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.
Authors
- Gyo Taek Jin (ORCID: https://orcid.org/0000-0002-9861-2069)
- Chanmin Lee
- Yeseo Park
- Yoonsang Lee (ORCID: https://orcid.org/0000-0002-5573-9414)
- Hun Kim (ORCID: https://orcid.org/0000-0003-2023-3453)
- Hwa Jeong Lee (ORCID: https://orcid.org/0000-0003-2618-8665)
Institutions
- Korea Advanced Institute of Science and Technology (KR)
- Dongguk University (KR)
- Korean Academy of Science and Technology (KR)
- Department of Mathematical Sciences (RU)
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
- Field-Weighted Citation Impact
- 0.00