Spanning Trees on Hypercubic Lattices and Non-orientable Surfaces

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dc.creatorTzeng, W. -J.
dc.creatorWu, F. Y.
dc.date2000-01-27
dc.date.accessioned2026-07-07T06:25:54Z
dc.date.available2026-07-07T06:25:54Z
dc.descriptionWe 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.
dc.descriptionlatex, 9 pages, no figures, to appear in Lett. Appl. Math
dc.identifierhttps://arxiv.org/abs/cond-mat/0001408
dc.identifierhttp://arxiv.org/abs/cond-mat/0001408
dc.identifierAppl. Math. Letters 13 (6), 19-25 (2000).
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/96960
dc.subjectStatistical Mechanics
dc.subjectCombinatorics
dc.titleSpanning Trees on Hypercubic Lattices and Non-orientable Surfaces
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