We compare our upper bounds on the exponential growth constant ϕ(Λ) characterizing the asymptotic behavior of spanning forests on Archimedean lattices Λ with recently derived upper bounds.Our upper bounds on ϕ(Λ), which are very close to the respective values of ϕ(Λ) that we have calculated, are shown to be significantly better for these lattices than the new upper bounds.

中文翻译：

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阿基米德格上跨越森林的指数增长常数：上界的值和比较

我们比较了指数增长常数的上限φ(Λ)表征阿基米德格上跨越森林的渐近行为Λ与最近派生的上限。我们的上限φ(Λ), 非常接近各自的值φ(Λ)我们计算出来的结果显示，这些晶格比新的上限要好得多。