论文标题
来自非最小实现的新超级桥索引计算
New Superbridge Index Calculations from Non-Minimal Realizations
论文作者
论文摘要
先前的工作使用结的多边形实现来减少对线性编程问题实现的超级桥数量的问题，从而导致许多结的超级桥索引上的新尖锐上限。目前的工作将这一技术扩展到了多边形的多边形实现，并确定了许多新结的确切超级桥指数，包括大多数以前未知的9跨结，并且首次是几个12个跨结。有趣的是，这些超桥最小化的多边形实现中至少有一半不会最大程度地减少结的棍子数量。这些似乎是第一个这样的例子。附录A提供了一个完整的摘要，概述了目前对Prime结的超级桥指数通过10个交叉点进行的，附录B通过16个交叉点为所有结提供了Superbridge Index的所有结。
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 9-crossing knots for which it was previously unknown and, for the first time, several 12-crossing knots. Interestingly, at least half of these superbridge-minimizing 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.
