Dimer coverings on the Tower of Hanoi graph

Wei Bang Li, Shu Chiuan Chang

Research output: Contribution to journalArticlepeer-review


We present the number of dimer coverings N d (n) on the Tower of Hanoi graph TH d (n) at n stage with dimension 2 ≤d ≤ 5. When the number of vertices v(n) is even, N d (n) gives the number of close-packed dimers; when the number of vertices is odd, it is impossible to have a close-packed configurations and one of the outmost vertices is allowed to be unoccupied. We define the entropy of absorption of diatomic molecules per vertex as STH d=limn→∞ln N d (n)/v(n), that can be shown exactly for TH 2 , while its lower and upper bounds can be derived in terms of the results at a certain n for TH d (n) with 3 ≤d ≤ 5. We find that the difference between the lower and upper bounds converges rapidly to zero as n increases, such that the value of STH d with d=3 and 5 can be calculated with at least 100 correct digits.

Original languageEnglish
Article number1950043
JournalInternational Journal of Modern Physics B
Issue number7
Publication statusPublished - 2019 Mar 20

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Condensed Matter Physics


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