Introduction to Enumerative and Analytic Combinatorics
Introduction to Enumerative and Analytic Combinatorics
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枚举和解析组合学简介
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发表时间：
2015
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通讯作者：
M. Bóna
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作者：
M. Bóna
当我们添加添加时，当我们划分基本计数原理的应用时，方法乘以鸽洞原理注释章节审查解决方案的补充方法和组成的应用程序练习练习多组和组成设置分区的分区，将练习解决方案，十二折言注释注释章节评论练习解决方案补充练习产生功能功能系列热身：求解复发关系产生功能的产生功能的构成产生函数的组成，一种不同类型的生成功能，章节审查练习解决方案练习解决练习的补充锻炼主题，计数eulererian dubmutation ulererian nubmitation eulererian dumbere eulerian nubmistion eulererian nubmita排列周期结构的周期结构和指数生成函数反转的高级应用程序，将功能生成置换枚举枚举注释注释章节审查练习解决方案，以练习补充练习计算图形和森林的图形和函数，当顶点没有在彩色的Vertices图形和图形图上和图形上自由地标记图形生成功能注释章节回顾练习解决方案，以练习补充练习极端组合学的极端图理论超图超图：存在更重要的是：存在证明注释注释章节审查练习解决方案的练习补充练习的补充方法分析分析型指数增长速度增长速度更精确的精确性审查章节综述章节章节章节分章章节章节章节练习解决方案的练习补充练习特殊主题对称结构设计有限的投影平面错误校正校正代码计数计算对称结构的对称结构注释，章节审查练习解决方案的练习补充锻炼序列序列序列序列序列序列序列序列典型性登记逻辑，计算魔法正方形和魔法立方体一个分布问题固定尺寸的魔法魔法正方形固定线的魔法平方。
METHODS Basic methods When we add and when we subtract When we multiply When we divide Applications of basic counting principles The pigeonhole principle Notes Chapter review Exercises Solutions to exercises Supplementary exercises Applications of basic methods Multisets and compositions Set partitions Partitions of integers The inclusion-exclusion principle The twelvefold way Notes Chapter review Exercises Solutions to exercises Supplementary exercises Generating functions Power series Warming up: Solving recurrence relations Products of generating functions Compositions of generating functions A different type of generating functions Notes Chapter review Exercises Solutions to exercises Supplementary exercises TOPICS Counting permutations Eulerian numbers The cycle structure of permutations Cycle structure and exponential generating functions Inversions Advanced applications of generating functions to permutation enumeration Notes Chapter review Exercises Solutions to exercises Supplementary exercises Counting graphs Trees and forests Graphs and functions When the vertices are not freely labeled Graphs on colored vertices Graphs and generating functions Notes Chapter review Exercises Solutions to exercises Supplementary exercises Extremal combinatorics Extremal graph theory Hypergraphs Something is more than nothing: Existence proofs Notes Chapter review Exercises Solutions to exercises Supplementary exercises AN ADVANCED METHOD Analytic combinatorics Exponential growth rates Polynomial precision More precise asymptotics Notes Chapter review Exercises Solutions to exercises Supplementary exercises SPECIAL TOPICS Symmetric structures Designs Finite projective planes Error-correcting codes Counting symmetric structures Notes Chapter review Exercises Solutions to exercises Supplementary exercises Sequences in combinatorics Unimodality Log-concavity The real zeros property Notes Chapter review Exercises Solutions to exercises Supplementary exercises Counting magic squares and magic cubes A distribution problem Magic squares of fixed size Magic squares of fixed line sum Why magic cubes are different Notes Chapter review Exercises Solutions to exercises Supplementary exercises Appendix: The method of mathematical induction Weak induction Strong induction