An affine index polynomial invariant and the forbidden move of virtual knots

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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.

Original languageEnglish
Article number1650040
JournalJournal of Knot Theory and its Ramifications
Issue number7
Publication statusPublished - 2016 Jun 1
Externally publishedYes



  • affine index polynomial invariant
  • forbidden move
  • Virtual knot

ASJC Scopus subject areas

  • Algebra and Number Theory

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