Classification of genus 1 virtual knots having at most five classical crossings
2014 ◽
Vol 23
(06)
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pp. 1450031
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Keyword(s):
The goal of this paper is to tabulate all genus one prime virtual knots having diagrams with ≤ 5 classical crossings. First, we construct all nonlocal prime knots in the thickened torus T × I which have diagrams with ≤ 5 crossings and admit no destabilizations. Then we use a generalized version of the Kauffman polynomial to prove that all those knots are different. Finally, we convert the knot diagrams in T thus obtained into virtual knot diagrams in the plane.
2020 ◽
Vol 29
(02)
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pp. 2040004
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Keyword(s):
2017 ◽
Vol 26
(13)
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pp. 1750090
Keyword(s):
2013 ◽
Vol 22
(13)
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pp. 1350073
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Keyword(s):
2006 ◽
Vol 15
(03)
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pp. 327-338
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2012 ◽
Vol 21
(13)
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pp. 1240005
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2015 ◽
Vol 24
(08)
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pp. 1550046
2002 ◽
Vol 11
(03)
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pp. 311-322
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Keyword(s):
2014 ◽
Vol 23
(10)
◽
pp. 1450053
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2008 ◽
Vol 17
(11)
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pp. 1311-1326
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Keyword(s):