Identifier
Identifier
Values
[1,0] generating graphics... => 1
[1,0,1,0] generating graphics... => 2
[1,1,0,0] generating graphics... => 2
[1,0,1,0,1,0] generating graphics... => 3
[1,0,1,1,0,0] generating graphics... => 3
[1,1,0,0,1,0] generating graphics... => 3
[1,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,0] generating graphics... => 2
[1,0,1,0,1,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,0,0] generating graphics... => 4
[1,0,1,1,0,0,1,0] generating graphics... => 4
[1,0,1,1,0,1,0,0] generating graphics... => 3
[1,0,1,1,1,0,0,0] generating graphics... => 3
[1,1,0,0,1,0,1,0] generating graphics... => 4
[1,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,1,0,0,1,0] generating graphics... => 3
[1,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,0,1,0] generating graphics... => 3
[1,1,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,0,1,0,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,0,1,0,1,0,1,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,0,0] generating graphics... => 5
[1,0,1,0,1,1,0,0,1,0] generating graphics... => 5
[1,0,1,0,1,1,0,1,0,0] generating graphics... => 4
[1,0,1,0,1,1,1,0,0,0] generating graphics... => 4
[1,0,1,1,0,0,1,0,1,0] generating graphics... => 5
[1,0,1,1,0,0,1,1,0,0] generating graphics... => 4
[1,0,1,1,0,1,0,0,1,0] generating graphics... => 4
[1,0,1,1,0,1,0,1,0,0] generating graphics... => 4
[1,0,1,1,0,1,1,0,0,0] generating graphics... => 4
[1,0,1,1,1,0,0,0,1,0] generating graphics... => 3
[1,0,1,1,1,0,0,1,0,0] generating graphics... => 4
[1,0,1,1,1,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,0,1,0,1,0,1,0] generating graphics... => 5
[1,1,0,0,1,0,1,1,0,0] generating graphics... => 4
[1,1,0,0,1,1,0,0,1,0] generating graphics... => 4
[1,1,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,1,0,0,1,1,1,0,0,0] generating graphics... => 3
[1,1,0,1,0,0,1,0,1,0] generating graphics... => 4
[1,1,0,1,0,0,1,1,0,0] generating graphics... => 4
[1,1,0,1,0,1,0,0,1,0] generating graphics... => 4
[1,1,0,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,0,0,1,0] generating graphics... => 4
[1,1,0,1,1,0,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,0,0,0,0] generating graphics... => 3
[1,1,1,0,0,0,1,0,1,0] generating graphics... => 4
[1,1,1,0,0,0,1,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,0,0,1,0] generating graphics... => 4
[1,1,1,0,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,1,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,0,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,0,0,0,0] generating graphics... => 3
[1,1,1,1,0,0,0,0,1,0] generating graphics... => 3
[1,1,1,1,0,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 6
[1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 6
[1,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 6
[1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,1,0,0,0] generating graphics... => 5
[1,0,1,0,1,1,0,0,1,0,1,0] generating graphics... => 6
[1,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 5
[1,0,1,0,1,1,0,1,0,0,1,0] generating graphics... => 5
[1,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 5
[1,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 5
[1,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 4
[1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 5
[1,0,1,0,1,1,1,0,1,0,0,0] generating graphics... => 4
[1,0,1,0,1,1,1,1,0,0,0,0] generating graphics... => 4
[1,0,1,1,0,0,1,0,1,0,1,0] generating graphics... => 6
[1,0,1,1,0,0,1,0,1,1,0,0] generating graphics... => 5
[1,0,1,1,0,0,1,1,0,0,1,0] generating graphics... => 4
[1,0,1,1,0,0,1,1,0,1,0,0] generating graphics... => 5
[1,0,1,1,0,0,1,1,1,0,0,0] generating graphics... => 4
[1,0,1,1,0,1,0,0,1,0,1,0] generating graphics... => 5
[1,0,1,1,0,1,0,0,1,1,0,0] generating graphics... => 5
[1,0,1,1,0,1,0,1,0,0,1,0] generating graphics... => 5
[1,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 5
[1,0,1,1,0,1,0,1,1,0,0,0] generating graphics... => 5
[1,0,1,1,0,1,1,0,0,0,1,0] generating graphics... => 5
[1,0,1,1,0,1,1,0,0,1,0,0] generating graphics... => 4
[1,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 4
[1,0,1,1,0,1,1,1,0,0,0,0] generating graphics... => 4
[1,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 4
[1,0,1,1,1,0,0,0,1,1,0,0] generating graphics... => 3
[1,0,1,1,1,0,0,1,0,0,1,0] generating graphics... => 5
[1,0,1,1,1,0,0,1,0,1,0,0] generating graphics... => 5
[1,0,1,1,1,0,0,1,1,0,0,0] generating graphics... => 4
[1,0,1,1,1,0,1,0,0,0,1,0] generating graphics... => 4
[1,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 4
[1,0,1,1,1,0,1,0,1,0,0,0] generating graphics... => 4
[1,0,1,1,1,0,1,1,0,0,0,0] generating graphics... => 4
[1,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 3
[1,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 4
[1,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 3
[1,1,0,0,1,0,1,0,1,0,1,0] generating graphics... => 6
[1,1,0,0,1,0,1,0,1,1,0,0] generating graphics... => 5
[1,1,0,0,1,0,1,1,0,0,1,0] generating graphics... => 5
[1,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 5
[1,1,0,0,1,0,1,1,1,0,0,0] generating graphics... => 4
[1,1,0,0,1,1,0,0,1,0,1,0] generating graphics... => 5
[1,1,0,0,1,1,0,0,1,1,0,0] generating graphics... => 4
[1,1,0,0,1,1,0,1,0,0,1,0] generating graphics... => 5
[1,1,0,0,1,1,0,1,0,1,0,0] generating graphics... => 5
[1,1,0,0,1,1,0,1,1,0,0,0] generating graphics... => 4
[1,1,0,0,1,1,1,0,0,0,1,0] generating graphics... => 3
[1,1,0,0,1,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,0,0,1,1,1,0,1,0,0,0] generating graphics... => 4
[1,1,0,0,1,1,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,0,0,1,0,1,0,1,0] generating graphics... => 5
[1,1,0,1,0,0,1,0,1,1,0,0] generating graphics... => 5
[1,1,0,1,0,0,1,1,0,0,1,0] generating graphics... => 5
[1,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,1,0,1,0,0,1,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 5
[1,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 5
[1,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 5
[1,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,0,0,0,1,0] generating graphics... => 5
[1,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,0,1,0,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,1,0,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 5
[1,1,0,1,1,0,0,0,1,1,0,0] generating graphics... => 4
[1,1,0,1,1,0,0,1,0,0,1,0] generating graphics... => 4
[1,1,0,1,1,0,0,1,0,1,0,0] generating graphics... => 4
[1,1,0,1,1,0,0,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,0,0,0,1,0] generating graphics... => 4
[1,1,0,1,1,0,1,0,0,1,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,0,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,1,0,0,0,0] generating graphics... => 4
[1,1,0,1,1,1,0,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,1,1,0,0,0,1,0,0] generating graphics... => 4
[1,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,1,0,0,0,0,0] generating graphics... => 3
[1,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 5
[1,1,1,0,0,0,1,0,1,1,0,0] generating graphics... => 4
[1,1,1,0,0,0,1,1,0,0,1,0] generating graphics... => 4
[1,1,1,0,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,0,1,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,1,0,0,1,0,1,0] generating graphics... => 5
[1,1,1,0,0,1,0,0,1,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,0,1,0,0,1,0] generating graphics... => 5
[1,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,0,1,1,0,0,0] generating graphics... => 4
[1,1,1,0,0,1,1,0,0,0,1,0] generating graphics... => 4
[1,1,1,0,0,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,1,0,1,0,0,0] generating graphics... => 4
[1,1,1,0,0,1,1,1,0,0,0,0] generating graphics... => 3
[1,1,1,0,1,0,0,0,1,0,1,0] generating graphics... => 4
[1,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 4
[1,1,1,0,1,0,0,1,0,0,1,0] generating graphics... => 4
[1,1,1,0,1,0,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,0,0,1,1,0,0,0] generating graphics... => 4
[1,1,1,0,1,0,1,0,0,0,1,0] generating graphics... => 4
[1,1,1,0,1,0,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,0,1,0,1,0,0,0] generating graphics... => 4
[1,1,1,0,1,0,1,1,0,0,0,0] generating graphics... => 4
[1,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 4
[1,1,1,0,1,1,0,0,0,1,0,0] generating graphics... => 3
[1,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,1,0,0,0,0,0] generating graphics... => 3
[1,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 4
[1,1,1,1,0,0,0,0,1,1,0,0] generating graphics... => 3
[1,1,1,1,0,0,0,1,0,0,1,0] generating graphics... => 4
[1,1,1,1,0,0,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,1,0,0,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 4
[1,1,1,1,0,0,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,1,0,0,1,0,1,0,0,0] generating graphics... => 4
[1,1,1,1,0,0,1,1,0,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,0,0,0,0,1,0] generating graphics... => 3
[1,1,1,1,0,1,0,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,0,1,0,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,1,0,0,0,0,0] generating graphics... => 3
[1,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 3
[1,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 3
[1,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 2
click to show generating function       
Description
The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path.
References
[1] Marczinzik, René Upper bounds for the dominant dimension of Nakayama and related algebras. zbMATH:06820683
Code
DeclareOperation("sumprojinjdimsimple",[IsList]);

InstallMethod(sumprojinjdimsimple, "for a representation of a quiver", [IsList],0,function(LIST)

local A,simA,TT;
A:=LIST[1];
simA:=SimpleModules(A);
TT:=[];for i in simA do Append(TT,[ProjDimensionOfModule(i,30)+InjDimensionOfModule(i,30)]);od;
return(Maximum(TT));

end);

Created
May 09, 2018 at 16:27 by Rene Marczinzik
Updated
May 09, 2018 at 16:27 by Rene Marczinzik