Kauffman defines an affine index polynomial invariant for virtual knots. The invariant is induced from a numerical invariant called an n-writhe. In this paper, we provide the difference of the values obtained from invariants between two virtual knots which can be transformed into each other by a single forbidden move. As a result, we make it possible for many virtual knots to determine the unknotting numbers by forbidden moves.
- affine index polynomial invariant
- forbidden move
- Virtual knot
ASJC Scopus subject areas
- Algebra and Number Theory