论文标题
领带的数学
The Mathematics of Tie Knots
论文作者
论文摘要
在2000年，托马斯·芬克（Thomas Fink）和年轻的毛泽东（Mao）研究了脖子领带，并以某些假设找到了85种不同的脖子领带方式。他们给出了一种形式的语言，描述了如何制作领带，为每条领带提供了一系列动作。可以将颈部领带的末端连接在一起，这给出了我们称为领带结的数学结的物理模型。在本文中，我们对Fink和Mao的85个领带的每种结的结式进行了分类。我们描述了如何从他们的动作序列中识别出左右三叶线，左右三叶草，扭曲结和$（2，p）$ torus结。我们还将领带结视为所有结中的家庭。除其他结果外，我们还证明任何领带结是素数和交替的。
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.
