Notebook containing a minimum quick width permutation presentation diagram. It can also be found in MinQuickWidthPresentation.wl but graphic visuals can be found here.

<<KnotTheory`MinimumQuickWidth`

The list of all knots in a minimum graphical/quick knot presentation:

quantitiesGivenCrossingNum = <|3 -> 1, 4 -> 1, 5 -> 2, 6 -> 3, 7 -> 7, 8 -> 21, 9 -> 49, 10 -> 165|>

Table[Knot[i,j] -> Graphics[MinWidthDiagram[PD[Knot[i,j]]], ImageSize -> 400], {i, 3,10}, {j, 1, quantitiesGivenCrossingNum[i]}]