Spanning trees on hypercubic lattices and nonorientable surfaces
نویسندگان
چکیده
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 N1×N2×· · ·×Nd 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 Möbius 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.
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ورودعنوان ژورنال:
- Appl. Math. Lett.
دوره 13 شماره
صفحات -
تاریخ انتشار 2000