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Title: Hamiltonian walks on the Sierpinski gasket
Authors: 陳隆奇
Chen, Lung-Chi
Contributors: 應數系
Date: 2011-09
Issue Date: 2014-11-13 17:23:44 (UTC+8)
Abstract: 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.
Relation: J. Math. Phys. 52, 023301 (2011)
Data Type: article
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