Generating links that are both quasi-alternating and almost alternating

Hamid Abchir; Mohammed Sabak

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arXiv · 2003.13725

Generating links that are both quasi-alternating and almost alternating

Hamid Abchir·Mohammed Sabak

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Abstract

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.

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Hamid Abchir, Mohammed Sabak. 2020-03-30. Generating links that are both quasi-alternating and almost alternating. https://arxiv.org/abs/2003.13725

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