Spanning Trees on Hypercubic Lattices and Non-orientable Surfaces

Preprint

27 January 2000

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.cond-mat/0001408

Abstract

We consider the problem of enumerating spanning trees on lattices. Closed-form expressions are obtained for the spanning tree generating function for a hypercubic lattice of size N_1 x N_2 x...x N_d in d dimensions under free, periodic, and a combination of free and periodic boundary conditions. Results are also obtained for a simple quartic net embedded on two non-orientable surfaces, a Moebius strip and the Klein bottle. Our results are based on the use of a formula expressing the spanning tree generating function in terms of the eigenvalues of an associated tree matrix. An elementary derivation of this formula is given.

Keywords

ORIENTABLE SURFACES
HYPERCUBIC LATTICE
TREE GENERATING
SPANNING TREE
EIGENVALUES
LATTICES
FORMULA

All Related Versions

Version 1, 2000-01-27, ArXiv

This publication has 0 references indexed in Scilit: