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Identifier
Values
=>
Cc0005;cc-rep
[1,0]=>1 [1,0,1,0]=>2 [1,1,0,0]=>1 [1,0,1,0,1,0]=>3 [1,0,1,1,0,0]=>3 [1,1,0,0,1,0]=>3 [1,1,0,1,0,0]=>3 [1,1,1,0,0,0]=>1 [1,0,1,0,1,0,1,0]=>4 [1,0,1,0,1,1,0,0]=>4 [1,0,1,1,0,0,1,0]=>3 [1,0,1,1,0,1,0,0]=>4 [1,0,1,1,1,0,0,0]=>4 [1,1,0,0,1,0,1,0]=>4 [1,1,0,0,1,1,0,0]=>4 [1,1,0,1,0,0,1,0]=>4 [1,1,0,1,0,1,0,0]=>4 [1,1,0,1,1,0,0,0]=>4 [1,1,1,0,0,0,1,0]=>4 [1,1,1,0,0,1,0,0]=>4 [1,1,1,0,1,0,0,0]=>4 [1,1,1,1,0,0,0,0]=>1 [1,0,1,0,1,0,1,0,1,0]=>5 [1,0,1,0,1,0,1,1,0,0]=>5 [1,0,1,0,1,1,0,0,1,0]=>5 [1,0,1,0,1,1,0,1,0,0]=>5 [1,0,1,0,1,1,1,0,0,0]=>5 [1,0,1,1,0,0,1,0,1,0]=>5 [1,0,1,1,0,0,1,1,0,0]=>4 [1,0,1,1,0,1,0,0,1,0]=>5 [1,0,1,1,0,1,0,1,0,0]=>5 [1,0,1,1,0,1,1,0,0,0]=>5 [1,0,1,1,1,0,0,0,1,0]=>4 [1,0,1,1,1,0,0,1,0,0]=>4 [1,0,1,1,1,0,1,0,0,0]=>5 [1,0,1,1,1,1,0,0,0,0]=>5 [1,1,0,0,1,0,1,0,1,0]=>5 [1,1,0,0,1,0,1,1,0,0]=>5 [1,1,0,0,1,1,0,0,1,0]=>4 [1,1,0,0,1,1,0,1,0,0]=>5 [1,1,0,0,1,1,1,0,0,0]=>5 [1,1,0,1,0,0,1,0,1,0]=>5 [1,1,0,1,0,0,1,1,0,0]=>5 [1,1,0,1,0,1,0,0,1,0]=>5 [1,1,0,1,0,1,0,1,0,0]=>4 [1,1,0,1,0,1,1,0,0,0]=>5 [1,1,0,1,1,0,0,0,1,0]=>4 [1,1,0,1,1,0,0,1,0,0]=>5 [1,1,0,1,1,0,1,0,0,0]=>5 [1,1,0,1,1,1,0,0,0,0]=>5 [1,1,1,0,0,0,1,0,1,0]=>5 [1,1,1,0,0,0,1,1,0,0]=>5 [1,1,1,0,0,1,0,0,1,0]=>5 [1,1,1,0,0,1,0,1,0,0]=>5 [1,1,1,0,0,1,1,0,0,0]=>5 [1,1,1,0,1,0,0,0,1,0]=>5 [1,1,1,0,1,0,0,1,0,0]=>5 [1,1,1,0,1,0,1,0,0,0]=>5 [1,1,1,0,1,1,0,0,0,0]=>5 [1,1,1,1,0,0,0,0,1,0]=>5 [1,1,1,1,0,0,0,1,0,0]=>5 [1,1,1,1,0,0,1,0,0,0]=>5 [1,1,1,1,0,1,0,0,0,0]=>5 [1,1,1,1,1,0,0,0,0,0]=>1 [1,0,1,0,1,0,1,0,1,0,1,0]=>6 [1,0,1,0,1,0,1,0,1,1,0,0]=>6 [1,0,1,0,1,0,1,1,0,0,1,0]=>6 [1,0,1,0,1,0,1,1,0,1,0,0]=>6 [1,0,1,0,1,0,1,1,1,0,0,0]=>6 [1,0,1,0,1,1,0,0,1,0,1,0]=>5 [1,0,1,0,1,1,0,0,1,1,0,0]=>6 [1,0,1,0,1,1,0,1,0,0,1,0]=>6 [1,0,1,0,1,1,0,1,0,1,0,0]=>6 [1,0,1,0,1,1,0,1,1,0,0,0]=>6 [1,0,1,0,1,1,1,0,0,0,1,0]=>6 [1,0,1,0,1,1,1,0,0,1,0,0]=>6 [1,0,1,0,1,1,1,0,1,0,0,0]=>6 [1,0,1,0,1,1,1,1,0,0,0,0]=>6 [1,0,1,1,0,0,1,0,1,0,1,0]=>6 [1,0,1,1,0,0,1,0,1,1,0,0]=>6 [1,0,1,1,0,0,1,1,0,0,1,0]=>4 [1,0,1,1,0,0,1,1,0,1,0,0]=>6 [1,0,1,1,0,0,1,1,1,0,0,0]=>5 [1,0,1,1,0,1,0,0,1,0,1,0]=>6 [1,0,1,1,0,1,0,0,1,1,0,0]=>6 [1,0,1,1,0,1,0,1,0,0,1,0]=>6 [1,0,1,1,0,1,0,1,0,1,0,0]=>6 [1,0,1,1,0,1,0,1,1,0,0,0]=>6 [1,0,1,1,0,1,1,0,0,0,1,0]=>6 [1,0,1,1,0,1,1,0,0,1,0,0]=>6 [1,0,1,1,0,1,1,0,1,0,0,0]=>6 [1,0,1,1,0,1,1,1,0,0,0,0]=>6 [1,0,1,1,1,0,0,0,1,0,1,0]=>6 [1,0,1,1,1,0,0,0,1,1,0,0]=>5 [1,0,1,1,1,0,0,1,0,0,1,0]=>6 [1,0,1,1,1,0,0,1,0,1,0,0]=>6 [1,0,1,1,1,0,0,1,1,0,0,0]=>5 [1,0,1,1,1,0,1,0,0,0,1,0]=>6 [1,0,1,1,1,0,1,0,0,1,0,0]=>6 [1,0,1,1,1,0,1,0,1,0,0,0]=>6 [1,0,1,1,1,0,1,1,0,0,0,0]=>6 [1,0,1,1,1,1,0,0,0,0,1,0]=>5 [1,0,1,1,1,1,0,0,0,1,0,0]=>5 [1,0,1,1,1,1,0,0,1,0,0,0]=>5 [1,0,1,1,1,1,0,1,0,0,0,0]=>6 [1,0,1,1,1,1,1,0,0,0,0,0]=>6 [1,1,0,0,1,0,1,0,1,0,1,0]=>6 [1,1,0,0,1,0,1,0,1,1,0,0]=>6 [1,1,0,0,1,0,1,1,0,0,1,0]=>6 [1,1,0,0,1,0,1,1,0,1,0,0]=>6 [1,1,0,0,1,0,1,1,1,0,0,0]=>6 [1,1,0,0,1,1,0,0,1,0,1,0]=>6 [1,1,0,0,1,1,0,0,1,1,0,0]=>5 [1,1,0,0,1,1,0,1,0,0,1,0]=>6 [1,1,0,0,1,1,0,1,0,1,0,0]=>6 [1,1,0,0,1,1,0,1,1,0,0,0]=>6 [1,1,0,0,1,1,1,0,0,0,1,0]=>5 [1,1,0,0,1,1,1,0,0,1,0,0]=>5 [1,1,0,0,1,1,1,0,1,0,0,0]=>6 [1,1,0,0,1,1,1,1,0,0,0,0]=>6 [1,1,0,1,0,0,1,0,1,0,1,0]=>6 [1,1,0,1,0,0,1,0,1,1,0,0]=>6 [1,1,0,1,0,0,1,1,0,0,1,0]=>6 [1,1,0,1,0,0,1,1,0,1,0,0]=>6 [1,1,0,1,0,0,1,1,1,0,0,0]=>6 [1,1,0,1,0,1,0,0,1,0,1,0]=>6 [1,1,0,1,0,1,0,0,1,1,0,0]=>6 [1,1,0,1,0,1,0,1,0,0,1,0]=>6 [1,1,0,1,0,1,0,1,0,1,0,0]=>6 [1,1,0,1,0,1,0,1,1,0,0,0]=>5 [1,1,0,1,0,1,1,0,0,0,1,0]=>6 [1,1,0,1,0,1,1,0,0,1,0,0]=>6 [1,1,0,1,0,1,1,0,1,0,0,0]=>5 [1,1,0,1,0,1,1,1,0,0,0,0]=>6 [1,1,0,1,1,0,0,0,1,0,1,0]=>6 [1,1,0,1,1,0,0,0,1,1,0,0]=>5 [1,1,0,1,1,0,0,1,0,0,1,0]=>6 [1,1,0,1,1,0,0,1,0,1,0,0]=>6 [1,1,0,1,1,0,0,1,1,0,0,0]=>6 [1,1,0,1,1,0,1,0,0,0,1,0]=>6 [1,1,0,1,1,0,1,0,0,1,0,0]=>6 [1,1,0,1,1,0,1,0,1,0,0,0]=>5 [1,1,0,1,1,0,1,1,0,0,0,0]=>6 [1,1,0,1,1,1,0,0,0,0,1,0]=>5 [1,1,0,1,1,1,0,0,0,1,0,0]=>5 [1,1,0,1,1,1,0,0,1,0,0,0]=>6 [1,1,0,1,1,1,0,1,0,0,0,0]=>6 [1,1,0,1,1,1,1,0,0,0,0,0]=>6 [1,1,1,0,0,0,1,0,1,0,1,0]=>6 [1,1,1,0,0,0,1,0,1,1,0,0]=>6 [1,1,1,0,0,0,1,1,0,0,1,0]=>5 [1,1,1,0,0,0,1,1,0,1,0,0]=>6 [1,1,1,0,0,0,1,1,1,0,0,0]=>6 [1,1,1,0,0,1,0,0,1,0,1,0]=>6 [1,1,1,0,0,1,0,0,1,1,0,0]=>6 [1,1,1,0,0,1,0,1,0,0,1,0]=>6 [1,1,1,0,0,1,0,1,0,1,0,0]=>5 [1,1,1,0,0,1,0,1,1,0,0,0]=>6 [1,1,1,0,0,1,1,0,0,0,1,0]=>5 [1,1,1,0,0,1,1,0,0,1,0,0]=>6 [1,1,1,0,0,1,1,0,1,0,0,0]=>6 [1,1,1,0,0,1,1,1,0,0,0,0]=>6 [1,1,1,0,1,0,0,0,1,0,1,0]=>6 [1,1,1,0,1,0,0,0,1,1,0,0]=>6 [1,1,1,0,1,0,0,1,0,0,1,0]=>6 [1,1,1,0,1,0,0,1,0,1,0,0]=>5 [1,1,1,0,1,0,0,1,1,0,0,0]=>6 [1,1,1,0,1,0,1,0,0,0,1,0]=>6 [1,1,1,0,1,0,1,0,0,1,0,0]=>5 [1,1,1,0,1,0,1,0,1,0,0,0]=>5 [1,1,1,0,1,0,1,1,0,0,0,0]=>6 [1,1,1,0,1,1,0,0,0,0,1,0]=>5 [1,1,1,0,1,1,0,0,0,1,0,0]=>6 [1,1,1,0,1,1,0,0,1,0,0,0]=>6 [1,1,1,0,1,1,0,1,0,0,0,0]=>6 [1,1,1,0,1,1,1,0,0,0,0,0]=>6 [1,1,1,1,0,0,0,0,1,0,1,0]=>6 [1,1,1,1,0,0,0,0,1,1,0,0]=>6 [1,1,1,1,0,0,0,1,0,0,1,0]=>6 [1,1,1,1,0,0,0,1,0,1,0,0]=>6 [1,1,1,1,0,0,0,1,1,0,0,0]=>6 [1,1,1,1,0,0,1,0,0,0,1,0]=>6 [1,1,1,1,0,0,1,0,0,1,0,0]=>6 [1,1,1,1,0,0,1,0,1,0,0,0]=>6 [1,1,1,1,0,0,1,1,0,0,0,0]=>6 [1,1,1,1,0,1,0,0,0,0,1,0]=>6 [1,1,1,1,0,1,0,0,0,1,0,0]=>6 [1,1,1,1,0,1,0,0,1,0,0,0]=>6 [1,1,1,1,0,1,0,1,0,0,0,0]=>6 [1,1,1,1,0,1,1,0,0,0,0,0]=>6 [1,1,1,1,1,0,0,0,0,0,1,0]=>6 [1,1,1,1,1,0,0,0,0,1,0,0]=>6 [1,1,1,1,1,0,0,0,1,0,0,0]=>6 [1,1,1,1,1,0,0,1,0,0,0,0]=>6 [1,1,1,1,1,0,1,0,0,0,0,0]=>6 [1,1,1,1,1,1,0,0,0,0,0,0]=>1
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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