Group Theory
Group Theory
L^n = R^n = 1
R L = L R = 1
Lp ^ (k n) = Rp ^ (k n) = 1
Lp R Lp R = Rp L Rp L = 1
L = TM moves left with changing the symbol
Lp = moves left “permuting” the symbol (e.g. 1 <-> 0), but for larger k (= # colors) probably needs to be a generator of symmetric group
R L = L R = 1
Lp ^ (k n) = Rp ^ (k n) = 1
Lp R Lp R = Rp L Rp L = 1
L = TM moves left with changing the symbol
Lp = moves left “permuting” the symbol (e.g. 1 <-> 0), but for larger k (= # colors) probably needs to be a generator of symmetric group
In[]:=
TMNCGraph[1,{1,2}]
Out[]=
In[]:=
TMNCGraphX[1,{1,2}]
Out[]=
In[]:=
SimpleGraph[TMNCGraph[2,{1,2}]]
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In[]:=
Graph3D[TMNCGraph[2,{1,2}]]
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In[]:=
FiniteGroupData[8]
Out[]=
{{CyclicGroup,8},{AbelianGroup,{4,2}},{AbelianGroup,{2,2,2}},{DihedralGroup,4},Quaternion}
In[]:=
FiniteGroupData[#,"CayleyGraph"]&/@%
Out[]=
,
,
,
,
In[]:=
TMNCGraph[3,{1,2}]
Out[]=
In[]:=
TMNCGraph[4,{1,2}]
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