Delta moves and Kauffman polynomials of virtual knots

Abstract

In 1990, Okada showed that the second coefficients of the Conway polynomials of two knots differ by 1 if the two knots are related by a single Δ-move. We extend the Okada's result for virtual knots by using a Vassiliev invariant v2 of virtual knots of degree 2 which is induced from the Kauffman polynomial of a virtual knot. We show that v2(K1) - v2(K2) = ±48, if K2 is a virtual knot obtained from a virtual knot K1 by applying a Δ-move. From this we have a lower bound [Formula: see text] for the number of Δ-moves if two virtual knots K1 and K2 are related by a sequence of Δ-moves.