Hard Diagrams of the Unknot
Publication date
2024-07
Authors
Burton, Benjamin A.
Chang, Hsien Chih
Löffler, Maarten
Maria, Clément
de Mesmay, Arnaud
Schleimer, Saul
Sedgwick, Eric
Spreer, Jonathan
Editors
Advisors
Supervisors
Document Type
Article
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taverne
Abstract
We present three “hard” diagrams of the unknot. They require (at least) three extra crossings before they can be simplified to the trivial unknot diagram via Reidemeister moves in (Formula presented.). Two of them are constructed by applying previously proposed methods. The proof of their hardness uses significant computational resources. We also determine that no small “standard” example of a hard unknot diagram requires more than one extra crossing for Reidemeister moves in (Formula presented.).
Keywords
Knot theory, mathematical software, Reidemeister moves, unknot, unknot recognition problem, Taverne, General Mathematics
Citation
Burton, B A, Chang, H C, Löffler, M, Maria, C, de Mesmay, A, Schleimer, S, Sedgwick, E & Spreer, J 2024, 'Hard Diagrams of the Unknot', Experimental Mathematics, vol. 33, no. 3, pp. 482-500. https://doi.org/10.1080/10586458.2022.2161676