Minimal grid diagrams of the prime knots with crossing number 14 and arc index 13, 14

There are 46,972 prime knots with crossing number 14. Among them 19,536 are alternating and have arc index 16. Among the non-alternating knots, 17, 477, and 3180 have arc index 10, 11, and 12, respectively. The remaining 23,762 have arc index 13 or 14. There are none with arc index smaller than 10 or larger than 14. We obtained 8027 knots having arc index 13 and 15,735 knots having arc index 14. We show them by their minimal grid diagrams.

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Publication Details

Journal
Journal of Knot Theory and Its Ramifications
Published
2025-10-15
DOI
https://doi.org/10.1142/s0218216525500907
Primary Topic
Mathematics and Applications
Type
article
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article

Minimal grid diagrams of the prime knots with crossing number 14 and arc index 13, 14

Gyo Taek Jin, A. Stoimenow, Minchae Kim, Hun Kim et al.
Journal of Knot Theory and Its Ramifications
Mathematics and Applications
article

Minimal grid diagrams of the prime knots with crossing number 14 and arc index 13, 14

Gyo Taek Jin, A. Stoimenow, Minchae Kim, Hun Kim, Hwa Jeong Lee, D.Y. Shin, S. Ryu
article en

Abstract

There are 46,972 prime knots with crossing number 14. Among them 19,536 are alternating and have arc index 16. Among the non-alternating knots, 17, 477, and 3180 have arc index 10, 11, and 12, respectively. The remaining 23,762 have arc index 13 or 14. There are none with arc index smaller than 10 or larger than 14. We obtained 8027 knots having arc index 13 and 15,735 knots having arc index 14. We show them by their minimal grid diagrams.

Journal of Knot Theory and Its Ramifications
Korea Advanced Institute of Science and Technology (KR), Dongguk University (KR), Korean Academy of Science and Technology (KR)
Openalex Percentile: Top 65%
Mathematics and Applications
DOISourceOpenAlex
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Minimal grid diagrams of the prime knots with crossing number 14 and arc index 13, 14 — Gyo Taek Jin, A. Stoimenow, et al. · Journal of Knot Theory and Its Ramifications (2025) | TGRS Research Map | TGRS