Pensieve header: A brute force program to compute the width of a knot.

<< KnotTheory`

pd=PD@Knot[8,17]

?FoldList

pd

FoldList[Complement[#1⋃#2,#1⋂#2]&, {}, List@@List@@@pd]

Max[Length/@FoldList[Complement[#1⋃#2,#1⋂#2]&, {}, List@@List@@@pd]]

Width[pd_PD]:=Max[Length/@FoldList[Complement[#1⋃#2,#1⋂#2]&, {}, List@@List@@@pd]]

Width[PD@Knot[8,17]]

Min[Width/@Permutations[PD@Knot[4,1]]]

Width[pd_PD]:=Max[Length/@FoldList[Complement[#1⋃#2,#1⋂#2]&, {}, List@@List@@@pd]];
Table[Echo[K->Min[Width/@Permutations[PD@K]]], {K, AllKnots[]}]