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

TL;DR

This paper compares new upper bounds on the exponential growth constants for spanning forests on Archimedean lattices with existing bounds, demonstrating that the new bounds are significantly tighter and closer to actual values.

Contribution

The paper introduces improved upper bounds for the exponential growth constants of spanning forests on Archimedean lattices, outperforming recent bounds in accuracy.

Findings

New upper bounds are very close to calculated values.

Improved bounds are significantly better than recent upper bounds.

Results enhance understanding of spanning forest growth on Archimedean lattices.

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.