本书向读者介绍了生成函数的语言，它是当今计数组合学的主要语言。本书从定义、简单的属性和许多生成函数的例子开始。然后讨论了形式语法、多变量生成函数、分拆和分解以及容斥原理等主题。在最后一章中，作者描述了树、平面图和嵌入在二维曲面中的图的计数应用。 在全书中，作者通过提供有趣的例子而不是一般理论来激发读者的兴趣。本书包含许多练习来帮助学生学习。唯一的先决条件是一门标准的微积分课程。本书是一学期的组合数学本科课程的优秀教材。

前辅文
Preface to the English Edition
  Preface
Chapter 1. Formal Power Series and Generating Functions.Operations with Formal Power Series. Elementary Generating Functions
  §1.1. The lucky tickets problem
  §1.2. First conclusions
  §1.3. Generating functions and operations with them
  §1.4. Elementary generating functions
  §1.5. Differentiating and integrating generating functions
  §1.6. The algebra and the topology of formal power series
  §1.7. Problems
Chapter 2. Generating Functions for Well-known Sequences
  §2.1. Geometric series
  §2.2. The Fibonacci sequence
  §2.3. Recurrence relations and rational generating functions
  §2.4. The Hadamard product of generating functions
  §2.5. Catalan numbers
  §2.6. Problems
Chapter 3. Unambiguous Formal Grammars. The Lagrange Theorem
  §3.1. The Dyck Language
  §3.2. Productions in the Dyck language
  §3.3. Unambiguous formal grammars
  §3.4. The Lagrange equation and the Lagrange theorem
  §3.5. Problems
Chapter 4. Analytic Properties of Functions Represented as Power Series and the Asymptotics of their Coefficients
  §4.1. Exponential estimates for asymptotics
  §4.2. Asymptotics of hypergeometric sequences
  §4.3. Asymptotics of coefficients of functions related by the Lagrange equation
  §4.4. Asymptotics of coefficients of generating series and singularities on the boundary of the disc of convergence
  §4.5. Problems
Chapter 5. Generating Functions of Several Variables
  §5.1. The Pascal triangle
  §5.2. Exponential generating functions
  §5.3. The Dyck triangle
  §5.4. The Bernoulli–Euler triangle and enumeration of snakes
  §5.5. Representing generating functions as continued fractions
  §5.6. The Euler numbers in the triangle with multiplicities
  §5.7. Congruences in integer sequences
  §5.8. How to solve ordinary differential equations in generating functions
  §5.9. Problems
Chapter 6. Partitions and Decompositions
  §6.1. Partitions and decompositions
  §6.2. The Euler identity
  §6.3. Set partitions and continued fractions
  §6.4. Problems
Chapter 7. Dirichlet Generating Functions and the Inclusion-Exclusion Principle
  §7.1. The inclusion-exclusion principle
  §7.2. Dirichlet generating functions and operations with them
  §7.3. M¨obius inversion
  §7.4. Multiplicative sequences
  §7.5. Problems
Chapter 8. Enumeration of Embedded Graphs
  §8.1. Enumeration of marked trees
  §8.2. Generating functions for non-marked, marked,ordered, and cyclically ordered objects
  §8.3. Enumeration of plane and binary trees
  §8.4. Graph embeddings into surfaces
  §8.5. On the number of gluings of a polygon
  §8.6. Proof of the Harer–Zagier theorem
  §8.7. Problems
Final and Bibliographical Remarks
Bibliography
Index