Two-variable polynomial invariants of virtual knots arising from flat virtual knot invariants

Abstract

We introduce two sequences of two-variable polynomials [Formula: see text] and [Formula: see text], expressed in terms of index value of a crossing and [Formula: see text]-dwrithe value of a virtual knot [Formula: see text], where [Formula: see text] and [Formula: see text] are variables. Basing on the fact that [Formula: see text]-dwrithe is a flat virtual knot invariant, we prove that [Formula: see text] and [Formula: see text] are virtual knot invariants containing Kauffman affine index polynomial as a particular case. Using [Formula: see text] we give sufficient conditions when virtual knot does not admit cosmetic crossing change.