Identifier
Identifier
Values
[1,0] generating graphics... => 1
[1,0,1,0] generating graphics... => 2
[1,1,0,0] generating graphics... => 1
[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... => 3
[1,1,1,0,0,0] generating graphics... => 1
[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... => 3
[1,0,1,1,0,1,0,0] generating graphics... => 4
[1,0,1,1,1,0,0,0] generating graphics... => 4
[1,1,0,0,1,0,1,0] generating graphics... => 4
[1,1,0,0,1,1,0,0] generating graphics... => 4
[1,1,0,1,0,0,1,0] generating graphics... => 4
[1,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,0,1,1,0,0,0] generating graphics... => 4
[1,1,1,0,0,0,1,0] generating graphics... => 4
[1,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,0,0,0] generating graphics... => 4
[1,1,1,1,0,0,0,0] generating graphics... => 1
[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... => 5
[1,0,1,0,1,1,1,0,0,0] generating graphics... => 5
[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... => 5
[1,0,1,1,0,1,0,1,0,0] generating graphics... => 5
[1,0,1,1,0,1,1,0,0,0] generating graphics... => 5
[1,0,1,1,1,0,0,0,1,0] generating graphics... => 4
[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... => 5
[1,0,1,1,1,1,0,0,0,0] generating graphics... => 5
[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... => 5
[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... => 5
[1,1,0,0,1,1,1,0,0,0] generating graphics... => 5
[1,1,0,1,0,0,1,0,1,0] generating graphics... => 5
[1,1,0,1,0,0,1,1,0,0] generating graphics... => 5
[1,1,0,1,0,1,0,0,1,0] generating graphics... => 5
[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... => 5
[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... => 5
[1,1,0,1,1,0,1,0,0,0] generating graphics... => 5
[1,1,0,1,1,1,0,0,0,0] generating graphics... => 5
[1,1,1,0,0,0,1,0,1,0] generating graphics... => 5
[1,1,1,0,0,0,1,1,0,0] generating graphics... => 5
[1,1,1,0,0,1,0,0,1,0] generating graphics... => 5
[1,1,1,0,0,1,0,1,0,0] generating graphics... => 5
[1,1,1,0,0,1,1,0,0,0] generating graphics... => 5
[1,1,1,0,1,0,0,0,1,0] generating graphics... => 5
[1,1,1,0,1,0,0,1,0,0] generating graphics... => 5
[1,1,1,0,1,0,1,0,0,0] generating graphics... => 5
[1,1,1,0,1,1,0,0,0,0] generating graphics... => 5
[1,1,1,1,0,0,0,0,1,0] generating graphics... => 5
[1,1,1,1,0,0,0,1,0,0] generating graphics... => 5
[1,1,1,1,0,0,1,0,0,0] generating graphics... => 5
[1,1,1,1,0,1,0,0,0,0] generating graphics... => 5
[1,1,1,1,1,0,0,0,0,0] generating graphics... => 1
[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... => 6
[1,0,1,0,1,0,1,1,1,0,0,0] generating graphics... => 6
[1,0,1,0,1,1,0,0,1,0,1,0] generating graphics... => 5
[1,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 6
[1,0,1,0,1,1,0,1,0,0,1,0] generating graphics... => 6
[1,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 6
[1,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 6
[1,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 6
[1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 6
[1,0,1,0,1,1,1,0,1,0,0,0] generating graphics... => 6
[1,0,1,0,1,1,1,1,0,0,0,0] generating graphics... => 6
[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... => 6
[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... => 6
[1,0,1,1,0,0,1,1,1,0,0,0] generating graphics... => 5
[1,0,1,1,0,1,0,0,1,0,1,0] generating graphics... => 6
[1,0,1,1,0,1,0,0,1,1,0,0] generating graphics... => 6
[1,0,1,1,0,1,0,1,0,0,1,0] generating graphics... => 6
[1,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 6
[1,0,1,1,0,1,0,1,1,0,0,0] generating graphics... => 6
[1,0,1,1,0,1,1,0,0,0,1,0] generating graphics... => 6
[1,0,1,1,0,1,1,0,0,1,0,0] generating graphics... => 6
[1,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 6
[1,0,1,1,0,1,1,1,0,0,0,0] generating graphics... => 6
[1,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 6
[1,0,1,1,1,0,0,0,1,1,0,0] generating graphics... => 5
[1,0,1,1,1,0,0,1,0,0,1,0] generating graphics... => 6
[1,0,1,1,1,0,0,1,0,1,0,0] generating graphics... => 6
[1,0,1,1,1,0,0,1,1,0,0,0] generating graphics... => 5
[1,0,1,1,1,0,1,0,0,0,1,0] generating graphics... => 6
[1,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 6
[1,0,1,1,1,0,1,0,1,0,0,0] generating graphics... => 6
[1,0,1,1,1,0,1,1,0,0,0,0] generating graphics... => 6
[1,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 5
[1,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 5
[1,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 5
[1,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 6
[1,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 6
[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... => 6
[1,1,0,0,1,0,1,1,0,0,1,0] generating graphics... => 6
[1,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 6
[1,1,0,0,1,0,1,1,1,0,0,0] generating graphics... => 6
[1,1,0,0,1,1,0,0,1,0,1,0] generating graphics... => 6
[1,1,0,0,1,1,0,0,1,1,0,0] generating graphics... => 5
[1,1,0,0,1,1,0,1,0,0,1,0] generating graphics... => 6
[1,1,0,0,1,1,0,1,0,1,0,0] generating graphics... => 6
[1,1,0,0,1,1,0,1,1,0,0,0] generating graphics... => 6
[1,1,0,0,1,1,1,0,0,0,1,0] generating graphics... => 5
[1,1,0,0,1,1,1,0,0,1,0,0] generating graphics... => 5
[1,1,0,0,1,1,1,0,1,0,0,0] generating graphics... => 6
[1,1,0,0,1,1,1,1,0,0,0,0] generating graphics... => 6
[1,1,0,1,0,0,1,0,1,0,1,0] generating graphics... => 6
[1,1,0,1,0,0,1,0,1,1,0,0] generating graphics... => 6
[1,1,0,1,0,0,1,1,0,0,1,0] generating graphics... => 6
[1,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 6
[1,1,0,1,0,0,1,1,1,0,0,0] generating graphics... => 6
[1,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 6
[1,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 6
[1,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 6
[1,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 6
[1,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 5
[1,1,0,1,0,1,1,0,0,0,1,0] generating graphics... => 6
[1,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 6
[1,1,0,1,0,1,1,0,1,0,0,0] generating graphics... => 5
[1,1,0,1,0,1,1,1,0,0,0,0] generating graphics... => 6
[1,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 6
[1,1,0,1,1,0,0,0,1,1,0,0] generating graphics... => 5
[1,1,0,1,1,0,0,1,0,0,1,0] generating graphics... => 6
[1,1,0,1,1,0,0,1,0,1,0,0] generating graphics... => 6
[1,1,0,1,1,0,0,1,1,0,0,0] generating graphics... => 6
[1,1,0,1,1,0,1,0,0,0,1,0] generating graphics... => 6
[1,1,0,1,1,0,1,0,0,1,0,0] generating graphics... => 6
[1,1,0,1,1,0,1,0,1,0,0,0] generating graphics... => 5
[1,1,0,1,1,0,1,1,0,0,0,0] generating graphics... => 6
[1,1,0,1,1,1,0,0,0,0,1,0] generating graphics... => 5
[1,1,0,1,1,1,0,0,0,1,0,0] generating graphics... => 5
[1,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 6
[1,1,0,1,1,1,0,1,0,0,0,0] generating graphics... => 6
[1,1,0,1,1,1,1,0,0,0,0,0] generating graphics... => 6
[1,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 6
[1,1,1,0,0,0,1,0,1,1,0,0] generating graphics... => 6
[1,1,1,0,0,0,1,1,0,0,1,0] generating graphics... => 5
[1,1,1,0,0,0,1,1,0,1,0,0] generating graphics... => 6
[1,1,1,0,0,0,1,1,1,0,0,0] generating graphics... => 6
[1,1,1,0,0,1,0,0,1,0,1,0] generating graphics... => 6
[1,1,1,0,0,1,0,0,1,1,0,0] generating graphics... => 6
[1,1,1,0,0,1,0,1,0,0,1,0] generating graphics... => 6
[1,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 5
[1,1,1,0,0,1,0,1,1,0,0,0] generating graphics... => 6
[1,1,1,0,0,1,1,0,0,0,1,0] generating graphics... => 5
[1,1,1,0,0,1,1,0,0,1,0,0] generating graphics... => 6
[1,1,1,0,0,1,1,0,1,0,0,0] generating graphics... => 6
[1,1,1,0,0,1,1,1,0,0,0,0] generating graphics... => 6
[1,1,1,0,1,0,0,0,1,0,1,0] generating graphics... => 6
[1,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 6
[1,1,1,0,1,0,0,1,0,0,1,0] generating graphics... => 6
[1,1,1,0,1,0,0,1,0,1,0,0] generating graphics... => 5
[1,1,1,0,1,0,0,1,1,0,0,0] generating graphics... => 6
[1,1,1,0,1,0,1,0,0,0,1,0] generating graphics... => 6
[1,1,1,0,1,0,1,0,0,1,0,0] generating graphics... => 5
[1,1,1,0,1,0,1,0,1,0,0,0] generating graphics... => 5
[1,1,1,0,1,0,1,1,0,0,0,0] generating graphics... => 6
[1,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 5
[1,1,1,0,1,1,0,0,0,1,0,0] generating graphics... => 6
[1,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 6
[1,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 6
[1,1,1,0,1,1,1,0,0,0,0,0] generating graphics... => 6
[1,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 6
[1,1,1,1,0,0,0,0,1,1,0,0] generating graphics... => 6
[1,1,1,1,0,0,0,1,0,0,1,0] generating graphics... => 6
[1,1,1,1,0,0,0,1,0,1,0,0] generating graphics... => 6
[1,1,1,1,0,0,0,1,1,0,0,0] generating graphics... => 6
[1,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 6
[1,1,1,1,0,0,1,0,0,1,0,0] generating graphics... => 6
[1,1,1,1,0,0,1,0,1,0,0,0] generating graphics... => 6
[1,1,1,1,0,0,1,1,0,0,0,0] generating graphics... => 6
[1,1,1,1,0,1,0,0,0,0,1,0] generating graphics... => 6
[1,1,1,1,0,1,0,0,0,1,0,0] generating graphics... => 6
[1,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 6
[1,1,1,1,0,1,0,1,0,0,0,0] generating graphics... => 6
[1,1,1,1,0,1,1,0,0,0,0,0] generating graphics... => 6
[1,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 6
[1,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 6
[1,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 6
[1,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 6
[1,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 6
[1,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 1
click to show generating function       
Description
Number of indecomposable injective modules whose socle has projective dimension at most g-1 when g denotes the global dimension in the corresponding Nakayama algebra.
References
[1] Marczinzik, René Upper bounds for the dominant dimension of Nakayama and related algebras. zbMATH:06820683
Code
DeclareOperation("numberindinjwithpdsocleatmostgldimminusone",[IsList]);

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

local A,g,projA,UU,priA,injA;

A:=LIST[1];
g:=GlobalDimensionOfAlgebra(A,100);
injA:=IndecInjectiveModules(A);UU:=Filtered(injA,x->ProjDimensionOfModule(SocleOfModule(x),30)<=g-1);
return(Size(UU));
end);


Created
Apr 29, 2018 at 14:14 by Rene Marczinzik
Updated
May 02, 2018 at 11:34 by Rene Marczinzik