[kmill]

This reminds me somewhat of Stanley's symmetric chromatic function, which I guess came about ten years later (1995). Actually, what you're describing seems to be something I rediscovered a couple years ago, where P_k is interpreted as the kth power sum symmetric polynomial in n variables.

I'd be interested in learning more about your invariant. Do you have a copy of your thesis anywhere?

[ColinWright]

I might have a soft copy of the thesis, but I can only guarantee hard copy. If you're interested then the best thing to do is email me so it goes into my work queue, then I can have a quick hunt and see what I can produce easily.

Email(s) in my profile.