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ON THE VA-POLYNOMIAL OF PERIODIC VIRTUAL KNOTS

In this paper, we investigate the behavior of the VA-polynomial over ℤ[t, t-1] for periodic virtual knots and give a necessary condition for a given virtual knot to have period p. Indeed, we show that if K is a p-periodic virtual knot, then p divides the VA-polynomial of K. As an application, we improve the Im–Lee's table of possible periods for 117 virtual knots with classical crossings ≤4.