In[]:=
HypergraphAutomorphismGroup/@({{1,2},{1,3}}{{1,2},{1,4},{2,4},{3,4}})
Out[]=
PermutationGroup[{Cycles[{{2,3}}]}]PermutationGroup[{}]
In[]:=
EnumerateHypergraphs[{{2,2}}]
Out[]=
{{{1,1},{1,1}},{{1,1},{1,2}},{{1,1},{2,1}},{{1,2},{1,2}},{{1,2},{2,1}},{{1,2},{1,3}},{{1,2},{2,3}},{{1,2},{3,2}}}
In[]:=
HypergraphAutomorphismGroup/@%
Out[]=
{PermutationGroup[{}],PermutationGroup[{}],PermutationGroup[{}],PermutationGroup[{}],PermutationGroup[{Cycles[{{1,2}}]}],PermutationGroup[{Cycles[{{2,3}}]}],PermutationGroup[{}],PermutationGroup[{Cycles[{{1,3}}]}]}
In[]:=
#->HypergraphAutomorphismGroup[#]&/@EnumerateHypergraphs[{{3,2}}]
Out[]=
In[]:=
Length[GroupElements[PermutationGroup[{Cycles[{{3,4}}],Cycles[{{2,3}}]}]]]
Out[]=
6
{{1,2},{2,3},{3,1}}XXXX
In[]:=
#->HypergraphAutomorphismGroup[#]&/@EnumerateHypergraphs[{{1,3}}]
Out[]=
{{{1,1,1}}PermutationGroup[{}],{{1,1,2}}PermutationGroup[{}],{{1,2,1}}PermutationGroup[{}],{{1,2,2}}PermutationGroup[{}],{{1,2,3}}PermutationGroup[{}]}
In[]:=
#->HypergraphAutomorphismGroup[#]&/@EnumerateHypergraphs[{{2,3}}]
Out[]=
In[]:=
GroupElements[PermutationGroup[{Cycles[{{1,2},{3,4}}]}]]
Out[]=
{Cycles[{}],Cycles[{{1,2},{3,4}}]}
In[]:=
#Length[GroupElements[HypergraphAutomorphismGroup[#]]]&/@EnumerateHypergraphs[{{2,3}}]
Out[]=
In[]:=
#Length[GroupElements[HypergraphAutomorphismGroup[#]]]&/@EnumerateHypergraphs[{{3,2}}]
Out[]=
In[]:=
WolframModelPlot[{{1,2},{1,3},{1,4}}]
Out[]=
In[]:=
#Length[GroupElements[HypergraphAutomorphismGroup[#]]]&/@EnumerateHypergraphs[{{3,3}}]
Out[]=
In[]:=
Counts[Last/@%]
Out[]=
13042,2204,310,612
In[]:=
#GroupOrder[HypergraphAutomorphismGroup[#]]&/@EnumerateHypergraphs[{{4,2}}]
Out[]=
LHS has larger automorphism than RHS broken symmetry
LHS has larger automorphism than RHS broken symmetry
Effective rules
Effective rules
“WolframModelRuleProduct2”
“WolframModelRuleProduct2”
Testing
Testing
For each LHS, just identify all possible namings
For each LHS, just identify all possible namings