Some exact results for spanning trees on lattices

For n-vertex, d-dimensional lattices Λ with d ≥ 2, the number of spanning trees N_ST(Λ) grows asymptotically as exp(nz _Λ) in the thermodynamic limit. We present an exact closed-form result for the asymptotic growth constant z_bcc(d) for spanning trees on the d-dimensional body-centred cubic lattice. We also give an exact integral expression for z_fcc on the face-centred cubic lattice and an exact closed-form expression for z₄₈₈ on the 4 8 8 lattice.