Learning Combinatorial Species.

Question

I have been reading the book conceptual mathematics(first edition) and I'm also about halfway through Diestel's Graph theory (4th edition). I was wondering if I was able to start learning about combinatorial species. This is very interesting to me because I love combinatorics and it makes direct use of category therory.

Also, what are some good resources to understand the main ideas behind the area and understand the juciest part of it?

Regards, and thanks to Anon who told me about this area of math.

Flajolet & Sedgewick, Analytic Combinatorics, actually does quite a bit early on with what amount to combinatorial species without actually using the term or any category theory. — Brian M. Scott, Apr 10 '13 at 20:44

score 7 · Answer 1 · answered Jun 16 '14 at 05:06

7

Applied Finite Group Actions by Adalbert Kerber roots most of its theory in combinatorial species, and begins with their comprehensive and intuitive introduction in the first chapter.

answered Jun 16 '14 at 05:06

Alexander Gruber

26,963

score 6 · Answer 2 · edited Aug 07 '17 at 08:02

6

For an easy to understand introduction, http://dept.cs.williams.edu/~byorgey/pub/species-pearl.pdf seems to be nice. But it leans more towards the computer science applications.

edited Aug 07 '17 at 08:02

M. Vinay

9,004

answered Apr 10 '13 at 20:00

Jonathan Gallagher

241

Thank you for pointing out that paper. Here's a very amusing, interesting, and informative talk based on the paper: https://vimeo.com/16753644. – M. Vinay Aug 07 '17 at 08:10
The link is broken. This is the article -- https://dl.acm.org/citation.cfm?id=1863542 – NonalcoholicBeer Sep 20 '18 at 11:59

score 6 · Accepted Answer · edited Apr 13 '17 at 12:20

Strictly speaking, my impression is that only a rudimentary understand of graphs is necessary to work with species. My potential interest in them is the convergence of my interest in group actions, generating functions, and basic category theory, and I think you'd want to have a basic working knowledge of all three of those areas. I imagine you could learn them as-you-go while studying species. I link to my favorite resource on the topic in this recent answer, among other things.

As a disclaimer, I haven't actually had the time to study this stuff. It's just on the bucket list, and it's something I've skimmed over to see if it's something I'd be interested in.

score 3 · Answer 4 · answered Dec 20 '23 at 16:14

3

A nice introduction to the use of combinatorial species in graphical enumeration is Combinatorial Species and Graph Enumeration by Andy Hardt, Pete McNeely,Tung Phan, and Justin M. Troyka, arXiv:1312.0542 [math.CO].

answered Dec 20 '23 at 16:14

Ira Gessel

285

Learning Combinatorial Species.

4 Answers4

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