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Title: Asymptotic enumeration of independent sets on the Sierpinski gasket
Authors: 張書銓;晏衛根
Chang, Shu-Chiuan
Chen, Lung-Chi
Yan, Weigen
Contributors: 應數系
Date: 2013.07
Issue Date: 2014-11-13 17:24:00 (UTC+8)
Abstract: 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.
Relation: Filomat, 27(1), 23-40
Data Type: article
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