高斯图诱导的计数图和突变交替结族

Alexei Lisitsa , Alexei Vernitski
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引用次数: 0

摘要

被称为高斯图或高斯词的构造是结理论中最古老的构造之一,在结和具有自交的封闭曲线中都得到了广泛的研究。当我们研究高斯图所诱导的图形时,我们产生了这些图形的所有小尺寸示例,并在 OEIS 中以序列 A343358 公布了这些图形的编号。本文旨在澄清有关 A343358 的几个微妙的理论观点。最重要的是,我们解释了为什么我们利用图论构造得出的数字反映了所谓突变结的数量。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Counting graphs induced by Gauss diagrams and families of mutant alternating knots
The construction known as Gauss diagrams or Gauss words is one of the oldest in knot theory and has been studied extensively both in the context of knots and in the context of closed curves with self-intersections. When we studied graphs induced by Gauss diagrams, we produced all examples of these graphs of small sizes, and we published the number of these graphs as sequence A343358 in the OEIS. The aim of this article is to clarify several subtle theoretical points concerning A343358. Most importantly, we explain why our numbers, produced using graph-theoretical constructions, reflect the number of so-called mutant knots.
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