Abstract

In this paper, the [Formula: see text]-move is defined. We show that for any knot [Formula: see text], there exists an infinite family of knots [Formula: see text] such that the Gordian distance [Formula: see text] and pass-move-Gordian distance [Formula: see text] for any [Formula: see text]. We also show that there is another infinite family of knots [Formula: see text] (where [Formula: see text]) such that the [Formula: see text]-move-Gordian distance [Formula: see text] and [Formula: see text]-Gordian distance [Formula: see text] for any [Formula: see text] and all [Formula: see text].

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