论文标题
扭曲的圆环结的带状长度
Ribbonlength of twisted torus knots
论文作者
论文摘要
一个结$ k $的带状肋骨$（k）$是任何平坦的打结色带的比例，核心$ k $的宽度为宽度。一个扭曲的圆环结$ t_ {p，q; r，s} $是从圆环结$ t_ {p，q} $中获得的，通过扭动$ r $ a相邻的链条$ s $ s $ full Twist。在本文中，我们证明了$ t_ {p，q; r，s} $的功能边长少于$ 2（\ max \ {p，q，r \} +| s | r）$，其中$ p $和$ p $和$ q $是正的。此外，如果$ r \ r \ leq p-q $，则$ t_ {p，q; r，s} $的功能区长度较小或等于$ 2（p+（| s | -1）r）$。
The ribbonlength Rib$(K)$ of a knot $K$ is the infimum of the ratio of the length of any flat knotted ribbon with core $K$ to its width. A twisted torus knot $T_{p,q;r,s}$ is obtained from the torus knot $T_{p,q}$ by twisting $r$ adjacent strands $s$ full twists. In this paper, we show that the ribbonlength of $T_{p,q;r,s}$ is less then or equal to $2(\max \{ p, q, r \} +|s|r)$ where $p$ and $q$ are positive. Furthermore, if $r \leq p-q$, then the ribbonlength of $T_{p,q;r,s}$ is less then or equal to $2(p+(|s|-1)r)$.
