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http://dx.doi.org/10.5666/KMJ.2018.58.1.183

Delta Moves and Arrow Polynomials of Virtual Knots  

Jeong, Myeong-Ju (Department of Mathematics, Korea Science Academy)
Park, Chan-Young (Department of Mathematics, College of Natural Sciences, Kyungpook National University)
Publication Information
Kyungpook Mathematical Journal / v.58, no.1, 2018 , pp. 183-202 More about this Journal
Abstract
${\Delta}-moves$ are closely related with a Vassiliev invariant of degree 2. For classical knots, M. Okada showed that the second coefficients of the Conway polynomials of two knots differ by 1 if the two knots are related by a single ${\Delta}-move$. The first author extended the Okada's result for virtual knots by using a Vassiliev invariant of virtual knots of type 2 which is induced from the Kauffman polynomial of a virtual knot. The arrow polynomial is a generalization of the Kauffman polynomial. We will generalize this result by using Vassiliev invariants of type 2 induced from the arrow polynomial of a virtual knot and give a lower bound for the number of ${\Delta}-moves$ transforming $K_1$ to $K_2$ if two virtual knots $K_1$ and $K_2$ are related by a finite sequence of ${\Delta}-moves$.
Keywords
${\Delta}-move$; arrow polynomial; Miyazawa polynomial; virtual knot; Vassiliev invariant;
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