Dimer Coverings on Random Polyomino Chains

作者：Xiao, Chuanqi; Chen, Haiyan^*

来源：Zeitschrift fur Naturforschung Section A-A Journal of Physical Sciences, 2015, 70(6): 465-470.

DOI：10.1515/zna-2015-0121

• Dimer Covering
• Expectation
• Polyomino Chain

A polyomino chain is a planar square lattice that can be constructed by successively attaching squares to the previous one in two possible ways. A random polyomino chain is then generated by incorporating the Bernoulli distribution to the two types of attachment, which describes a zeroth-order Markov process. Let (R-n, p) be the ensemble of random polyomino chains with n squares, where p is an element of [0,1] is a constant. Then, in this paper, we determine the explicit expression for the expectation of the number of dimer coverings over (R-n, p). Our result shows that, with only one exception, i.e., p = 0, the average of the logarithm of this expectation is asymptotically nonzero when n -> infinity.

• 出版日期2015-6
• 单位集美大学