具有多个顶点的二维格上的生成树
Spanning Trees on the Two-Dimensional Lattices with More Than One Type of Vertex
摘要：
对于具有$n$顶点的二维格点$Λ$，生成树$N_{ST}(Λ)$的数目在热力学极限下渐近地增长为$\exp(n z_Λ)$。本文给出了\cite{Okeeffe}中给出的具有多种顶点的二维格上生成树的渐近增长常数$z_Λ$的精确积分表达式和数值。对于网14，导出了渐近增长常数的精确闭合表达式，网27和三角形格子的渐近增长常数具有简单的关系式$z_{27} = (z_{tri}+\ln 4)/4$ .还得到了一些积分恒等式。
英文摘要：
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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