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Spanning Trees on Hypercubic Lattices and Non-orientable Surfaces | | W.-J. Tzeng
; F. Y. Wu
; | | Date: |
27 Dec 1999 | | Subject: | Statistical Mechanics; Combinatorics | cond-mat.stat-mech math.CO | | 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. | | Source: | arXiv, cond-mat/0001408 | | Services: | Forum | Review | PDF | Favorites | |
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