论文标题
跨越森林的渐近行为和二维晶格上的跨度子图的渐近行为
Asymptotic Behavior of Spanning Forests and Connected Spanning Subgraphs on Two-Dimensional Lattices
论文作者
论文摘要
我们计算指数增长常数$ ϕ $和$σ$，描述了跨越森林的渐近行为和在带图上的跨越子图的渐近行为，其任意长度，包括几个二维晶格，包括正方形，三角形，蜜蜂，蜜蜂，以及某些杂质的杂物型杂物。通过研究限制值，随着条带宽度变大，我们可以推断出各自无限晶格的这些指数生长常数的下限和上限。由于我们的下限和上限非常接近，因此我们可以推断出这些指数增长常数非常准确的近似值，其分数不确定性从$ O（10^{ - 4}）$到$ O（10^{ - 2}）$。我们表明，对于这些晶格而言，$ ϕ $和$σ$是单调增加的顶点学位功能。
We calculate exponential growth constants $ϕ$ and $σ$ describing the asymptotic behavior of spanning forests and connected spanning subgraphs on strip graphs, with arbitrarily great length, of several two-dimensional lattices, including square, triangular, honeycomb, and certain heteropolygonal Archimedean lattices. By studying the limiting values as the strip widths get large, we infer lower and upper bounds on these exponential growth constants for the respective infinite lattices. Since our lower and upper bounds are quite close to each other, we can infer very accurate approximate values for these exponential growth constants, with fractional uncertainties ranging from $O(10^{-4})$ to $O(10^{-2})$. We show that $ϕ$ and $σ$, are monotonically increasing functions of vertex degree for these lattices.
