Spanning forests on the Sierpinski gasket

Details Spanning forests on the Sierpinski gasket Spanning forests on the Sierpinski gasket

2006-12-28

arxiv.org/abs/math-ph/0612083v1

Physics

Mathematical Physics

31 pages, 9 figures, 7 tables

Scientific paper

We present the numbers of spanning forests on the Sierpinski gasket $SG_d(n)$
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 $SG_{d,b}(n)$ with $d=2$ and $b=3,4$ are obtained. We also derive the
upper bounds of the asymptotic growth constants for both $SG_d$ and $SG_{2,b}$.

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