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Spanning trees on the Sierpinski gasket. (English) Zbl 1110.82007
Summary: We present the numbers of spanning trees on the Sierpinski gasket \(SG _{d}(n)\) at stage \(n\) with dimension \(d\) equal to two, three and four. The general expression for the number of spanning trees on \(SG_{d}(n)\) with arbitrary \(d\) is conjectured. The numbers of spanning trees on the generalized Sierpinski gasket \(SG_{d, b}(n)\) with \(d = 2\) and \(b = 3, 4\) are also obtained.

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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