Suppose G is some finite group acting on the set A, with the special condition that each element of G fixes n points of A. Then we can write n(|G|-1) = \sum_{a \in A}{(S_G(a)-1). (Counting the non-identity elements of G in two different ways.)

Now this formula strongly resembles the Riemann-Hurwiz formula, which relates the Euler characteristics of two Riemann surfaces M_1\to M_2, one of which is a degree n ramified covering of the other : we then have have \chi(M_1)=N\chi(M_2)-\sum_{p \in M_1} (r_{p} -1), where r_p is the ramification index at p.

Are these formulas related directly?