SetDirectory["C:\\drorbn\\AcademicPensieve\\Talks\\ICERM-2305"];
<< Signatures`

Kas[X[1,5,2,4]]⋃Kas[X[2,5,3,6]]⋃Kas[X[7,8,9,10]]//(Subscript[FM, -2,5])

Table[K->BR@K, {K,AllKnots[{3,7}]}]

OPD[BR[n_,l_List]]:=Module[{σ,f,y,r=PD[]},
σ=Range[n];f=Table[0,n];
Do[y=Abs@x; ++f[[σ[[{y,y+1}]]]]; σ[[{y,y+1}]]=σ[[{y+1,y}]] ,{x,l}] ;
σ=Range[n];f=Most@FoldList[Plus,1,f+1];
Do[y=Abs@x;
AppendTo[r,If[Sign[x]>0,
X[f[[σ[[y+1]]]],f[[σ[[y]]]]+1,f[[σ[[y+1]]]]+1,f[[σ[[y]]]]],
X[f[[σ[[y]]]],f[[σ[[y+1]]]],f[[σ[[y]]]]+1,f[[σ[[y+1]]]]+1]
]];
++f[[σ[[{y,y+1}]]]]; σ[[{y,y+1}]]=σ[[{y+1,y}]] ,
{x,l}];
r]
OPD@BR[Knot[5,2]]

f={3,5,7};

Most@FoldList[Plus,1,f+1]

Kas[b_BR]:=Kas@OPD@b; TL[b_BR]:=TL@OPD@b;

BR[Knot[7,2]]

TL@BR[Knot[7,2]]

Kas@BR[Knot[7,2]]

TL@BR[3,{1,2,-2,-1}]

Do[Print[TL@BR[2,Table[-1,k]]/.{u->0,ω->-1}],{k,10,15}];

Do[Print[Kas@BR[2,Table[-1,k]]/.u->0],{k,10,15}];

Echo[#->TL[#][[2,1]]]&/@Get["../../Projects/OU/Data/B_3_3.m"];

BR[3,{-2,-1,2}]//BraidPlot

BR[3,{-2,-1,2}]//TL

BR[3,{1,-2,-1}]//TL

Echo[#->Kas[#][[2,1]]]&/@Get["../../Projects/OU/Data/B_3_3.m"];

Select[Get["../../Projects/OU/Data/B_3_4.m"], Length[TL[#][[2,1]]]>1&]

Select[Get["../../Projects/OU/Data/B_3_5.m"], Length[TL[#][[2,1]]]>1&]

Select[Get["../../Projects/OU/Data/B_4_4.m"], Length[TL[#][[2,1]]]>1&]

Select[Get["../../Projects/OU/Data/B_4_5.m"], Length[TL[#][[2,1]]]>1&]

TL@BR[4,{1,-2,3,2,-1}]

BraidPlot@BR[4,{1,-2,3,2,-1}]

Kas@BR[4,{1,-2,3,2,-1}]

Select[Get["../../Projects/OU/Data/B_3_3.m"], Length[Kas[#][[2,1]]]>0&]

Select[Get["../../Projects/OU/Data/B_3_4.m"], Length[Kas[#][[2,1]]]>0&]

Select[Get["../../Projects/OU/Data/B_3_5.m"], Length[Kas[#][[2,1]]]>0&]

BR[3,{-1,2,1,1,2}]//BraidPlot

Kas@BR[3,{-1,2,1,1,2}]

TL@BR[3,{-1,2,1,1,2}]

Column@DeleteCases[_->{0,0}][#->{Length[TL[#][[2,1]]], Length[Kas[#][[2,1]]]}&/@ Get["../../Projects/OU/Data/B_3_5.m"]]

Column@DeleteCases[_->{0,0}][#->{Length[TL[#][[2,1]]], Length[Kas[#][[2,1]]]}&/@ Get["../../Projects/OU/Data/B_4_3.m"]]

Column@DeleteCases[_->{0,0}][#->{Length[TL[#][[2,1]]], Length[Kas[#][[2,1]]]}&/@ Get["../../Projects/OU/Data/B_4_4.m"]]

Column@DeleteCases[_->{0,0}][#->{Length[TL[#][[2,1]]], Length[Kas[#][[2,1]]]}&/@ Get["../../Projects/OU/Data/B_4_5.m"]]

B1=BR[4,{1,-2,3,2,-1}];
B2=BR[4,{1,-2,1,-3,2}];

BraidPlot/@{B1,B2}

OPD/@{B1,B2}

Kas/@OPD/@{B1,B2}

TL/@OPD/@{B1,B2}

Grid@Table[
f1=TLSig[β]; f2=KasSig[β];
{β, Plot[f1,{u,-1,1}], Plot[f2,{u,-1,1}]},
{β,Get["../../Projects/OU/Data/B_4_3.m"]}
]