the unknotting number one. The disk matrix of the 52 knot shows that, as the chain forming the 52 knot is shortened, it can transition either to a 31 knot or to an unknot. This resembles the situation in which a minimal Vans Game Over Shoes
22 since they typically have a smaller minimal crossing number than the knot type . To b.
It is tempting, therefore, to conjecture that this is always the case for knot types with Vans Era White Gum
The next example (Fig. 2C) is the 52 knot, a twist knot (as are 31 and 41). Twist knots always have unknotting number equal to one. Again, as in the case of disk matrices for the 31 and the 41 knots, one can pass directly from the global knot zone to the unknot zone. One also can pass through the 31 intermediate zone on the way to the zone of unknots. The disk matrices we have computed for the KnotPlot configurations (and later ideal knots) with the unknotting number equal to one always showed a direct passage from the zone of the global knot to the zone of the unknot.
atrix by the direct passage from the global knot type to the gray colored zone as the length of the subchains gets shorter. Fig. 2B shows the disk matrix for the 51 knot, another torus knot. Subchains of the 51 knot are capable of forming the 31 knot type. Of course, subknots forming the unknot are always observed since any polygon with fewer than six edges (and, thus, subchain with four or fewer edges) is unknotted33. The KnotPlot configuration of the 51 knot has a toroidal five fold symmetry that can be seen in its disk matrix. The unknotting number of the 51 knot is two, which also is visible in the disk matrix, since to pass from the green colored 51 zone to the zone where the subchains only form unknots, one needs to pass through the zone of subchains forming 31 subknots.
diagram of the 52 knot is subject to single crossing changes22. The knots resulting from single crossing changes are either 31 knots or unknots. Knot types arising from individual crossing changes performed on a minimal crossing Vans Usa diagram of knot type have been called predecessors of Vans High Tops Mens
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