and many examples of generating functions. It discusses topics such as formal grammars, generating functions in several variables, and the exclusion-inclusion principle.
Table of ContentsFormal 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.
