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 S 2 and in ℝ2.
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The research of J. Hass was supported in part by NSF grant DMS-0306602.
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Hass, J., Nowik, T. Unknot Diagrams Requiring a Quadratic Number of Reidemeister Moves to Untangle. Discrete Comput Geom 44, 91–95 (2010). https://doi.org/10.1007/s00454-009-9156-4
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DOI: https://doi.org/10.1007/s00454-009-9156-4