We study Kauffman’s model of folded ribbon knots: knots made of a thin strip of paper folded flat in the plane. The ribbonlength is the length to width ratio of such a folded ribbon knot. We show for any knot or link type that there exist constants c1,c2 > 0 such that the ribbonlength is bounded above by c1Cr(K)2, and also by c2Cr(K)3/2. We use a different method for each bound. The constant c1 is quite small in comparison to c2, and the first bound is lower than the second for knots and links with Cr(K) ≤ 12,748.

中文翻译：

---

折叠丝带结的丝带长度和交叉数

我们研究了考夫曼的折叠丝带结模型：由在平面上平折的薄纸条制成的结。丝带长度是这种折叠丝带结的长宽比。我们为任何结或链接类型显示存在常数C1,C2 > 0使得ribbonlength的边界为C1铬(ķ)2, 也由C2铬(ķ)3/2. 我们对每个边界使用不同的方法。常数C1与C2，对于结和链接，第一个界限低于第二个界限铬(ķ) ≤12,748。