Nontrivial knots have resultant probability below one half
Nontrivial knots have resultant probability below one half
Let a free knot diagram be given, and let a nontrivial knot be a knot other than the unknot. The resultant knot probability is the proportion of crossing assignments of the free knot diagram that produce that specified nontrivial knot. Resultant-probability half-bound conjecture. For all free knot diagrams and nontrivial knots, the resultant knot probability is less than . The claim proposes a universal upper bound on the probability of any nontrivial resultant; the source gives no proof or resolution in the supplied context.
Sources & referencesView supporting material
Primary source
Andrew Ducharme and Emily Peters, “Combinatorial Random Knots”, arXiv:1912.06286 (2020).
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