Dimer-monomer model on the Sierpinski gasket
Dimer-monomer model on the Sierpinski gasket
复制标题
DOI：
10.1016/j.physa.2007.10.057
复制
发表时间：
2007-02
影响因子：
3.3
通讯作者：
Shu-Chiuan Chang;Lung-Chi Chen
中科院分区：
文献类型：
--
作者：
Shu-Chiuan Chang;Lung-Chi Chen
在阶段n，我们给出了Sierpinski垫片SGD(N)上的二聚单体Md(N)的个数，其中d=2，3，4。渐近增长常数的上界和下界定义为[公式：见正文]，其中v是SGD(N)上的顶点数，是根据某一阶段的结果导出的。随着计算阶段的增加，这些界限之间的差值迅速收敛到零，[公式：参见文本]的数值可以用一百多个有效数字进行准确评估。从d=2，3，4的结果中，我们猜想[公式：见正文]的一般尺寸的上下界。在d=2，b=3，4的广义Sierpinski垫片SGD，b(N)上也得到了相应的结果。
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 [Formula: see text] where v is the number of vertices on SGd(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 [Formula: see text] 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 [Formula: see text] for general dimension. The corresponding results on the generalized Sierpinski gasket SGd,b(n) with d=2 and b=3,4 are also obtained.