论文标题
椭圆上的沙珀斯身份元素
The sandpile identity element on an ellipse
论文作者
论文摘要
我们考虑方格的某些椭圆形子集。该图上沙珀斯组的身份元素的复发代表主要由双层模式以及一些噪声组成。我们表明，随着晶格间距趋向于0，身份元素中图案所吸收的面积的比例趋向于1。
We consider certain elliptical subsets of the square lattice. The recurrent representative of the identity element of the sandpile group on this graph consists predominantly of a biperiodic pattern, along with some noise. We show that as the lattice spacing tends to 0, the fraction of the area taken up by the pattern in the identity element tends to 1.
