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https://ah.lib.nccu.edu.tw/handle/140.119/71422
題名: | Hamiltonian walks on the Sierpinski gasket | 作者: | 陳隆奇 Chen, Lung-Chi |
貢獻者: | 應數系 | 日期: | Sep-2011 | 上傳時間: | 13-Nov-2014 | 摘要: | We derive exactly the number of Hamiltonian paths H(n) on the two dimensional Sierpinski gasket SG(n) at stage n, whose asymptotic behavior is given by 3√(23√)3n−13×(52×72×172212×35×13)(16)n. We also obtain the number of Hamiltonian paths with one end at a certain outmost vertex of SG(n), with asymptotic behavior 3√(23√)3n−13×(7×1724×33)4n. The distribution of Hamiltonian paths on SG(n) with one end at a certain outmost vertex and the other end at an arbitrary vertex of SG(n) is investigated. We rigorously prove that the exponent for the mean ℓ displacement between the two end vertices of such Hamiltonian paths on SG(n) is ℓlog2/log3 for ℓ>0. | 關聯: | J. Math. Phys. 52, 023301 (2011) | 資料類型: | article | DOI: | http://dx.doi.org/10.1063/1.3545358 |
Appears in Collections: | 期刊論文 |
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