Intermediate Text in Combinatorics?

Question

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.

Answer 1

If you read French, you must read Analyse Combinatoire of L. Comtet at PUF edition. It's two short books full of fascinating materials.

Answer 2

How about Concrete Mathematics?

Answer 3

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.

Answer 4

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 (Miklós Bóna) or Combinatorics: Topics, Techniques and Algorithms (Cameron).

Answer 5

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.)