A LOWER BOUND FOR THE NUMBER OF FORBIDDEN MOVES TO UNKNOT A LONG VIRTUAL KNOT
2013 ◽
Vol 22
(06)
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pp. 1350024
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Keyword(s):
Nelson and Kanenobu showed that forbidden moves unknot any virtual knot. Similarly a long virtual knot can be unknotted by a finite sequence of forbidden moves. Goussarov, Polyak and Viro introduced finite type invariants of virtual knots and long virtual knots and gave combinatorial representations of finite type invariants. We introduce Fn-moves which generalize the forbidden moves. Assume that two long virtual knots K and K′ are related by a finite sequence of Fn-moves. We show that the values of the finite type invariants of degree 2 of K and K′ are congruent modulo n and give a lower bound for the number of Fn-moves needed to transform K to K′.
2012 ◽
Vol 21
(13)
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pp. 1240001
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Keyword(s):
2019 ◽
Vol 28
(10)
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pp. 1950064
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2013 ◽
Vol 22
(03)
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pp. 1350009
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2013 ◽
Vol 22
(08)
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pp. 1350042
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2016 ◽
Vol 25
(08)
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pp. 1650045
Keyword(s):
2017 ◽
Vol 26
(13)
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pp. 1750090
Keyword(s):
2014 ◽
Vol 23
(10)
◽
pp. 1450053
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