On the Statistics of Dimer Coverings and Spanning Trees on the Silicate-Type Sierpinski Gasket

Abstract

Chang and Chen (J Stat Phys 131(4):631–650, 2008) and Chang et al. (J Stat Phys 126(3):649–667, 2007) present the number of dimer coverings and spanning trees on the Sierpinski gasket \(SG_b(n)\) at stage n with the side length b equal to two, three and four, respectively. In this paper, we obtain the exact closed formula of the number of dimer coverings and spanning trees on the silicate-type Sierpinski gasket \(SO_b(n)\) at stage n with the side length \(b=2,3,4\).