Minimal grid diagrams of the prime knots with crossing number 14 and arc index 13, 14
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arXiv
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| Format: | Preprint |
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2024
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| author | Lee, Hwa Jeong Stoimenow, Alexander Kim, Hun Kim, Minchae Ryu, Songwon Shin, Dongju Choi, Joon Hyeok Choi, Woo Jin Park, Jin Seong Jin, Gyo Taek |
| author_facet | Lee, Hwa Jeong Stoimenow, Alexander Kim, Hun Kim, Minchae Ryu, Songwon Shin, Dongju Choi, Joon Hyeok Choi, Woo Jin Park, Jin Seong Jin, Gyo Taek |
| contents | 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 3,180 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 8,027 knots having arc index 13 and 15,735 knots having arc index 14. We show them by their minimal grid diagrams. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_15859 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimal grid diagrams of the prime knots with crossing number 14 and arc index 13, 14 Lee, Hwa Jeong Stoimenow, Alexander Kim, Hun Kim, Minchae Ryu, Songwon Shin, Dongju Choi, Joon Hyeok Choi, Woo Jin Park, Jin Seong Jin, Gyo Taek Geometric Topology 57K10 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 3,180 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 8,027 knots having arc index 13 and 15,735 knots having arc index 14. We show them by their minimal grid diagrams. |
| title | Minimal grid diagrams of the prime knots with crossing number 14 and arc index 13, 14 |
| topic | Geometric Topology 57K10 |
| url | https://arxiv.org/abs/2407.15859 |