Spanning Trees on Hypercubic Lattices and Non-orientable Surfaces
统计力学
2007-05-23 v1 组合数学
摘要
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.
引用
@article{arxiv.cond-mat/0001408,
title = {Spanning Trees on Hypercubic Lattices and Non-orientable Surfaces},
author = {W. -J. Tzeng and F. Y. Wu},
journal= {arXiv preprint arXiv:cond-mat/0001408},
year = {2007}
}
备注
latex, 9 pages, no figures, to appear in Lett. Appl. Math