Some Exact Results for Spanning Trees on Lattices

الأصل · EN

For n-vertex, d-dimensional lattices Λ with d ≥ 2, the number of spanning trees NST(Λ) grows asymptotically as (n zΛ) in the thermodynamic limit. We present an exact closed-form result for the asymptotic growth constant zbcc(d) for spanning trees on the d-dimensional body-centered cubic lattice. We also give an exact integral expression for zfcc on the face-centered cubic lattice and an exact closed-form expression for z₄₈₈ on the 4 · 8 · 8 lattice.