Abstract

For a virtual knot [Formula: see text] and an integer [Formula: see text], the [Formula: see text]-covering [Formula: see text] is defined by using the indices of chords on a Gauss diagram of [Formula: see text]. In this paper, we prove that for any finite set of virtual knots [Formula: see text], there is a virtual knot [Formula: see text] such that [Formula: see text], [Formula: see text], and otherwise [Formula: see text].

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