KnotPlot and ideal knot configurations of all prime knots through 10 crossings, only 31 and 41 do not contain subknots other than the global knot and the unknot. Furthermore, all KnotPlot and ideal knot configurations contain either a 31 or 41 subknot. An analysis of second and higher generation predecessors and subknotsIn all but one of the ideal configurations of knot types with nine or fewer crossings for which the predecessors are defined, 67 in total, we found that the set of predecessor knots and the set of subknots of Vans Shoes For Girls 2017
This is not the case, however, for the KnotPlot configurations where some of the first generation predecessors do not reach the strict criterion of 50% closures (see Table 1). Among Vans Shoes For Girls Black And Blue
second and higher generations. All first generation predecessors are present among the majority subknots of ideal knots.
4 shows the disk matrix of the one exceptional case, an ideal 919 knot. This positive 919 knot has a 77 knot as one of its first generation subknots. The predecessors of the 77 knot are 41, 31, and 01. However, the Vans All Red High Tops 31 subknot is not observed as a second generation subknot of the ideal 919 configuration. Instead of extending the rays to infinity, the rays are cut as soon they leave the the convex hull of the analyzed subchain and then are closed with an additional segment, yielding a configuration equiva.
closure procedure, the fraction of closures forming 73 knots is around 20%. This observation prompted us to consider a more discriminating class of subknots, which we call the majority subknots, consisting of knot types that are formed in at least 50% of the closures for some subchain. Interestingly, all of the majority subknots observed in the analyzed ideal and KnotPlot configurations belong to the set of predecessors of the corresponding knot types. We then analyzed whether all predecessor knots are observed among the majority subknots of ideal knots. Some predecessors are not represented amongst the majority subknots but only for predecessors of Vans Atwood Hi
the ideal configurations were the same. Fig.
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