In[]:=
Graph3D[GeneralizedGridGraph[{4"Directed",4"Directed",4"Directed"}]]
Out[]=
Projective Space
Projective Space
Metric in branch space
Metric in branch space
Minimum number of updates to derive both points
(i.e. its the common ancestor distance in the tree)
Finding that common ancestor distance might be computationally hard
---> geometric group theory
(i.e. its the common ancestor distance in the tree)
Finding that common ancestor distance might be computationally hard
---> geometric group theory
In[]:=
TransitiveClosureGraph[GridGraph[{5,5}]]
Out[]=
In[]:=
TransitiveReductionGraph
Out[]=
In[]:=
TransitiveReductionGraph
,VertexLabelsAutomatic
Out[]=
In[]:=
Table[TransitiveReductionGraph[MultiwaySystem[{"A""AB","B""A"},"A",t,"BranchialGraph"]],{t,2,5}]
Out[]=
Projective space
Projective space
Modding out the metric by a constant
In[]:=
Tuples[Range[3],2]
Out[]=
{{1,1},{1,2},{1,3},{2,1},{2,2},{2,3},{3,1},{3,2},{3,3}}
If these were critical pairs, this must define a transitive binary relation......
What are the transitive binary relations on n elements?
https://math.stackexchange.com/questions/243773/amount-of-transitive-relations-on-a-finite-set
https://oeis.org/A006905
https://oeis.org/A000798/a000798_12.pdf
[ Quantum states are rays in Hilbert space ]
<Transitivity is discrete rescaling>
<Transitivity is discrete rescaling>