领带结的数学
The Mathematics of Tie Knots
摘要：
2000年，托马斯·芬克（Thomas Fink）和杨茂（Young Mao）研究了领带，并在一定的假设下，发现了85种不同的领带系法。他们给出了一种形式语言来描述领带是如何制作的，给出了每个领带的动作序列。领带的两端可以连接在一起，这给出了一个数学结的物理模型，我们称之为领带结。本文对Fink和Mao的85个结的类型进行了分类。我们描述了如何解开，左，右三叶，扭曲结和$(2,p)$环面结可以从他们的移动序列识别。我们也将打结视为所有结中的一个系列。在其他结果中，我们证明了任何领带结是素数和交替。
英文摘要：
In 2000, Thomas Fink and Young Mao studied neck ties and, with certain assumptions, found 85 different ways to tie a neck tie. They gave a formal language which describes how a tie is made, giving a sequence of moves for each neck tie. The ends of a neck tie can be joined together, which gives a physical model of a mathematical knot that we call a tie knot. In this paper we classify the knot type of each of Fink and Mao's 85 tie knots. We describe how the unknot, left and right trefoil, twist knots and $(2,p)$ torus knots can be recognized from their sequence of moves. We also view tie knots as a family within the set of all knots. Among other results, we prove that any tie knot is prime and alternating.
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。
