Burton, Benjamin A., Chang, Hsien-Chih, Löffler, Maarten, Maria, Clément, de Mesmay, Arnaud, Schleimer, Saul, Sedgwick, Eric and Spreer, Jonathan (2023) Hard diagrams of the unknot. Experimental Mathematics . pp. 1-19. doi:10.1080/10586458.2022.2161676 ISSN 1944-950X. (In Press)

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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 S2. 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 S2.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
SWORD Depositor:	Library Publications Router
Library of Congress Subject Headings (LCSH):	Knot theory
Journal or Publication Title:	Experimental Mathematics
Publisher:	Taylor & Francis
ISSN:	1944-950X
Official Date:	7 February 2023
Dates:	Date Event 7 February 2023 Available 2023 Accepted
Page Range:	pp. 1-19
DOI:	10.1080/10586458.2022.2161676
Status:	Peer Reviewed
Publication Status:	In Press
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	11 September 2023
Open Access Version:	ArXiv

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