2-桥纽结上Ohtsuki-Riley-Sakuma偏序的上界
Upper bounds in the Ohtsuki-Riley-Sakuma partial order on 2-bridge knots
摘要：
在本文中，我们使用连分数来研究一个偏序的2-桥结来自Ohtsuki，Riley和Sakuma的工作。我们建立了任意2-桥纽结集合关于偏序有一个上界的充要条件。此外，给定任何2-桥纽结K，我们刻画所有其他2-桥纽结J，使得{K，J}有一个上界。作为应用，我们回答了铃木的一个问题，表明没有上界的集合组成的三叶形和8字结。
英文摘要：
In this paper we use continued fractions to study a partial order on the set of 2-bridge knots derived from the work of Ohtsuki, Riley, and Sakuma. We establish necessary and sufficient conditions for any set of 2-bridge knots to have an upper bound with respect to the partial order. Moreover, given any 2-bridge knot K we characterize all other 2-bridge knots J such that {K, J} has an upper bound. As an application we answer a question of Suzuki, showing that there is no upper bound for the set consisting of the trefoil and figure-eight knots.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
