A sequence of F-polynomials {FKn(t,ℓ)} n=1∞ of virtual knots K was defined by Kaur et al. in 2018. These polynomials have been expressed in terms of index value of crossing and n-writhe of K. By the construction, F-polynomials are generalizations of Kauffman's Affine Index Polynomial, and are invariants of virtual knot K. We present values of F-polynomials of oriented virtual knots having at most four classical crossings in a diagram.

Original languageEnglish
Article number2050054
Number of pages17
JournalJournal of Knot Theory and its Ramifications
Issue number8
Publication statusPublished - 1 Jul 2020


  • affine index polynomial
  • Virtual knot


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