Pensieve header: Tabulating virtual 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]});
AllVPBs[n_,m_]:=DeleteDuplicatesBy[CVD@*(OverBar[Γ])]@Flatten@Table[b, {k,0,m},{b,ProudVPBs[n,k]}]

AllVPBs[2,2]/. (Subscript[(OverBar[σ]), i_,j_]):>xm[i,j] /. (Subscript[σ, i_,j_])->xp[i,j]

SaveList[n_,m_]:=Module[{fname, VPBs,t, c},
fname="Data/VPB_"<>ToString[n]<>"_"<>ToString[m]<>".m";
If[FileType[fname]===File, VPBs=Get[fname]; t="Cached",
t=First@Timing[VPBs=Select[AllVPBs[n,m] /. (Subscript[(OverBar[σ]), i_,j_]):>xm[i,j] /. (Subscript[σ, i_,j_])->xp[i,j], (Length[#]==m+1)&]];
Echo@"Saving...";
Put[VPBs, fname]
];
c=Length[VPBs];
Echo[{n,m}->{t,c}];
c
];

SaveList[3,3]

1561-145

(tab=Table[SaveList[n,m],{n,2,6},{m,0,4}]) // MatrixForm

(({{1, 4, 12, 36, 108}, {1, 12, 132, 1416, 15156}, {1, 24, 504, 10344, 211416}, {1, 40, 1320, 41760, 1308360}, {1, 60, 2820, 124140, 5357700}}))//Transpose//MatrixForm

SaveList[2,5]

SaveList[2,6]

SaveList[3,5]

SaveList[3,6]

SaveList[4,5]

Exit[]