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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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