Path count asymptotics and Stirling numbers
K. Petersen, A. Varchenko
TL;DR
This paper derives formulas for counting paths in infinite Eulerian graphs and uncovers identities linking Stirling numbers of both kinds, advancing combinatorial enumeration methods.
Contribution
It introduces new formulas for path growth rates in infinite graphs and establishes novel identities between Stirling numbers of the first and second kinds.
Findings
Formulas for path count asymptotics in infinite Eulerian graphs
Identities relating Stirling numbers of the first and second kinds
Enhanced understanding of combinatorial structures in graph theory
Abstract
We obtain formulas for the growth rate of the numbers of certain paths in infinite graphs built on the two-dimensional Eulerian graph. Corollaries are identities relating Stirling numbers of the first and second kinds.
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Taxonomy
TopicsGraph theory and applications · Stochastic processes and statistical mechanics · Advanced Combinatorial Mathematics