  We prove a generalization of Kirchhoff's matrix-tree theorem in which a large
class of combinatorial objects are represented by non-Gaussian Grassmann
integrals. As a special case, we show that unrooted spanning forests, which
arise as a q \to 0 limit of the Potts model, can be represented by a Grassmann
theory involving a Gaussian term and a particular bilocal four-fermion term. We
show that this latter model can be mapped, to all orders in perturbation
theory, onto the N-vector model at N=-1 or, equivalently, onto the sigma-model
taking values in the unit supersphere in R^{1|2}. It follows that, in two
dimensions, this fermionic model is perturbatively asymptotically free.
