| dc.contributor.advisor | 陳隆奇 | zh_TW |
| dc.contributor.advisor | Lung-Chi Chen | en_US |
| dc.contributor.author (Authors) | 呂存策 | zh_TW |
| dc.contributor.author (Authors) | LYU CUNCE | en_US |
| dc.creator (作者) | 呂存策 | zh_TW |
| dc.creator (作者) | CUNCE, LYU | en_US |
| dc.date (日期) | 2021 | en_US |
| dc.date.accessioned | 10-Feb-2022 13:06:31 (UTC+8) | - |
| dc.date.available | 10-Feb-2022 13:06:31 (UTC+8) | - |
| dc.date.issued (上傳時間) | 10-Feb-2022 13:06:31 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0104751019 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/138940 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學系 | zh_TW |
| dc.description (描述) | 104751019 | zh_TW |
| dc.description.abstract (摘要) | 本文給出了 n 階 2 維漢諾圖（又稱漢諾塔圖、河內圖）上哈密頓路徑的數量，其漸進表現是 h(n) ∼ 25×16^n/624 。這類漢諾圖上的哈密頓路徑總數量與起點在最上面的顶點的哈密頓路徑數量的對數的比值漸進至 2。同時，當這類漢諾圖上三個方向的平行邊分別被 x, y, z 這三個數加權後，我們也推導出了它們的哈密頓路徑的加權和，其漸進表現為h′(n) ∼(25w*16^n(xyz)^(3n−1))/(16*27*13)其中 w =(x + y + z)^2/(xyz)。 | zh_TW |
| dc.description.abstract (摘要) | We’ve derived the number of Hamiltonian walks on the twodimensional Hanoi graph at stage n, whose asymptotic behaviour is given by h(n) ∼ 25×16^n/624 .And the asymptotic behaviour the logarithmic ratio of the number of Hamiltonian walks on these Hanoi graphs with that one end at the topmost vertex is given by 2. When the parallel edges in the three directions on these Hanoi graphs are weighted by three numbers, x, y, z, the weighted sum of their Hamiltonian paths is also derived by us, and the asymptotic behaviour of it is given byh′(n) ∼(25w*16^n(xyz)^(3n−1))/(16*27*13) in which w =(x + y + z)^2/(xyz). | en_US |
| dc.description.tableofcontents | 致謝 i中文摘要 iiAbstract iiiContents ivList of Figures v1 Introduction 11.1 Hanoi graphs 11.2 Hamiltonian walk 22 Hamiltonian paths in weightless Hanoi graph 42.1 Preliminaries 42.2 Building recursions to count the number of Hamiltonian walks 62.3 Number of Hamiltonian walks 83 Hamiltonian paths in weighted Hanoi graph 113.1 Preliminaries 113.2 Building recursions to calculate the weighted sum of Hamiltonian walks 163.3 Get the weighted sum 22Bibliography 29 | zh_TW |
| dc.format.extent | 507539 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0104751019 | en_US |
| dc.subject (關鍵詞) | 漢諾圖 | zh_TW |
| dc.subject (關鍵詞) | 哈密頓路徑 | zh_TW |
| dc.subject (關鍵詞) | 漸進表現 | zh_TW |
| dc.subject (關鍵詞) | Hanoi graph | en_US |
| dc.subject (關鍵詞) | Hamiltonian walk | en_US |
| dc.subject (關鍵詞) | Asymptotic behaviour | en_US |
| dc.title (題名) | 漢諾圖上的哈密頓路徑 | zh_TW |
| dc.title (題名) | Hamiltonian Walks on the Hanoi Graph | en_US |
| dc.type (資料類型) | thesis | en_US |
| dc.relation.reference (參考文獻) | [1] RM Bradley. Analytical enumeration of hamiltonian walks on a fractal. Journal of Physics A: Mathematical and General, 22(1):L19, 1989.[2] ShuChiuan Chang and LungChi Chen. Structure of spanning trees on the twodimensional sierpinski gasket, 2008.[3] ShuChiuan Chang and LungChi Chen. Hamiltonian paths on the sierpinski gasket, 2009.[4] Sunčica ElezovićHadžić, Dušanka Marčetić, and Slobodan Maletić. Scaling of hamiltonian walks on fractal lattices. Physical Review E, 76(1):011107, 2007.[5] Andreas M Hinz, Sandi Klavžar, Uroš Milutinović, and Ciril Petr. The Tower of Hanoimyths and maths. Springer, 2013.[6] Wilfried Imrich, Sandi Klavzar, and Douglas F Rall. Topics in graph theory: Graphs and their Cartesian product. CRC Press, 2008.[7] Sandi Klavžar and Uroš Milutinović. Graphs s (n, k) and a variant of the tower of hanoi problem. Czechoslovak Mathematical Journal, 47(1):95–104, 1997.[8] Dušanka Lekić and Sunčica ElezovićHadžić. Semiflexible compact polymers on fractal lattices. Physica A: Statistical Mechanics and its Applications, 390(11):1941–1952, 2011. | zh_TW |
| dc.identifier.doi (DOI) | 10.6814/NCCU202101772 | en_US |
