Asymptotic enumeration of independent sets on the Sierpinski gasket

Shu Chiuan Chang, Lung Chi Chen, Weigen Yan

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)23-40
Number of pages18
JournalFilomat
Volume27
Issue number1
DOIs
Publication statusPublished - 2013 Jul 19

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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