Abstract
Let [Formula: see text] be a Montesinos link [Formula: see text] with positive rational numbers [Formula: see text] and [Formula: see text], each less than 1, and [Formula: see text] the minimal crossing number of [Formula: see text]. Herein, we construct arc presentations of [Formula: see text] with [Formula: see text], [Formula: see text] and [Formula: see text] arcs under some conditions for [Formula: see text], [Formula: see text] and [Formula: see text]. Furthermore, we determine the arc index of infinitely many Montesinos links.
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