On the arc index of Kanenobu knots
2017 ◽
Vol 26
(04)
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pp. 1750015
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In this paper, we calculate the Kauffman polynomials [Formula: see text] of Kanenobu knots [Formula: see text] with [Formula: see text] half twists and determine their spans on the variable [Formula: see text] completely. As an application, we determine the arc index of infinitely many Kanenobu knots. In particular, we give sharper lower bounds of the arc index of [Formula: see text] by using canonical cabling algorithm and the 2-cable [Formula: see text]-polynomials. Moreover, we give sharper upper bounds of the arc index of some Kanenobu knots by using their braid presentations.
2008 ◽
Vol 45
(2)
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pp. 498-512
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2012 ◽
Vol 10
(3)
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pp. 455-488
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2017 ◽
Vol 5
(5)
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pp. 694-711
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1999 ◽
Vol 36
(01)
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pp. 105-118
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