Unknot diagrams requiring a quadratic number of reidemeister moves to untangle

Joel Hass, Tahl Nowik

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

Given any knot diagram E, we present a sequence of knot diagrams of the same knot type for which the minimum number of Reidemeister moves required to pass to E is quadratic with respect to the number of crossings. These bounds apply both in S2 and in ℝ2.

Original languageEnglish
Pages (from-to)91-95
Number of pages5
JournalDiscrete and Computational Geometry
Volume44
Issue number1
DOIs
StatePublished - Jul 2010

Bibliographical note

Funding Information:
The research of J. Hass was supported in part by NSF grant DMS-0306602.

Funding

The research of J. Hass was supported in part by NSF grant DMS-0306602.

FundersFunder number
National Science FoundationDMS-0306602
Directorate for Mathematical and Physical Sciences0306602

    Keywords

    • Reidemister moves
    • Unknot

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