The asymptotic growth constant formula for Sierpinski gaskets

From papers

Let SGd(n)SG_d(n) be the dd-dimensional Sierpinski gasket at stage nn, and let zSGdz_{SG_d} denote its asymptotic growth constant for spanning trees. Then

Asymptotic growth constant conjecture. The asymptotic growth constant is

zSGd=d1d(d+1)[dln2+(d+1)ln(d+1)+ln(d+3)].z_{SG_d}=\frac{d-1}{d(d+1)}\bigl[d\ln 2+(d+1)\ln(d+1)+\ln(d+3)\bigr].

This formula is presented as a consequence of the preceding spanning-tree conjecture and the known vertex-count formula for SGd(n)SG_d(n). Its general status is not resolved in the supplied text.

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Sources & referencesView supporting material

Primary source

Shu-Chiuan Chang and Lung-Chi Chen, “Spanning trees on the Sierpinski gasket”, arXiv:cond-mat/0609453 (2006).

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