All Prime Knots Through 10 Crossings Have Superbridge Index $\le 5$

Abstract

This paper gives new upper bounds on the stick numbers of the knots $9_{18}$, $10_{18}$, $10_{58}$, $10_{66}$, $10_{68}$, $10_{80}$, $10_{82}$, $10_{84}$, $10_{93}$, $10_{100}$, and $10_{152}$, as well as on the equilateral stick number of $10_{79}$. These bounds imply that the knots $10_{58}$, $10_{66}$, and $10_{80}$ have superbridge index $\le 5$, completing the project of showing that no prime knots through 10 crossings can have superbridge index larger than 5. The current best bounds on stick number and superbridge index for prime knots through 10 crossings are given in Appendix A.

13 pages, 1 figure, 3 appendices

References in corpus (2)

• New Stick Number Bounds from Random Sampling of Confined Polygons
• New Computations of the Superbridge Index

Cited by in corpus (3)

• New Superbridge Index Calculations from Non-Minimal Realizations
• New Upper Bounds for Stick Numbers
• The stick number of rail arcs