On the arc index of Kanenobu knots
- Title
- On the arc index of Kanenobu knots
- Author(s)
- Lee, Hwa Jeong ; Takioka, Hideo
- Issued Date
- 2017-04
- Citation
- Journal of Knot Theory and its Ramifications, v.26, no.4
- Type
- Article
- Author Keywords
- Arc index ; braid index ; Kanenobu knot ; Kauffman polynomial ; Gamma-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
- Publisher
- World Scientific Publishing Co. Pte Ltd
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- Appears in Collections:
- ETC 1. Journal Articles
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