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Some Exact Results for Spanning Trees on Lattices

Shu-Chiuan Chang·Robert Shrock
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Abstract

For $n$-vertex, $d$-dimensional lattices $Λ$ with $d \ge 2$, the number of spanning trees $N_{ST}(Λ)$ grows asymptotically as $\exp(n z_Λ)$ in the thermodynamic limit. We present an exact closed-form result for the asymptotic growth constant $z_{bcc(d)}$ for spanning trees on the $d$-dimensional body-centered cubic lattice. We also give an exact integral expression for $z_{fcc}$ on the face-centered cubic lattice and an exact closed-form expression for $z_{488}$ on the $4 \cdot 8 \cdot 8$ lattice.

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Shu-Chiuan Chang, Robert Shrock. 2006-02-24. Some Exact Results for Spanning Trees on Lattices. https://doi.org/10.1088/0305-4470%2F39%2F20%2F001

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