论文标题
关于结的替代分层
On an alternative stratification of knots
论文作者
论文摘要
我们引入了一个替代性的结：通过晶格的大小，可以首先满足结的晶格。使用此分类，我们发现在不同晶格内有10个以上的交叉口的Unnonk和打结比例，并回答以下问题，可以在$ 3 \ times 3 $和$ 5 \ times 5 $ lattices中实现哪些结。根据先前的研究，未结的比率随晶格大小的生长而呈指数降低。我们的计算结果得到了理论估算的批准，其结的量固定的交叉数位于给定尺寸的晶格内。
We introduce an alternative stratification of knots: by the size of lattice on which a knot can be first met. Using this classification, we find ratio of unknots and knots with more than 10 minimal crossings inside different lattices and answer the question which knots can be realized inside $3\times 3$ and $5\times 5$ lattices. In accordance with previous research, the ratio of unknots decreases exponentially with the growth of the lattice size. Our computational results are approved with theoretical estimates for amounts of knots with fixed crossing number lying inside lattices of given size.
