组合论(英文影印版)
出版时间:2011年版
内容简介
《组合论(英文影印版)》是一部介绍组合数的入门书籍,几乎包括了枚举和序论的全部内容。框架脉络清晰,第一部分讲述了映射和偏序集的;第二部分讲述枚举;第三部分讲述序理论方面。将枚举组合数在一个强有力的代数的框架内解释清楚是本书一大特色,非常值得一读。书中将代数中许多比较熟悉的结果再次纳入本书的范围,使得本书的可读性更强,内容结构更完整。读者对象:数学专业的研究生,教师和相关的科研人员。
目录
preliminaries
1. sets
2. graphs
3. posets
4. miscellaneous notation
chapter ⅰ mappings
1. classes of mappings
2. fundamental orders
3. permutations
4. patterns
notes
chapter ⅱ lattices
1. distributive lattices
2. modular and semimodular lattices
3. geometric lattices
4. the fundamental examples
notes
chapter ⅲ counting functions
1. the elementary counting coefficients
2. recursion and inversion
3. binomial sequences
4. order functions
notes
chapter ⅳ incidence functions
1. the incidence algebra
2. m6bius inversion
3. the m6bius function
4. valuations
notes
chapter ⅴ generating functions
1. ordered structures
2. unordered structures
3. g-patterns
4. g,h-patterns
notes
chapter ⅵ matroids: introduction
1. fundamental concepts
2. fundamental examples
3. construction of matroids
4. duality and connectivity
notes
chapter ⅶ matroids: further theory
1. linear matroids
2. binary matroids
3. graphic matroids
4. transversal matroids
notes
chapter ⅷ combinatorial order theory
1. maximum-minimum theorems
2. transversal theorems
3. sperner theorems
4. ramsey theorems
notes
bibliography
list of symbols
subject index