Abstract
In 2013, Adams introduced the [Formula: see text]-crossing number of a knot [Formula: see text], denoted by [Formula: see text]. Inequalities between the [Formula: see text]-, [Formula: see text]-, [Formula: see text]- and [Formula: see text]-crossing numbers have been previously established. We prove [Formula: see text] for all knots [Formula: see text] that are not the trivial, trefoil, or figure-eight knot. We show this inequality is optimal and obtain previously unknown values for [Formula: see text].
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