In[]:=
MultiwaySystem[{"""A"},"",3,"StatesGraph",GraphLayout->"LayeredDigraphEmbedding"]
Out[]=
In[]:=
MultiwaySystem[{"""A","""B"},"",3,"StatesGraph",GraphLayout->"LayeredDigraphEmbedding"]
Out[]=
In[]:=
CausalInvariantQ[{"""A","""B"},"",2]
Out[]=
True
In[]:=
EdgeCount/@
,
,
,
Out[]=
{1,5,19,63}
In[]:=
Table[MultiwaySystem[{"""A","""B"},"",t,"BranchialGraphStructure"],{t,8}]
Out[]=
In[]:=
Table[MultiwaySystem[{"""A","""B"},"",t,"BranchialGraphStructure"],{t,9}];
In[]:=
EdgeCount/@%
Out[]=
{1,5,19,63,191,543,1471,3839,9727}
In[]:=
FindSequenceFunction[%,n]
Out[]=
1
4
2+n
2
n
2
n
2
2
n
In[]:=
FullSimplify[%]
Out[]=
-1+(4+(-1+n)n)
-2+n
2
In[]:=
VertexCount/@%159
Out[]=
{2,4,8,16,32,64,128,256}
In[]:=
2^(n-2)(n^2-n+4)-1
Out[]=
-1+(4-n+)
-2+n
2
2
n
In[]:=
Table[%,{n,10}]
Out[]=
{1,5,19,63,191,543,1471,3839,9727,24063}
In[]:=
MultiwaySystem[{"""A","""B"},"",4,"BranchialGraph"]
Out[]=
In[]:=
EdgeList[%]
Out[]=
In[]:=
Map[StringJoin[Sort[Characters[#]]]&,%,{-1}]
Out[]=
Graph{"AAAA""AAAB","AAAA""AAAB","AAAA""AAAB","AAAA""AAAB","AAAB""AAAB","AAAB""AABB","AAAB""AAAB","AAAB""AABB","AAAB""AAAB","AAAB""AABB","AAAB""AABB","AAAB""AAAB","AAAB""AABB","AAAB""AABB","AAAB""AAAB","AAAB""AABB","AAAB""AABB","AABB""AABB","AABB""AABB","AABB""ABBB","AABB""AABB","AABB""ABBB","AAAB""AABB","AAAB""AABB","AAAB""AAAB","AAAB""AABB","AAAB""AABB","AAAB""AABB","AABB""AABB","AABB""ABBB","AABB""AABB","AABB""AABB","AABB""ABBB","AABB""ABBB","AABB""ABBB","AABB""AABB","AABB""ABBB","AABB""AABB","AABB""ABBB","AABB""ABBB","ABBB""ABBB","ABBB""ABBB","ABBB""ABBB","ABBB""BBBB","AAAB""AABB","AAAB""AABB","AAAB""AABB","AABB""AABB","AABB""ABBB","AABB""AABB","AABB""ABBB","AABB""ABBB","AABB""AABB","AABB""ABBB","AABB""ABBB","ABBB""ABBB","ABBB""ABBB","ABBB""BBBB","AABB""ABBB","AABB""ABBB","ABBB""ABBB","ABBB""BBBB","ABBB""BBBB"},PerformanceGoal"Quality",VertexShapeFunctionText,#1,{0,0}&
Out[]=
In[]:=
MultiwaySystem[{"""A","""B"},"",4,"BranchialGraph"]//Options
Out[]=
PerformanceGoalQuality,VertexShapeFunctionText,#1,{0,0}&
In[]:=
Graph3D/@%169
Out[]=
In[]:=
EdgeList@
[From CausalInvariance-12.nb]
[From CausalInvariance-12.nb]
General Inventory
General Inventory