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題名 Asymptotic enumeration of independent sets on the Sierpinski gasket 作者 張書銓;晏衛根
Chang, Shu-Chiuan
陳隆奇
Chen, Lung-Chi
晏衛根
Yan, Weigen貢獻者 應數系 日期 2013.07 上傳時間 13-Nov-2014 17:24:00 (UTC+8) 摘要 The number of independent sets is equivalent to the partition function of the hard-core lattice gas model with nearest-neighbor exclusion and unit activity. We study the number of independent sets md,b(n) on the generalized Sierpinski gasket SGd,b(n) at stage n with dimension d equal to two, three and four for b = 2, and layer b equal to three for d = 2. Upper and lower bounds for the asymptotic growth constant, defined as zSGd,b = limv→∞ lnmd,b(n)/v where v is the number of vertices, on these Sierpinski gaskets are derived in terms of the numbers at a certain stage. The numerical values of these zSGd,b are evaluated with more than a hundred significant figures accurate. We also conjecture upper and lower bounds for the asymptotic growth constant zSGd,2 with general d, and an approximation of zSGd,2 when d is large. 關聯 Filomat, 27(1), 23-40 資料類型 article DOI http://dx.doi.org/10.2298/FIL1301023C dc.contributor 應數系 en_US dc.creator (作者) 張書銓;晏衛根 zh_TW dc.creator (作者) Chang, Shu-Chiuan en_US dc.creator (作者) 陳隆奇 zh_TW dc.creator (作者) Chen, Lung-Chi en_US dc.creator (作者) 晏衛根 zh_TW dc.creator (作者) Yan, Weigen en_US dc.date (日期) 2013.07 en_US dc.date.accessioned 13-Nov-2014 17:24:00 (UTC+8) - dc.date.available 13-Nov-2014 17:24:00 (UTC+8) - dc.date.issued (上傳時間) 13-Nov-2014 17:24:00 (UTC+8) - dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/71424 - dc.description.abstract (摘要) The number of independent sets is equivalent to the partition function of the hard-core lattice gas model with nearest-neighbor exclusion and unit activity. We study the number of independent sets md,b(n) on the generalized Sierpinski gasket SGd,b(n) at stage n with dimension d equal to two, three and four for b = 2, and layer b equal to three for d = 2. Upper and lower bounds for the asymptotic growth constant, defined as zSGd,b = limv→∞ lnmd,b(n)/v where v is the number of vertices, on these Sierpinski gaskets are derived in terms of the numbers at a certain stage. The numerical values of these zSGd,b are evaluated with more than a hundred significant figures accurate. We also conjecture upper and lower bounds for the asymptotic growth constant zSGd,2 with general d, and an approximation of zSGd,2 when d is large. en_US dc.format.extent 123165 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.relation (關聯) Filomat, 27(1), 23-40 en_US dc.title (題名) Asymptotic enumeration of independent sets on the Sierpinski gasket en_US dc.type (資料類型) article en dc.identifier.doi (DOI) 10.2298/FIL1301023C - dc.doi.uri (DOI) http://dx.doi.org/10.2298/FIL1301023C -
