Please use this identifier to cite or link to this item:
|Title:||Asymptotic enumeration of independent sets on the Sierpinski gasket|
|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|
|Appears in Collections:||[應用數學系] 期刊論文|
Files in This Item:
All items in 學術集成 are protected by copyright, with all rights reserved.