We present the numbers of dimer-monomers Md (n) on the Sierpinski gasket S Gd (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 zS Gd = limv → ∞ ln Md (n) / v where v is the number of vertices on S Gd (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 zS Gd 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 zS Gd for general dimension. The corresponding results on the generalized Sierpinski gasket S Gd, b (n) with d = 2 and b = 3, 4 are also obtained.
|Number of pages||16|
|Journal||Physica A: Statistical Mechanics and its Applications|
|Publication status||Published - 2008 Mar 1|
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Condensed Matter Physics