### 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 |
---|---|

Article number | 1950043 |

Journal | International Journal of Modern Physics B |

Volume | 33 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2019 Mar 20 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Condensed Matter Physics

### Cite this

*International Journal of Modern Physics B*,

*33*(7), [1950043]. https://doi.org/10.1142/S0217979219500437

}

*International Journal of Modern Physics B*, vol. 33, no. 7, 1950043. https://doi.org/10.1142/S0217979219500437

**Dimer coverings on the Tower of Hanoi graph.** / Li, Wei Bang; Chang, Shu Chiuan.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Dimer coverings on the Tower of Hanoi graph

AU - Li, Wei Bang

AU - Chang, Shu Chiuan

PY - 2019/3/20

Y1 - 2019/3/20

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85062348353&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062348353&partnerID=8YFLogxK

U2 - 10.1142/S0217979219500437

DO - 10.1142/S0217979219500437

M3 - Article

AN - SCOPUS:85062348353

VL - 33

JO - International Journal of Modern Physics B

JF - International Journal of Modern Physics B

SN - 0217-9792

IS - 7

M1 - 1950043

ER -