Lower Bounds for the Ropelength of Reduced Conformations
نویسنده
چکیده
This paper generalizes the results of Sadjadi [4] and Alley [1] by providing an algorithm to find a lower bound on the ropelength of any knot which admits a reduced diagram. This lower bound is found by changing this problem of geometry into one of linear programming, which is then solved by the simplex algorithm.
منابع مشابه
Quadrisecants Give New Lower Bounds for the Ropelength of a Knot
Using the existence of a special quadrisecant line, we show the ropelength of any nontrivial knot is at least 15.66. This improves the previously known lower bound of 12. Numerical experiments have found a trefoil with ropelength less than 16.372, so our new bounds are quite sharp.
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