组合论

《组合论(英文)》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《组合论(英文)》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《组合论(英文)》的范围，使得《组合论(英文)》的可读性更强，内容结构更完整。

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