In[]:=
InteractiveListSelectorSW[ParallelMapMonitored[Framed[TimeConstrained[MultiwaySystem[WolframModel[#],e23,3,"StatesGraph",VertexSize1],5]]#&,Table[RandomWolframModelRule[{{2,3}}{{3,3}}],20]]]
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In[]:=
InteractiveListSelectorSW[ParallelMapMonitored[Framed[TimeConstrained[MultiwaySystem[WolframModel[#],e23,4,"StatesGraph",VertexSize1],5]]#&,{{{1,1,2},{3,4,1}}{{5,6,5},{5,4,2},{6,2,3}},{{1,1,1},{2,3,1}}{{4,4,5},{4,1,1},{3,6,1}},{{1,2,3},{2,4,5}}{{5,6,1},{5,4,2},{6,7,8}}}]]
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General rule automorphism
General rule automorphism
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6!
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720
{{1,1,2},{3,4,1}}{{5,6,5},{5,4,2},{6,2,3}}
If the RHS is at least as symmetric as the LHS
http://people.cs.uchicago.edu/~laci/handbook/handbookchapter27.pdf
In[]:=
HypergraphAutomorphismGroup[{{1,1,2},{3,4,1}}]
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PermutationGroup[{}]
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HypergraphAutomorphismGroup[First[#]]&/@{{{1,2,3},{1,2,3}}{{1,2,3},{1,2,3},{1,2,3}},{{1,2,3},{2,3,1}}{{1,2,3},{2,3,1},{3,1,2}},{{1,2,3},{2,3,1}}{{2,2,4},{1,5,1},{6,3,3}}}
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{PermutationGroup[{}],PermutationGroup[{}],PermutationGroup[{}]}
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WolframModelPlot[{{1,2,3},{1,2,3}}]
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{{1,2,3},{1,2,3}}{{1,2,3},{1,2,3},{1,2,3}}
Edge-based global symmetry
Edge-based global symmetry
If you permute the underlying hypergraph edges as you permute the right