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We show that a link is adequate if the breadth of its Jones polynomial equals the difference between its crossing number and its Turaev genus. Combining this result with its converse obtained by Abe 1, Theorem 3.2, we get a simple characterization of adequate links based on these numerical link invariants. As an application, we provide a simple obstruction for a link to be quasi-alternating. Moreover, we use this result to give a lower bound for the crossing number of some classes of links which would be very useful to determine the crossing number in certain cases.
Qazaqzeh et al. (Thu,) studied this question.
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