Exponential Growth Constants for Spanning Forests on Archimedean Lattices: Values and Comparisons of Upper Bounds

Abstract

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