论文标题
折叠色带系的缎带长度
Ribbonlength of families of folded ribbon knots
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色带结的长度与宽度比。我们在2桥，$（2，Q）$ torus，Twist和Pretzel结上的折叠式带上界，这些上限在交叉数字中是线性的。我们提供了一种新的方法来折叠$（P，Q）$ torus结，并表明其折叠式功能表的折叠率在上方$ 2p $。例如，这意味着可以用折叠的色带长度为6。然后，我们证明任何$（p，q）$ torus n ok $ k $带有$ p \ geq q> 2 $具有常数$ c> 0 $，因此，折叠的色带长度在上面的折叠式cr（k）^cr（k）^$ c \ cdot cr（k）^$ c \ cdot cr（k）^1/2} $。这提供了一个折叠式功能线上的上限的示例，该折叠线在交叉数中是亚线性的。
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 ribbon knot. We give upper bounds on the folded ribbonlength of 2-bridge, $(2,q)$ torus, twist, and pretzel knots, and these upper bounds turn out to be linear in the crossing number. We give a new way to fold $(p,q)$ torus knots and show that their folded ribbonlength is bounded above by $2p$. This means, for example, that the trefoil knot can be constructed with a folded ribbonlength of 6. We then show that any $(p,q)$ torus knot $K$ with $p\geq q>2$ has a constant $c>0$, such that the folded ribbonlength is bounded above by $c\cdot Cr(K)^{1/2}$. This provides an example of an upper bound on folded ribbonlength that is sub-linear in crossing number.
