On determinant of checkerboard colorable virtual knots

Abstract

For classical knots, it is well known that their determinants mod $8$ are classified by the Arf invariant. Boden and Karimi introduced a determinant of checkerboard colorable virtual knots. We prove that their determinant mod $8$ is classified by the coefficient of $z^2$ in the ascending polynomial which is an extension of the Conway polynomial for classical knots.