Minimal grid diagrams of 11 crossing prime alternating knots-Reference-Cited by-同舟云学术

Minimal grid diagrams of 11 crossing prime alternating knots

Published:2020-10 Issue:11 Volume:29 Page:2050076
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Jin Gyo Taek¹,Lee Hwa Jeong²^ORCID

Affiliation:

1. Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea

2. Department of Mathematics Education, Dongguk University-Gyeongju, Gyeongju 38066, Korea

Abstract

The arc index of a knot is the minimal number of arcs in all arc presentations of the knot. An arc presentation of a knot can be shown in the form of a grid diagram which is a closed plane curve consisting of finitely many horizontal line segments and the same number of vertical line segments. The arc index of an alternating knot is its minimal crossing number plus two. In this paper, we give a list of minimal grid diagrams of the 11 crossing prime alternating knots obtained from arc presentations with 13 arcs.

Funder

National Research Foundation of Korea

Dongguk University

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216520500765

Reference6 articles.

1. An upper bound of arc index of links

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

3. PRIME KNOTS WITH ARC INDEX UP TO 11 AND AN UPPER BOUND OF ARC INDEX FOR NON-ALTERNATING KNOTS

4. A TABULATION OF PRIME KNOTS UP TO ARC INDEX 11

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1. Minimal grid diagrams of the prime alternating knots with 12 crossings;Journal of Knot Theory and Its Ramifications;2022-01