Pensieve header: Tabulating classical braids.

SetDirectory@"C:\\drorbn\\AcademicPensieve\\Projects\\OU";
<< "OU-Programs.m"

CVD[vd_VD]:=((CVD@@vd)/.{_EOS->Sequence[],(Subscript[X, s_])[i_,j_]:>Sequence[s i,j]});
AllBs[n_,m_]:=DeleteDuplicatesBy[CVD@*(OverBar[Γ])]@Flatten@Table[b, {k,0,m},{b,ProudBs[n,k]}]

BR[3,{2,-1,-1,-1,-1}]//(CVD@*(OverBar[Γ]))

SaveList[n_,m_]:=Module[{fname, Bs,t, c},
fname="Data/B_"<>ToString[n]<>"_"<>ToString[m]<>".m";
If[FileType[fname]===File, Bs=Get[fname]; t="Cached",
t=First@Timing[Bs=Select[AllBs[n,m], (Length[#[[2]]]==m)&]];
Echo@"Saving...";
Put[Bs, fname]
];
c=Length[Bs];
Echo[{n,m}->{t,c}];
c
];

SaveList[4,3]

(tab=Table[SaveList[n,m],{m,0,9},{n,2,6}]) // MatrixForm

Table[6×(2^m)-2Fibonacci[m+3]-2, {m,12}]

SaveList[3,10]

SaveList[3,11]

SaveList[3,12]