Tight open knots
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Abstract:The tightest open conformations of a few prime knots (31, 41, 51, 52, and 63) found with the use of the SONO algorithm are presented and discussed. The conformations are obtained from the tightest closed conformations of the knots by cutting and opening them at different locations. The length of the rope engaged in each of the open conformations is calculated. The curvature and torsion profiles of the unique tightest conformations of the 31 and 41 open knots are presented and discussed. In particular, symmetry properties of the knots reflected within their curvature and torsion profiles are analysed. Connections with the physics of polymers are discussed.
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