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Creators/Authors contains: "Davis, Lowell"

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  1. ; (, Journal of Knot Theory and Its Ramifications)
    A well-known algorithm for unknotting knots involves traversing a knot diagram and changing each crossing that is first encountered from below. The minimal number of crossings changed in this way across all diagrams for a knot is called the ascending number of the knot. The ascending number is bounded below by the unknotting number. We show that for knots obtained as the closure of a positive braid, the ascending number equals the unknotting number. We also present data indicating that a similar result may hold for positive knots. We use this data to examine which low-crossing knots have the property that their ascending number is realized in a minimal crossing diagram, showing that there are at most 5 hyperbolic, alternating knots with at most 12 crossings with this property. 
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    Free, publicly-accessible full text available January 1, 2027