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I'm currently attending a somewhat disorganized seminar on combinatorics that follows no textbook. So far we have covered the orbit-stabilizer theorem, some recursion, and we're heading into the Möbius inversion formula.

Can anyone suggest a text that approaches combinatorics at this level for a 2nd-3rd year undergrad who already knows some algebra and the more basic combinatorics like combinations, permutations, stars-and-bars, generating functions? Most introductory combinatorics books I've found are more suited to a discrete math class and cover stuff which I already know. I'm looking for something to supplement this lecture. Thank you.

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    You would probably be interested in this:http://math.stackexchange.com/questions/6245/good-resources-book-or-otherwise-to-learn-study-basic-combinatorics/6246#62462011-02-12

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I can't say I can predict what direction your seminar will head in, but an amazing one-stop-shop for combinatorics is Richard Stanley's Enumerative Combinatorics (both volumes). You will learn a tremendous amount if you get through both of these (and the revised version of volume 1 is currently available online!). In particular Volume I has a thorough discussion of Möbius inversion.

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I did a reading course in Combinatorics while a PhD student, and we used van Lint and Wilson which I thought was very hard, but very good. You don't need any more background than you already have, and you will learn a ton from this text.

It's definitely not as well-known as the other suggested texts, but it many ways it's superior. (Although Concrete Mathematics is a better book overall for its sheer beauty.)

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    I second van Lint and Wilson. It is structured as a menu of stand alone topics, but hits the full range of them (but at a little past intermediate level).2011-04-05
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I think Stanley's Enumerative Combinatorics is not an "intermediate" level book, it's the canonical advanced book on combinatorics.

I'd recommend Aigner's "A Course on Enumeration" (from Springer's GTM series) for a lighter level (but certainly beyond apples and oranges) go A Walk Through Combinatorics (Miklos Bona) or Combinatorics: Topics, Techcniques and Algorithms (Cameron)

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    Yes, Introduction to Enumerative Combinatorics is great too, but as you $p$oint, a bit harder. I find for example, generating funcions and matchings are better covered here that on Walkthrough, but it quickly goes into specialized topics you might not be as interested unless you're particularly into combinatorics2011-04-07
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If you read French, you must read Analyse Combinatoire of L. Comtet at PUF edition. It's two short books full of fascinating materials.

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    In English it's *Advanced Combinatorics* and is definitely worth a look.2011-02-12
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How about Concrete Mathematics?

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    I love GKP's 'Concrete Mathematics' but it covers a very particular subarea of combinatorics, and fran$k$ly is more like applied algebraic manipulation. That is, it is a very narrow view of combinatorics, hardly a mention of graphs, designs, or partial orders.2011-04-05