We present the number of dimers Nd(n) on the Sierpinski gasket SGd(n)
at stage n with dimension d equal to two, three, four or five, where one of
the outmost vertices is not covered when the number of vertices v(n) is an
odd number. The entropy of absorption of diatomic molecules per site, defined
as SSGd=limn→∞lnNd(n)/v(n), is calculated to be
ln(2)/3 exactly for SG2(n). The numbers of dimers on the generalized
Sierpinski gasket SGd,b(n) with d=2 and b=3,4,5 are also obtained
exactly. Their entropies are equal to ln(6)/7, ln(28)/12, ln(200)/18,
respectively. The upper and lower bounds for the entropy are derived in terms
of the results at a certain stage for SGd(n) with d=3,4,5. As the
difference between these bounds converges quickly to zero as the calculated
stage increases, the numerical value of SSGd with d=3,4,5 can be
evaluated with more than a hundred significant figures accurate.Comment: 35 pages, 20 figures and 1 tabl