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Publication Type : Journal Article
Publisher : Topology and its Applications
Source : Topology and its Applications, vol. 194, pp. 4–21, Oct. 2015
Url : https://www.sciencedirect.com/science/article/pii/S0166864115003119
Campus : Amritapuri
School : School of Computing
Department : Computer Science and Engineering
Year : 2015
Abstract : We use the Chebyshev knot diagram model of Koseleff and Pecker in order to introduce a random knot diagram model by assigning the crossings to be positive or negative uniformly at random. We give a formula for the probability of choosing a knot at random among all knots with bridge index at most 2. Restricted to this class, we define internal and external reduction moves that decrease the number of crossings of the diagram. We make calculations based on our formula, showing the numerics in graphs and providing evidence for our conjecture that the probability of any knot appearing in this model decays to zero as the number of crossings goes to infinity.
Cite this Research Publication : M. Cohen and S. R. Krishnan∗, “Random knots using Chebyshev billiard table diagrams,” Topology and its Applications, vol. 194, pp. 4–21, Oct. 2015