On the arc index of cable links and Whitehead doubles-Reference-Cited by-同舟云学术

On the arc index of cable links and Whitehead doubles

Published:2016-06 Issue:07 Volume:25 Page:1650041
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Lee Hwa Jeong¹,Takioka Hideo²^ORCID

Affiliation:

1. School of Undergraduate Studies, Daegu Gyeongbuk Institute of Science & Technology (DGIST), Techno jungang-daero, Hyeonpung-myeon, Dalseong-gun, Daegu 42988, Korea

2. Osaka City University Advanced Mathematical Institute (OCAMI), Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

Abstract

In this paper, we construct an algorithm to produce canonical grid diagrams of cable links and Whitehead doubles, which give sharper upper bounds of the arc index of them. Moreover, we determine the arc index of [Formula: see text]-cable links and Whitehead doubles of all prime knots with up to eight crossings.

Funder

National Research Foundation of Korea

Japan Society for the Promotion of Science (JP)

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216516500413

Reference12 articles.

1. An upper bound of arc index of links

2. ARC INDEX OF NON-ALTERNATING LINKS

3. Embedding knots and links in an open book I: Basic properties

4. Embedding knots and links in an open book II. Bounds on arc index

5. Knots and Contact Geometry I: Torus Knots and the Figure Eight Knot

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