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系統識別號 U0026-0510201908554500
論文名稱(中文) 在漢諾以圖形上的雙體與單體-雙體模型
論文名稱(英文) Dimer coverings and dimer-monomer model on the Tower of Hanoi graph
校院名稱 成功大學
系所名稱(中) 物理學系
系所名稱(英) Department of Physics
學年度 108
學期 1
出版年 108
研究生(中文) 黎維邦
研究生(英文) Wei-Bang Li
學號 L28031075
學位類別 博士
語文別 中文
論文頁數 68頁
口試委員 指導教授-張書銓
口試委員-盧炎田
口試委員-林明發
口試委員-陳隆奇
口試委員-李紀倫
中文關鍵字 單體  單體-雙體 
英文關鍵字 Dimers  dimer-monomers  Tower of Hanoi graph  entropy  recursion relations  exact solution. 
學科別分類
中文摘要 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。
英文摘要 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.
論文目次 I. Abstract (p.1)
II. Introduction (p.2)
III. Preliminaries(p.4)
IV. The number of dimer coverings on TH_d(n) with
d=2,3,4,5 (p.6)
A.TH_2(n) (p.6)
B.TH_3(n) (p.9)
C.TH_4(n) (p.17)
D.TH_5(n) (p.22)
V. The number of dimer-monomers on TH_d(n) with
d=3,4 (p.26)
A.TH_3(n) (p.26)
B.TH_4(n) (p.43)
VI. Summary (p.47)
Appendix A Relation between alpha(n), beta(n),
gamma(n), omega(n) dor z_TH3(n) of dimer-
monomers (p.49)
Appendix B The recursion relationship of f_4(n),
g_4(n), h_4(n), t_4(n), s_4(n), u_4(n) for
TH_4(n) in section V.B (p.53)
References (p.66)
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