Spanning forests on the Sierpinski gasket

Shu-Chiuan Chang, Lung-Chi Chen
We study the number 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 upper bounds for the asymptotic growth constants for both SG d and SG 2,b .