We present the numbers of dimer–monomers Md(n) on the Sierpinski gasket SGd(n) at stage n with dimension d equal to two, three and four. The upper and lower bounds for the asymptotic growth constant, defined as zSGd=limv→∞lnMd(n)/v where v is the number of vertices on SGd(n), are derived...

We present the numbers of ice model configurations (with Boltzmann factors equal to one) I(n) on the two-dimensional Sierpinski gasket SG(n) at stage n. The upper and lower bounds for the entropy per site, defined as limv→∞lnI(n)/v, where v is the number of vertices on SG(n), are derived in...