论文标题
椒盐脆饼结至九个十字路口
Pretzel knots up to nine crossings
论文作者
论文摘要
与相同的亚历山大多项式（实际上与琐碎的亚历山大多项式）有无限的椒盐脆饼联系。相比之下，在本说明中，我们重新审视了椒盐脆饼链接的琼斯多项式，并证明，鉴于自然数量，只有有限数量的椒盐脆饼链接，其琼斯多项式具有跨度S。 更具体地说，我们提供了一种用于确定给定结是否椒盐脆饼的算法。作为一个应用程序，我们确定所有椒盐脆饼结的最高九个交叉点，特别是证明$ 8_ {12} $是第一个非杂交结。
There are infinitely many pretzel links with the same Alexander polynomial (actually with trivial Alexander polynomial). By contrast, in this note we revisit the Jones polynomial of pretzel links and prove that, given a natural number S, there is only a finite number of pretzel links whose Jones polynomials have span S. More concretely, we provide an algorithm useful for deciding whether or not a given knot is pretzel. As an application we identify all the pretzel knots up to nine crossings, proving in particular that $8_{12}$ is the first non-pretzel knot.
