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On the arc index of Kanenobu knots

Title
On the arc index of Kanenobu knots
Author(s)
Lee, Hwa JeongTakioka, Hideo
Issued Date
2017-04
Citation
Journal of Knot Theory and its Ramifications, v.26, no.4
Type
Article
Author Keywords
Arc indexbraid indexKanenobu knotKauffman polynomialGamma-polynomial
ISSN
0218-2165
Abstract
In this paper, we calculate the Kauffman polynomials (Formula presented.) of Kanenobu knots (Formula presented.) with (Formula presented.) half twists and determine their spans on the variable (Formula presented.) 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 presented.) by using canonical cabling algorithm and the 2-cable (Formula presented.)-polynomials. Moreover, we give sharper upper bounds of the arc index of some Kanenobu knots by using their braid presentations. ? 2017 World Scientific Publishing Company
URI
http://hdl.handle.net/20.500.11750/2069
DOI
10.1142/S0218216517500158
Publisher
World Scientific Publishing Co. Pte Ltd
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