论文标题
折叠色带的缎带长度和交叉数
Ribbonlength and crossing number for 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。带状长度是这种折叠的色带结的长度与宽度比。我们显示出存在常数$ C_1，C_2> 0 $的任何结或链接类型，因此功能边长以上由$ C_1 \ CDOT CR（K）^2 $以及$ C_2 \ CDOT CR（k）^{3/2} $界定。我们为每个界限使用不同的方法。与$ c_2 $相比，常数$ C_1 $非常小，第一键低于与$ CR（k）\ leq $ 12,748的打结和链接的第二个界限。
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 $c_1, c_2>0$ such that the ribbonlength is bounded above by $c_1\cdot Cr(K)^2$, and also by $c_2\cdot Cr(K)^{3/2}$. We use a different method for each bound. The constant $c_1$ is quite small in comparison to $c_2$, and the first bound is lower than the second for knots and links with $Cr(K)\leq$ 12,748.
