Spanning trees and Lattice Green Functions
by Tony Guttmann
Abstract: By defining a spanning tree generating function (STGF), I make systematic a connection between spanning trees on a lattice, and lattice Green functions (LGF). This connection makes it possible to obtain new results for one or the other, an/or discover possibly new identities involving integrals of elliptic integrals and sums of binomial coefficients. New results for LGF in 2d, and d > 3 are obtained, as are new results for the spanning tree constant on various lattices.
This is work in progress, and accordingly the presentation will be erratic, incomplete and highly non-linear.
For More Information: contact: Iwan Jensen. email: I.Jensen@ms.unimelb.edu.au