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Crossing numbers of random two-bridge knots

Publication Type : Journal Article

Publisher : Topology and its Applications

Source : Topology and its Applications, vol. 247, pp. 100–114, Sept. 2018

Url : https://arxiv.org/abs/1606.00277

Campus : Amritapuri

School : School of Computing

Department : Computer Science and Engineering

Year : 2018

Abstract : In a previous work, the first and third authors studied a random knot model for all two-bridge knots using billiard table diagrams. Here we present a closed formula for the distribution of the crossing numbers of such random knots. We also show that the probability of any given knot appearing in this model decays to zero at an exponential rate as the length of the billiard table goes to infinity. This confirms a conjecture from the previous work.

Cite this Research Publication : M. Cohen, C. Even-Zohar, and S. R. Krishnan∗, “Crossing numbers of random two-bridge knots,” Topology and its Applications, vol. 247, pp. 100–114, Sept. 2018

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