Unknot Diagrams Requiring a Quadratic Number of Reidemeister Moves to Untangle
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- Hass, J. & Nowik, T. Discrete Comput Geom (2010) 44: 91. doi:10.1007/s00454-009-9156-4
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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.