2018/12/19 by Wei Bang Li, Li, Wei-Bang, Shu Chiuan Chang +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Graph theory and applications #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1812.08060
openalex publication_date 2018/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the number of dimer-monomers Md(n) on the Tower of Hanoi graphs THd(n) at stage n with dimension d equal to 3 and 4. The entropy per site is defined as zTHd=limv → ∞ ln Md(n)/v, where v is the number of vertices on THd(n). We obtain the lower and upper bounds of the entropy per site, and the convergence of these bounds approaches to zero rapidly when the calculated stage increases. The numerical value of zTHd is evaluated to more than a hundred digits correct. Using the results with d less than or equal to 4, we predict the general form of the lower and upper bounds for zTHd with arbitrary d.