Existence of an exponential growth limit for |(n)|

Establish the existence of the limit δ = lim_{n → ∞} (|(n)|)^{1/n}, where (n) denotes the set of numbers of spanning trees of connected planar simple graphs on n vertices.

Background

The quantity |(n)| counts distinct spanning tree numbers realized by connected planar simple graphs on n vertices. The paper proves exponential lower bounds and discusses upper bounds, suggesting that a limiting exponential growth rate δ should exist. The conjecture formalizes this by positing the existence of δ.

References

Conjecture\label{conj:set-limit} There is a limit δ := \lim_{n \to \infty} \big(|(n)|\big)^{{\frac{1}{n}}.}

— Spanning trees and continued fractions (2411.18782 - Chan et al., 27 Nov 2024) in Section 5.2 (Final remarks), Conjecture 5.1

Existence of an exponential growth limit for |(n)|

Background

References

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