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Spanning forests on the Sierpinski gasket. (English) Zbl 1151.82316
Summary: 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 $$SG_{2,b}$$.

##### MSC:
 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics 82B10 Quantum equilibrium statistical mechanics (general)
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