此論文中，我們表示出了在n階漢諾以圖形上雙體數N_d (n)及單體-雙體數M_d (n)，其中N_d (n)維度d=2、3、4、5，M_d (n)維度d=3、4。當漢諾以圖形的頂點個數，記做v(n)，為偶數時N_d (n)為最密堆積，但當頂點個數為奇數時，N_d (n)不可能為最密堆積，並允許最外層之其中一個頂點不被雙體佔據。S_(〖TH〗_d )及z_(〖TH〗_d )之entropy分別定義為lim┬(n→∞)⁡〖ln⁡〖N_d (n)〗⁄(v(n))〗、lim┬(n→∞)⁡〖ln⁡〖M_d (n)〗⁄(v(n))〗，我們分別求得S_(〖TH〗_d )及z_(〖TH〗_d )之上、下界。當計算的階數增加時，上、下界差值的會收斂趨近於零，並且雙體數N_d (n)的entropy在三維和五維、單體-雙體數M_d (n)的entropy在三維和四維時，均可精確至小數點下百位以上。但雙體數N_d (n)的entropy在四維時僅精確到小數點下第六位數。

We present the number of dimer coverings N_d(n) and the number of dimer-monomers M_d(n) on the Tower of Hanoi graph TH_d(n) at stage n with dimension d equal to two, three, four and ve for N_d(n), and d equal to three and four for M_d(n). When the number of vertices, denoted as v(n), of the Tower of Hanoi graph is an even number, Nd(n) is the number of close-packed dimers. When the number of vertices is an odd number, no close-packed con gurations are possible and we allow one of the outmost vertices uncovered. The entropy of both S_TH_d and z_TH_d are, respectively, de ned as STHd = lim lnN_d(n)/v(n) and zTHd = lim lnM_d(n)/v. We get the upper bounds and the lower bounds for S_TH_d and z_TH_d , respectively. As the di erence between these bounds converges to zero as the calculated stage increases with d = 3; 5 for dimer coverings and with d = 3; 4 for dimer-monomers, the numerical value of both S_TH_d and z_TH_d can be evaluated with more than a hundred signi ficant fi gures accurate. But the dimer covering with d = 4 is merely evaluated with more than six signifi cant fi gures accurate.

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