Dimer-monomer model on the Sierpinski gasket

Abstract

We present the numbers of dimer-monomers on the Sierpinski gasket $S{G}_d(n)$ 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 $S{G}_{d,b}(n)$ with $d=2$ and $b=3,4$ are obtained.

30 pages, 10 figures, 10 tables

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• Approximating the Ising model on fractal lattices of dimension below two
• Ice model and eight-vertex model on the two-dimensional Sierpinski gasket
• Potts Partition Function Zeros and Ground State Entropy on Hanoi Graphs
• Isomorphism classification of infinite Sierpinski carpet graphs