Spanning Trees on Hypercubic Lattices and Non-orientable Surfaces Export

@misc{citeulike:2328365, 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.}, archivePrefix = {arXiv}, author = {Tzeng, W. J. and Wu, F. Y.}, citeulike-article-id = {2328365}, citeulike-linkout-0 = {http://arxiv.org/abs/cond-mat/0001408v1}, citeulike-linkout-1 = {http://arxiv.org/pdf/cond-mat/0001408v1}, comment = {* p.5 derivation of eigenvalues of circulant matrix}, day = {27}, eprint = {cond-mat/0001408v1}, keywords = {linear-algebra, resistance}, month = {Jan}, posted-at = {2008-02-04 05:54:48}, priority = {2}, title = {Spanning Trees on Hypercubic Lattices and Non-orientable Surfaces}, url = {http://arxiv.org/abs/cond-mat/0001408v1}, year = {2000} }

TY - ELEC ID - citeulike:2328365 L3 - citeulike-article-id:2328365 N2 - 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. TI - Spanning Trees on Hypercubic Lattices and Non-orientable Surfaces KW - linear-algebra KW - resistance N1 - * p.5 derivation of eigenvalues of circulant matrix AU - Tzeng, WJ AU - Wu, FY PY - 2000/Jan/27/ UR - http://arxiv.org/abs/cond-mat/0001408v1 ER -