图书信息
图书目录
生成函数讲义（影印版）
暂无简介
作者：
S. K. Lando
定价：
99.00元
出版时间：
2020-04-22
ISBN：
978-7-04-053500-6
物料号：
53500-00
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
重点项目：
暂无
版面字数：
270.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
- 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
