Spanning forests on the Sierpinski gasket
Shu-Chiuan Chang, Lung-Chi Chen
Abstract
We present the numbers of spanning forests on the Sierpinski gasket SGd(n) at stage n with dimension d equal to two, three and four, and determine the asymptotic behaviors. The corresponding results on the generalized Sierpinski gasket SGd,b(n) with d=2 and b=3,4 are obtained. We also derive the upper bounds of the asymptotic growth constants for both SGd and SG2,b.
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