New computations of the superbridge index-Reference-Cited by-同舟云学术

New computations of the superbridge index

Published:2020-12 Issue:14 Volume:29 Page:2050096
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Shonkwiler Clayton¹^ORCID

Affiliation:

1. Department of Mathematics, Colorado State University, Fort Collins, CO 80523, USA

Abstract

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], [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] all have superbridge index equal to 4. This follows from new upper bounds on superbridge index not coming from the stick number and increases the number of knots from the Rolfsen table for which superbridge index is known from 29 to 49. Appendix A gives the current state of knowledge of superbridge index for prime knots through 10 crossings.

Funder

Simons Foundation

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216520500960

Reference24 articles.

1. A brief introduction to knot theory from the physical point of view

2. The spiral index of knots

3. Coxeter groups and meridional rank of links

4. Symmetric quotients of knot groups and a filtration of the Gordian graph

5. Knots with exactly 10 sticks

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1. Coxeter Quotients of Knot Groups through 16 Crossings;Experimental Mathematics;2024-03-12

2. New superbridge index calculations from non-minimal realizations;Journal of Knot Theory and Its Ramifications;2022-08-31

3. All prime knots through 10 crossings have superbridge index ≤ 5;Journal of Knot Theory and Its Ramifications;2022-04