• 대한수학회지
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• 제52권5호
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• pp.929-944
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• 2015

We give a quotient of the ring ${\mathbb{Q}}[A^{{\pm}1},\;t^{{\pm}1]$ so that the Miyazawa polynomial is a non-trivial invariant of welded links. Furthermore we show that this is also an invariant under the other forbidden move $F_u$, and so it is a fused isotopy invariant. Also, we give some quotient ring so that the index polynomial can be an invariant for welded links.

• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.801-809
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• 2009

By using a tangle decomposition of a knot, we give a method for the construction of a knot with the lowest trivial HOMFLY coefficient polynomial. Applying this, we show that there exist infinitely many 2-bridge knots with such a coefficient polynomial.

• Kyungpook Mathematical Journal
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• 제58권1호
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• pp.183-202
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• 2018

${\Delta}-moves$ 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 ${\Delta}-moves$.