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 non-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 (6), 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 Theorem 3.3 of Qazaqzeh et al. (JKTR 24 (1), 2015) is false.

中文翻译：

---

生成准交替和几乎交替的链接

我们从一个给定的表示准交替链接的几乎交替图或连接和减少的交替缠结图构建了一个无限的链接系列，它们几乎是交替的和准交替的。为此，我们使用我们所谓的交流发电机扩展，它包括用扩展它的理性缠结替换交流发电机。我们注意到，所有非交替和准交替的 Montesinos 链接都可以通过这种方式获得。我们检查所有获得的准交替链接是否满足 Qazaqzeh 等人的猜想 3.1。(JKTR 22 (6), 2013)，即准交替链路的交叉数小于或等于其行列式。我们还证明了 Qazaqzeh 等人的定理 3.3 的逆。（JKTR 24 (1), 2015）是错误的。