论文标题
链接数字和折叠的丝带解开
Linking number and folded ribbon unknots
论文作者
论文摘要
我们研究考夫曼（Kauffman）的折叠色带结构模型：由平面折叠的薄纸制成的结。折叠的带状长度是这种折叠的色带结的长度与宽度比。折叠的缎带结也是一个框结，色带链接数是结节的链接数和一个边界成分。我们发现最小折叠的功能纤维长度为$ 3 $ stick Unnkots，带有功能区链接数字$ \ pm1 $和$ \ pm 3 $，我们证明，当$ n $ gon是常规的时，可以实现具有缩放内部角度的$ n $ gons的最小折叠色带长度。除其他结果外，我们证明了任何折叠功能带Unkonot的最小折叠式色带长度，这是一个拓扑环，带有带链接的$ \ pm n $从上面的$ 2N $限制。
We study Kauffman's model of folded ribbon knots: knots made of a thin strip of paper folded flat in the plane. The folded ribbonlength is the length to width ratio of such a folded ribbon knot. The folded ribbon knot is also a framed knot, and the ribbon linking number is the linking number of the knot and one boundary component of the ribbon. We find the minimum folded ribbonlength for $3$-stick unknots with ribbon linking numbers $\pm1$ and $\pm 3$, and we prove that the minimum folded ribbonlength for $n$-gons with obtuse interior angles is achieved when the $n$-gon is regular. Among other results, we prove that the minimum folded ribbonlength of any folded ribbon unknot which is a topological annulus with ribbon linking number $\pm n$ is bounded from above by $2n$.
