Lisitsa, Alexei and Vernitski, Alexei (2024) Counting graphs induced by Gauss diagrams and families of mutant alternating knots. Examples and Counterexamples, 6. p. 100162. DOI https://doi.org/10.1016/j.exco.2024.100162
Lisitsa, Alexei and Vernitski, Alexei (2024) Counting graphs induced by Gauss diagrams and families of mutant alternating knots. Examples and Counterexamples, 6. p. 100162. DOI https://doi.org/10.1016/j.exco.2024.100162
Lisitsa, Alexei and Vernitski, Alexei (2024) Counting graphs induced by Gauss diagrams and families of mutant alternating knots. Examples and Counterexamples, 6. p. 100162. DOI https://doi.org/10.1016/j.exco.2024.100162
Abstract
The construction known as Gauss diagrams or Gauss words is one of the oldest in knot theory and has been studied extensively both in the context of knots and in the context of closed curves with self-intersections. When we studied graphs induced by Gauss diagrams, we produced all examples of these graphs of small sizes, and we published the number of these graphs as sequence A343358 in the OEIS. The aim of this article is to clarify several subtle theoretical points concerning A343358. Most importantly, we explain why our numbers, produced using graph-theoretical constructions, reflect the number of so-called mutant knots.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Gauss diagram; Interlacement graph; Circle graph; Alternating knot; Mutant knot |
| Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
| SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
| Depositing User: | Unnamed user with email elements@essex.ac.uk |
| Date Deposited: | 21 Oct 2024 08:04 |
| Last Modified: | 13 Nov 2024 17:23 |
| URI: | http://repository.essex.ac.uk/id/eprint/39441 |
Available files
Filename: 1-s2.0-S2666657X24000284-main.pdf
Licence: Creative Commons: Attribution-Noncommercial-No Derivative Works 4.0