计数组合学
Enumerative combinatorics
Richard P. Stanley · 初版 1986 年
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出版商简介（未经编辑的出版商数据）这部两卷本枚举组合学基础导论的第二卷涵盖生成函数的复合、树、代数生成函数、D-有限生成函数、非交换生成函数以及对称函数。关于对称函数的一章提供了唯一适合组合学研究生入门课程的该主题论述，并包含重要的 Robinson-Schensted-Knuth 算法。书中还涉及对称函数与表示之间的联系
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Lovasz 的《Combinatorial Problems and Exercises》。除了主题更聚焦的《Generatingfunctionology》（Wilf）和已经提到的《Enumerative Combinatorics》（Stanley）之外，关于更进阶的导论性组合数学书籍我了解得不多。
Combinatorial Problems and Exercises by Lovasz I don't know much in the way of more advanced expository combinatorics books, other than the more narrow Generatingfunctionology (Wilf) and the already mentioned Enumerative Combinatorics (Stanley).
……与加法组合学直接相关。分析学背景会很有用，比如施坦因和沙卡奇那套教材里的内容。学一些组合学入门知识也会有帮助（比如斯坦利的《计数组合学》，或者范林特和威尔逊的书）。最后，解析数论也很值得一学。比如你可以读读达文波特的《乘法数论》。（特别是如果你想看看积分是如何在……出现的
…directly relevant to additive combinatorics. Analysis background would be useful, such as to be found in Stein and Shakarchi's series. Some introductory combinatorics would also be good (e.g. Stanley's Enumerative Combinatorics, or Van Lint and Wilson). Finally, analytic number theory would also be good to learn. For example, you might read Davenport's Multiplicative Number Theory. (Especially if you want to see integrals come…
有几个相当大的细分领域，不过大多数都有经典教材覆盖。这里列举几本：经典计数组合学方面，有理查德·斯坦利的《计数组合学》（Enumerative Combinatorics）。图论方面，迪斯特尔的《图论》（Graph Theory）在入门课程中很受欢迎，而鲍洛巴什的《现代图论》（Modern Graph Theory）则更进阶，且……
There are a few quite large sub-fields, but there are classic textbooks covering most of these. Here are some: For classical enumerative combinatorics, there is Richard Stanley's 'Enumerative Combinatorics'. For graph theory, Diestel's book 'Graph Theory' is popular for introductory courses, and Bollobas' 'Modern Graph Theory' is more advanced and…
经典的建议是布鲁阿尔迪的书，还有理查德·斯坦利的《计数组合学》http://www-math.mit.edu/~rstan/ec/ ，不过我现在正从S.吉尔·威廉森的《组合学基础及应用》的基础部分学起。我不排斥纯理论推导，但我需要能用在实际编程上的……
The classic suggestion is Brualdi, there's also R. Stanley Enumerative Combinatorics http://www-math.mit.edu/~rstan/ec/ but right now I'm starting with basics on S. Gill Williamson Foundations of Combinatorics with Application. I don't mind pure reasoning, but I need practical programming…
你指的是勒鲁和拉贝尔写的这本书吗？http://bergeron.math.uqam.ca/species/ （前3章：http://bergeron.math.uqam.ca/wp-content/uploads/2013/11/book...）《计数组合学》是另一位作者（理查德·P·斯坦利，https://en.wikipedia.org/wiki/Richard_P._Stanley）写的完全不同的另一本书。
You mean this book by Leroux and Labelle? http://bergeron.math.uqam.ca/species/ (First 3 chapters: http://bergeron.math.uqam.ca/wp-content/uploads/2013/11/book...) "Enumerative Combinatorics" is a different book by a different author (Richard P. Stanley, https://en.wikipedia.org/wiki/Richard_P._Stanley).
……纯数学中的“代数”概念，与计算机科学中的有限状态机和下推自动机是一一对应的。研究这些最简便的工具就是母函数（generating functions）。正如理查德·斯坦利在《计数组合学》第二卷中所解释的，除了代数母函数之外还有第三类：D-有限（D-Finite）。粗略来说，这对应于在常微分方程（ODE）中如何把微分方程的解展开为幂级数。……
…"algebraic" from pure mathematics match up with finite state machines and push-down automata from computer science. One studies these most easily using generating functions. As Richard Stanley explains in Enumerative Combinatorics Vol. 2, there's a third class of generating functions beyond algebraic: D-Finite. Roughly, this corresponds to how one learns to expand the solution to a differential equation in ODEs as a power series.…