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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.

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    $\begingroup$ 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. $\endgroup$ Apr 10, 2013 at 20:44

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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.

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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.

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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.

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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].

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