Intermediate Text in Combinatorics?

Solution 1:

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.

Solution 2:

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.)

Solution 3:

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)

Solution 4:

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