Minimal grid diagrams of the prime knots with crossing number 13 and arc index 13

We give a list of minimal grid diagrams of the 13 crossing prime non-alternating knots which have arc index 13. There are 9,988 prime knots with crossing number 13. Among them 4,878 are alternating and have arc index 15. Among the other non-alternating knots, 49, 399, 1,412, and 3,250 have arc index 10, 11, 12, and 13, respectively. We used the Dowker–Thistlethwaite code of the 3,250 knots provided by the program Knotscape to generate spanning trees of the corresponding knot diagrams to obtain minimal arc presentations in the form of grid diagrams.

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Publication Details

Journal
Journal of Knot Theory and Its Ramifications
Published
2025-02-06
DOI
https://doi.org/10.1142/s0218216525500099
Primary Topic
Mathematics and Applications
Type
article
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article

Minimal grid diagrams of the prime knots with crossing number 13 and arc index 13

Gyo Taek Jin, Chanmin Lee, Yeseo Park, Yoonsang Lee et al.
Journal of Knot Theory and Its Ramifications
Mathematics and Applications
article

Minimal grid diagrams of the prime knots with crossing number 13 and arc index 13

Gyo Taek Jin, Chanmin Lee, Yeseo Park, Yoonsang Lee, Hun Kim, Hwa Jeong Lee
article en

Abstract

We give a list of minimal grid diagrams of the 13 crossing prime non-alternating knots which have arc index 13. There are 9,988 prime knots with crossing number 13. Among them 4,878 are alternating and have arc index 15. Among the other non-alternating knots, 49, 399, 1,412, and 3,250 have arc index 10, 11, 12, and 13, respectively. We used the Dowker–Thistlethwaite code of the 3,250 knots provided by the program Knotscape to generate spanning trees of the corresponding knot diagrams to obtain minimal arc presentations in the form of grid diagrams.

Journal of Knot Theory and Its RamificationsVol. 34(04)
Korea Advanced Institute of Science and Technology (KR), Dongguk University (KR), Korean Academy of Science and Technology (KR), Department of Mathematical Sciences (RU)
Sustainable cities and communities
Openalex Percentile: Top 95%
Mathematics and Applications
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