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- Title
Twist moves and the affine index polynomials of virtual knots.
- Authors
Jeong, Myeong-Ju; Choi, Younhee; Kim, Dojin
- Abstract
In this paper, we give a necessary condition for two virtual knots to be related by a finite sequence of twist moves by using the affine index polynomial, which is a Vassiliev invariant of degree 1. Trapp showed that a numerical Vassiliev invariant of degree n has a polynomial growth of degree ≤ n on a twist sequence of knots, which can be extended to a twist sequence of virtual knots. We calculate the growth of the affine index polynomial for a twist sequence of virtual knots and find the difference of the affine index polynomials of two virtual knots, which are related by a twist move. Moreover, we give a lower bound for the number of twist moves needed to transform K to K ′ if K and K ′ are virtual knots related by a finite sequence of twist moves.
- Subjects
POLYNOMIALS; KNOT theory; FINITE, The
- Publication
Journal of Knot Theory & Its Ramifications, 2022, Vol 31, Issue 7, p1
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S0218216522500420