This paper marks the beginning of my investigations into various problems in equivariant enumerative geometry. From my perspective, it concerns the counting of point-configurations. By a point-configuration P, I mean a projective equivalence class of ordered n-tuple of points in projective space P^r. Now suppose that one has a family of point configurations over a base variety B, meaning a P^r bundle over B together with n chosen sections. Assuming B is the right dimension for the question to make sense, how many times does this family visit a particular point-configuration P?

One of the main results of this paper states that the answer to this type of enumerative question is encoded by an explicit expression in characteristic classes of the P^r-bundle, and this expression is purely a function of the matroid of the point-configuration P being counted. Another way of phrasing the result is: We calculate the fundamental class of the point P in the quotient stack [ (P^r)^n / GL(r+1) ], and the answer is purely a function of the matroid of P!