Abstract:The structure of classical minimal prime knot presentations suggests that there are often, perhaps always, subsegments that present either the trefoil or the figure-eight knot. A comprehensive study of the subknots of the minimal prime knot presentations through 15 crossings shows that this is always the case for these knot presentations. Among this set of 313, 258 prime knot presentation, there are only 547, or 0.17%, that do not contain a trefoil subknot. Thus, 99.83% of minimal prime knot presentations thro… Show more
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