Affiliation:
1. Department of Mathematics, Colorado State University, Fort Collins, CO 80523, USA
Abstract
This paper gives new upper bounds on the stick numbers of the knots [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], as well as on the equilateral stick number of [Formula: see text]. These bounds imply that the knots [Formula: see text], [Formula: see text], and [Formula: see text] have superbridge index [Formula: see text], 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.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Algebra and Number Theory
Cited by
2 articles.
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1. The stick number of rail arcs;Journal of Knot Theory and Its Ramifications;2023-04
2. New superbridge index calculations from non-minimal realizations;Journal of Knot Theory and Its Ramifications;2022-08-31