小交叉数结与链的纱带长度上界

给定一薄纸片，将一个结系在上面，将端部相连并平整到平面。这是一个折叠纱带结在平面上的物理模型，首次由 Louis Kauffman 引入。我们研究这些折叠纱带结的折叠纱带长度，即结的长度至宽度比。{\em 纱带长度问题}要求找到结或链的最小折叠纱带长度。通过 finding new methods of creating folded ribbon knots, we improve upon existing upper bounds for the folded ribbonlength of $(2,q)$-torus links, twist knots, and pretzel links. These give the best known bounds to date for small crossing knots in these families. For example, there is a folded ribbonlength twist knot $T_n$ with folded ribbonlength $\text{Rib}(T_n) = n +6$. Applying this to the figure-eight knot $T_2$ yields a folded ribbonlength $\text{Rib}(T_2)= 8$, which we conjecture is the infimum.