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. 2017 Jun 28;9(7):252. doi: 10.3390/polym9070252

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© 2017 by the authors.

Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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Knotting probabilities of the trefoil knot ( $3_{1}$ ) and its composite knots $3_{1} # 3_{1}$ , $3_{1} # 4_{1}$ , $3_{1} # 3_{1} # 3_{1}$ and $3_{1} # 3_{1} # 4_{1}$ with versus the number of segments N with good fitted curves for cylindrical self-avoiding polygons (SAP) with cylindrical radius $r_{ex} = 0.03$ . The knotting probabilities of composite knots such as $3_{1} # 3_{1}$ , $3_{1} # 4_{1}$ and $3_{1} # 3_{1} # 3_{1}$ are plotted for the Gaussian random polygons with N up to 1600 in less good statistics in [66].