A zero polynomial of virtual knots
2016 ◽
Vol 25
(01)
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pp. 1550078
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In 2013, Cheng and Gao introduced the writhe polynomial of virtual knots and Kauffman introduced the affine index polynomial of virtual knots. We introduce a zero polynomial of virtual knots of a similar type by considering weights of a suitable collection of crossings of a virtual knot diagram. We show that the zero polynomial gives a Vassiliev invariant of degree 1. It distinguishes a pair of virtual knots that cannot be distinguished by the affine index polynomial and the writhe polynomial.
2003 ◽
Vol 12
(06)
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pp. 767-779
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2014 ◽
Vol 23
(10)
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pp. 1450053
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2013 ◽
Vol 22
(01)
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pp. 1250133
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2018 ◽
Vol 27
(08)
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pp. 1850049
2013 ◽
Vol 22
(12)
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pp. 1341004
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2020 ◽
Vol 29
(02)
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pp. 2040004
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Keyword(s):
2013 ◽
Vol 22
(06)
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pp. 1350024
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2001 ◽
Vol 10
(06)
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pp. 931-935
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2011 ◽
Vol 20
(12)
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pp. 1649-1667
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2012 ◽
Vol 21
(13)
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pp. 1240001
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Keyword(s):