论文标题
生成既准替代又几乎交替的链接
Generating links that are both quasi-alternating and almost alternating
论文作者
论文摘要
我们构建了一个无限的链接家族，这些链接几乎是与给定的几乎代表准偏置链路的几乎交替图的交替和准脉络，或者连接和还原交替的缠结图。为此，我们使用所谓的Dealternator扩展名，其中包括通过将其延伸的理性缠结代替Dealternator。我们注意到，可以以这种方式获得所有交替和准偏置的蒙特西诺斯链接。我们检查所有获得的准偏置链接是否满足了Qazaqzeh等人的猜想3.1。 （JKTR 22（06），2013年），即准偏置链接的交叉数小于或等于其决定因素。我们还证明了Qazaqzeh等人的定理3.3的相反。 （JKTR 24（01），2015年）是错误的。
We construct an infinite family of links which are both almost alternating and quasi-alternating from a given either almost alternating diagram representing a quasi-alternating link, or connected and reduced alternating tangle diagram. To do that we use what we call a dealternator extension which consists in replacing the dealternator by a rational tangle extending it. We note that all not alternating and quasi-alternating Montesinos links can be obtained in that way. We check that all the obtained quasi-alternating links satisfy Conjecture 3.1 of Qazaqzeh et al. (JKTR 22 (06), 2013), that is the crossing number of a quasi-alternating link is less than or equal to its determinant. We also prove that the converse of the Theorem 3.3 of Qazaqzeh et al. (JKTR 24 (01), 2015) is false.
