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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… Click to show full abstract
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.
Keywords:
bridge knots;
two bridge;
crossing numbers;
numbers random;
random two
Journal Title: Topology and its Applications
Year Published: 2018
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Journal Title: Topology and its Applications
Year Published: 2018
Link to full text (if available)
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recommendations!