Ribbonlength of twisted torus knots
Hyoungjun Kim, Sungjong No, Hyungkee Yoo

TL;DR
This paper establishes upper bounds for the ribbonlength of twisted torus knots, relating it to their parameters, which advances understanding of their geometric properties.
Contribution
It provides new upper bounds for the ribbonlength of twisted torus knots based on their defining parameters.
Findings
Ribbonlength of $T_{p,q;r,s}$ is at most $2( ext{max}igracevert p,q,r igracevert +|s|r)$.
If $r \
The bounds depend on the parameters $p, q, r, s$, with a tighter bound when $r \
Abstract
The ribbonlength Rib of a knot is the infimum of the ratio of the length of any flat knotted ribbon with core to its width. A twisted torus knot is obtained from the torus knot by twisting adjacent strands full twists. In this paper, we show that the ribbonlength of is less then or equal to where and are positive. Furthermore, if , then the ribbonlength of is less then or equal to .
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Taxonomy
TopicsGeometric and Algebraic Topology · Biochemical and Structural Characterization
