Coxeter Quotients of Knot Groups through 16 Crossings

IF 0.7 4区数学 Q2 MATHEMATICS Experimental Mathematics Pub Date : 2024-03-12 DOI:10.1080/10586458.2024.2309507

Ryan Blair, Alexandra Kjuchukova, Nathaniel Morrison

引用次数: 0

Abstract

We find explicit maximal rank Coxeter quotients for the knot groups of 595,515 out of the 1,701,936 knots through 16 crossings. We thus calculate the bridge numbers and verify Cappell and Shaneson’...

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通过 16 个交叉点的结群考斯特四分体

在 1,701,936 个结中，我们通过 16 次交叉，为 595,515 个结的结群找到了明确的最大秩 Coxeter 商。因此，我们计算了桥数，并验证了 Cappell 和 Shaneson 的...

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Experimental Mathematics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses. Experiment has always been, and increasingly is, an important method of mathematical discovery. (Gauss declared that his way of arriving at mathematical truths was "through systematic experimentation.") Yet this tends to be concealed by the tradition of presenting only elegant, fully developed, and rigorous results. Experimental Mathematics was founded in the belief that theory and experiment feed on each other, and that the mathematical community stands to benefit from a more complete exposure to the experimental process. The early sharing of insights increases the possibility that they will lead to theorems: An interesting conjecture is often formulated by a researcher who lacks the techniques to formalize a proof, while those who have the techniques at their fingertips have been looking elsewhere. Even when the person who had the initial insight goes on to find a proof, a discussion of the heuristic process can be of help, or at least of interest, to other researchers. There is value not only in the discovery itself, but also in the road that leads to it.

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