## Abstract

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 language | English |
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Article number | 1950043 |

Journal | International Journal of Modern Physics B |

Volume | 33 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2019 Mar 20 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Condensed Matter Physics