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生成函数讲义（影印版）

样章
作者：
S. K. Lando
定价：
99.00元
ISBN：
978-7-04-053500-6
版面字数：
270.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2020-04-22
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
组合数学与图论
暂无
  • 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

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