New Superbridge Index Calculations from NonMinimal Realizations
Abstract
Previous work used polygonal realizations of knots to reduce the problem of computing the superbridge number of a realization to a linear programming problem, leading to new sharp upper bounds on the superbridge index of a number of knots. The present work extends this technique to polygonal realizations with an odd number of edges and determines the exact superbridge index of many new knots, including the majority of the 9crossing knots for which it was previously unknown and, for the first time, several 12crossing knots. Interestingly, at least half of these superbridgeminimizing polygonal realizations do not minimize the stick number of the knot; these seem to be the first such examples. Appendix A gives a complete summary of what is currently known about superbridge indices of prime knots through 10 crossings and Appendix B gives all knots through 16 crossings for which the superbridge index is known.
 Publication:

arXiv eprints
 Pub Date:
 June 2022
 arXiv:
 arXiv:2206.06950
 Bibcode:
 2022arXiv220606950S
 Keywords:

 Mathematics  Geometric Topology;
 57K10 (primary);
 53A04 (secondary)
 EPrint:
 23 pages, 4 figures, 3 appendices