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arXiv · 0808.3041

Spanning Trees on the Two-Dimensional Lattices with More Than One Type of Vertex

Shu-Chiuan Chang
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Abstract

For a two-dimensional lattice $Λ$ with $n$ vertices, the number of spanning trees $N_{ST}(Λ)$ grows asymptotically as $\exp(n z_Λ)$ in the thermodynamic limit. We present exact integral expression and numerical value for the asymptotic growth constant $z_Λ$ for spanning trees on various two-dimensional lattices with more than one type of vertex given in \cite{Okeeffe}. An exact closed-form expression for the asymptotic growth constant is derived for net 14, and the asymptotic growth constants of net 27 and the triangle lattice have the simple relation $z_{27} = (z_{tri}+\ln 4)/4$. Some integral identities are also obtained.

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Shu-Chiuan Chang. 2008-08-22. Spanning Trees on the Two-Dimensional Lattices with More Than One Type of Vertex. https://doi.org/10.1088/1751-8113%2F42%2F1%2F015208

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