A multivariable polynomial invariant of virtual knots

In this paper, we introduce a multivariable polynomial invariant of virtual knots by using weights of crossings. This polynomial generalizes the affine index polynomial and the zero polynomial. We provide a lower bound on the number of crossings of a virtual knot by using the multivariable polynomial. If two virtual knot diagrams can be related by a sequence of crossing changes, Reidemeister moves and virtual moves then we give a lower bound on the number of crossing changes and a strategy to map out a sequence of crossing changes by comparing the terms in the multivariable polynomials of the two virtual knot diagrams.