Abstract
We present the numbers of dimer–monomers M d ( n ) on the Sierpinski gasket S G d ( 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 z S G d = lim v → ∞ ln M d ( n ) / v where v is the number of vertices on S G d ( n ) , are derived in terms of the results at a certain stage. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of z S G d can be evaluated with more than a hundred significant figures accurate. From the results for d = 2 , 3 , 4 , we conjecture the upper and lower bounds of z S G d for general dimension. The corresponding results on the generalized Sierpinski gasket S G d , b ( n ) with d = 2 and b = 3 , 4 are also obtained.
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