Name: Enumerative combinatorics
ISBN: 9780534065461

Enumerative combinatorics

Publisher Description (unedited publisher data) This second volume of a two-volume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, D-finite generating functions, noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course on combinatorics, and includes the important Robinson-Schensted-Knuth algorithm. Also covered are connections between symmetric functions and representation theory. An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory, including jeu de taquin and the Littlewood-Richardson rule. As in Volume 1, the exercises play a vital role in developing the material. There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference. Library of Congress subject headings for this publication: Combinatorial enumeration problems.

What Hacker News says

impendiaDec 2019

If you want to understand Peluse's paper, I think the most directly relevant background reading would be Tao and Vu's Additive Combinatorics.

Dummit and Foote's Abstract Algebra is an excellent book -- even if not very 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 into the picture.)

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agumonkeyJul 2019

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 uses to at some point. (maybe joblessness anxiety showing)

I also have some graph books but since it relies on combinatorics rapidly ..

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harshrealityJul 2019

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).

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rjtobinAug 2015

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 (as the title says) modern.

And there is Laszlo Lovasz's fantastic 'Combinatorial Problems and Exercises', which is a collection of problems and answers, and is a great way to get a feel for the subject.

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082349872349872Aug 2023

> The goal of this document is to describe a single APL primitive to both count and generate various Combinatorial Arrays: permutations, combinations, compositions, partitions, etc. The unifying (and very APL-like) principle for such a primitive is Gian-Carlo Rota's Twelvefold Way as described in Richard Stanley's "Enumerative Combinatorics", Knuth’s TAoCP, Vol. 4A, and Wikipedia among other references.

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SyzygiesAug 2022

So, what's interesting about differential equations for someone who doesn't find analysis or physics particularly compelling? Say, a computer scientist with a greater love for discrete math?

Linear differential equations are a great introduction to eigenvalues. There's a chicken-and-egg problem understanding this, and it would be helpful to take ODEs and Linear Algebra together.

As I first read in Feller, generating functions are a formation that runs the full length of mathematics and beyond; the Laplace transform from ODEs is just a continuous version of a generating function.

As Marcel-Paul Schützenberger first made clear, the notions of "rational" and "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. The true significance of this class in both pure mathematics and computer science is poorly understood, but there's something clearly out there as significant as rational and algebraic. That is intrinsically fascinating.

When I see someone filling a blackboard with equations, I see someone flailing because they don't know what to do. The best math is simple, and can be expressed as philosophy, like recognizing this formation crossing the sky.

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