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- Title
Two-variable polynomial invariants of virtual knots arising from flat virtual knot invariants.
- Authors
Kaur, Kirandeep; Prabhakar, Madeti; Vesnin, Andrei
- Abstract
We introduce two sequences of two-variable polynomials { L K n (t , ℓ) } n = 1 ∞ and { F K n (t , ℓ) } n = 1 ∞ , expressed in terms of index value of a crossing and n -dwrithe value of a virtual knot K , where t and ℓ are variables. Basing on the fact that n -dwrithe is a flat virtual knot invariant, we prove that L K n and F K n are virtual knot invariants containing Kauffman affine index polynomial as a particular case. Using L K n we give sufficient conditions when virtual knot does not admit cosmetic crossing change.
- Subjects
INVARIANTS (Mathematics); KNOT theory; INTEGERS; ADDITION (Mathematics); NUMBER theory
- Publication
Journal of Knot Theory & Its Ramifications, 2018, Vol 27, Issue 13, pN.PAG
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S0218216518420154