The first few most recent pending statistics:

Identifier
St000000: Dyck paths ⟶ ℤ
Values
[1,0] generating graphics... => 0
[1,0,1,0] generating graphics... => 0
[1,1,0,0] generating graphics... => 1
[1,0,1,0,1,0] generating graphics... => 0
[1,0,1,1,0,0] generating graphics... => 1
[1,1,0,0,1,0] generating graphics... => 1
[1,1,0,1,0,0] generating graphics... => 1
[1,1,1,0,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,0] generating graphics... => 0
[1,0,1,0,1,1,0,0] generating graphics... => 1
[1,0,1,1,0,0,1,0] generating graphics... => 1
[1,0,1,1,0,1,0,0] generating graphics... => 1
[1,0,1,1,1,0,0,0] generating graphics... => 1
[1,1,0,0,1,0,1,0] generating graphics... => 1
[1,1,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,1,0,0,1,0] generating graphics... => 1
[1,1,0,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,0,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,0] generating graphics... => 1
[1,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,0] generating graphics... => 1
[1,1,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,0,1,0,1,0,1,0] generating graphics... => 0
[1,0,1,0,1,0,1,1,0,0] generating graphics... => 1
[1,0,1,0,1,1,0,0,1,0] generating graphics... => 1
[1,0,1,0,1,1,0,1,0,0] generating graphics... => 1
[1,0,1,0,1,1,1,0,0,0] generating graphics... => 1
[1,0,1,1,0,0,1,0,1,0] generating graphics... => 1
[1,0,1,1,0,0,1,1,0,0] generating graphics... => 2
[1,0,1,1,0,1,0,0,1,0] generating graphics... => 1
[1,0,1,1,0,1,0,1,0,0] generating graphics... => 2
[1,0,1,1,0,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,0,1,0] generating graphics... => 1
[1,0,1,1,1,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,1,0,0,0] generating graphics... => 1
[1,0,1,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,0,1,0] generating graphics... => 1
[1,1,0,0,1,0,1,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,0,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,0,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,0,1,0,0,1,0,1,0] generating graphics... => 1
[1,1,0,1,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,1,0,1,0,0,1,0] generating graphics... => 2
[1,1,0,1,0,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,0,1,1,0,0,0] generating graphics... => 2
[1,1,0,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,0,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,0,1,0,0,0] generating graphics... => 2
[1,1,0,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,0,1,0] generating graphics... => 1
[1,1,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,0,1,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,1,1,0,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,0,1,0] generating graphics... => 1
[1,1,1,0,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,0,0] generating graphics... => 2
[1,1,1,0,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,0,0] generating graphics... => 2
[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... => 0
[1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 1
[1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,1,1,0,0,0] generating graphics... => 1
[1,0,1,0,1,1,0,0,1,0,1,0] generating graphics... => 1
[1,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 2
[1,0,1,0,1,1,0,1,0,0,1,0] generating graphics... => 1
[1,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 2
[1,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 2
[1,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 1
[1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 2
[1,0,1,0,1,1,1,0,1,0,0,0] generating graphics... => 1
[1,0,1,0,1,1,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,0,0,1,0,1,0,1,0] generating graphics... => 1
[1,0,1,1,0,0,1,0,1,1,0,0] generating graphics... => 2
[1,0,1,1,0,0,1,1,0,0,1,0] generating graphics... => 2
[1,0,1,1,0,0,1,1,0,1,0,0] generating graphics... => 2
[1,0,1,1,0,0,1,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,0,1,0,0,1,0,1,0] generating graphics... => 1
[1,0,1,1,0,1,0,0,1,1,0,0] generating graphics... => 2
[1,0,1,1,0,1,0,1,0,0,1,0] generating graphics... => 2
[1,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 2
[1,0,1,1,0,1,0,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,0,1,1,0,0,0,1,0] generating graphics... => 2
[1,0,1,1,0,1,1,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 2
[1,0,1,1,0,1,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 1
[1,0,1,1,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,1,0,0,1,0] generating graphics... => 2
[1,0,1,1,1,0,0,1,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,1,0,0,0,1,0] generating graphics... => 1
[1,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,1,0,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,0,1,0,1,0] generating graphics... => 1
[1,1,0,0,1,0,1,0,1,1,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,1,0,0,1,0] generating graphics... => 2
[1,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,0,0,1,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,0,1,0,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,0,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,0,1,0,0,0] generating graphics... => 2
[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... => 1
[1,1,0,1,0,0,1,0,1,1,0,0] generating graphics... => 2
[1,1,0,1,0,0,1,1,0,0,1,0] generating graphics... => 2
[1,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,0,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 2
[1,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 2
[1,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,0,1,0,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,1,0,1,0,0,0] generating graphics... => 2
[1,1,0,1,0,1,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 2
[1,1,0,1,1,0,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,1,0,0,1,0] generating graphics... => 2
[1,1,0,1,1,0,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,1,1,0,0,0] generating graphics... => 3
[1,1,0,1,1,0,1,0,0,0,1,0] generating graphics... => 2
[1,1,0,1,1,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,1,0,1,0,0,0] generating graphics... => 2
[1,1,0,1,1,0,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,0,1,1,1,0,0,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 2
[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... => 1
[1,1,1,0,0,0,1,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,1,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,0,1,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,1,0,0,1,0,0,1,0,1,0] generating graphics... => 2
[1,1,1,0,0,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,0,1,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,1,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,0,1,0,0,0] generating graphics... => 2
[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... => 1
[1,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,1,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,0,0,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,1,1,0,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,0,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 2
[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... => 2
[1,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 2
[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... => 2
[1,1,1,1,0,0,0,1,0,1,0,0] generating graphics... => 3
[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... => 2
[1,1,1,1,0,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,0,0,1,0,1,0,0,0] generating graphics... => 2
[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... => 2
[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... => 2
[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... => 2
[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... => 3
Description
For a Nakayama algebra corresponding to a Dyck path, we define the matrix C with entries the Hom-spaces between $e_i J$ and $e_j J$ (the radical of the indecomposable projective modules).
The statistic gives half of the rank of the matrix C^t-C.
Code


DeclareOperation("radicalmathelp",[IsList]);

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

local A,projA,U,W,i,WW,injA,j,g,l,RegA,R,GG;

A:=LIST[1];
M:=LIST[2];
projA:=IndecProjectiveModules(A);
GG:=[];for i in projA do Append(GG,[RadicalOfModule(i)]);od;
W:=[];for i in GG do Append(W,[Size(HomOverAlgebra(i,M))]);od;
return(W);

end);





DeclareOperation("radicalmat",[IsList]);

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

local A,projA,U,W,i,WW,injA,j,g,l,RegA,R,GG;

A:=LIST[1];
g:=GlobalDimensionOfAlgebra(A,33);
projA:=IndecProjectiveModules(A);
GG:=[];for i in projA do Append(GG,[RadicalOfModule(i)]);od;
W:=[];for i in GG do Append(W,[radicalmathelp([A,i])]);od;
return(TransposedMat(W)-W);

end);
Created
Jan 05, 2020 at 16:56 by Rene Marczinzik
Updated
Jan 05, 2020 at 16:56 by Rene Marczinzik
Identifier
St000000: Dyck paths ⟶ ℤ
Values
[1,0] generating graphics... => 1
[1,0,1,0] generating graphics... => 3
[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... => 4
[1,1,1,0,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,0] generating graphics... => 5
[1,0,1,0,1,1,0,0] generating graphics... => 3
[1,0,1,1,0,0,1,0] generating graphics... => 5
[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... => 3
[1,1,0,0,1,1,0,0] generating graphics... => 3
[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... => 3
[1,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,0,0,0] generating graphics... => 5
[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... => 6
[1,0,1,0,1,1,1,0,0,0] generating graphics... => 3
[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... => 5
[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... => 6
[1,0,1,1,0,1,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,0,0,0,1,0] generating graphics... => 5
[1,0,1,1,1,0,0,1,0,0] generating graphics... => 6
[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... => 3
[1,1,0,0,1,1,0,0,1,0] generating graphics... => 5
[1,1,0,0,1,1,0,1,0,0] generating graphics... => 3
[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... => 6
[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... => 6
[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... => 6
[1,1,0,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,1,0,0,0,0] generating graphics... => 4
[1,1,1,0,0,0,1,0,1,0] generating graphics... => 3
[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... => 4
[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... => 3
[1,1,1,1,0,0,0,1,0,0] generating graphics... => 4
[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... => 6
[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... => 7
[1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 7
[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... => 5
[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... => 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... => 5
[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... => 7
[1,0,1,0,1,1,1,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,0,0,1,0,1,0,1,0] generating graphics... => 7
[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... => 7
[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... => 5
[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... => 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... => 5
[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... => 7
[1,0,1,1,0,1,1,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 5
[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... => 6
[1,0,1,1,1,0,1,0,0,0,1,0] generating graphics... => 5
[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... => 7
[1,0,1,1,1,0,1,1,0,0,0,0] generating graphics... => 3
[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... => 6
[1,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 7
[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... => 5
[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... => 6
[1,1,0,0,1,0,1,1,1,0,0,0] generating graphics... => 3
[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... => 5
[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... => 6
[1,1,0,0,1,1,0,1,1,0,0,0] generating graphics... => 3
[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... => 6
[1,1,0,0,1,1,1,0,1,0,0,0] generating graphics... => 3
[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... => 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... => 7
[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... => 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... => 7
[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... => 6
[1,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 7
[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... => 6
[1,1,0,1,1,0,0,0,1,1,0,0] generating graphics... => 6
[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... => 7
[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... => 6
[1,1,0,1,1,0,1,0,0,1,0,0] generating graphics... => 7
[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... => 6
[1,1,0,1,1,1,0,0,0,1,0,0] generating graphics... => 7
[1,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,1,0,1,0,0,0,0] generating graphics... => 4
[1,1,0,1,1,1,1,0,0,0,0,0] generating graphics... => 4
[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... => 3
[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... => 3
[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... => 6
[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... => 6
[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... => 6
[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... => 4
[1,1,1,0,1,0,0,0,1,0,1,0] generating graphics... => 7
[1,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 5
[1,1,1,0,1,0,0,1,0,0,1,0] generating graphics... => 7
[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... => 5
[1,1,1,0,1,0,1,0,0,0,1,0] generating graphics... => 7
[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... => 5
[1,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 7
[1,1,1,0,1,1,0,0,0,1,0,0] generating graphics... => 5
[1,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 5
[1,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 5
[1,1,1,0,1,1,1,0,0,0,0,0] generating graphics... => 5
[1,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 3
[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... => 4
[1,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 5
[1,1,1,1,0,0,1,0,0,1,0,0] generating graphics... => 5
[1,1,1,1,0,0,1,0,1,0,0,0] generating graphics... => 5
[1,1,1,1,0,0,1,1,0,0,0,0] generating graphics... => 5
[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... => 3
[1,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 4
[1,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 5
[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... => 7
[1,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 1
Description
The number of indecomposable injective modules with even projective dimension in the corresponding Nakayama algebra.
Code

DeclareOperation("numberevenprojdiminj", [IsList]);

InstallMethod(numberevenprojdiminj, "for a representation of a quiver", [IsList],0,function(L)


local U,A,injA,W;

A:=L[1];
injA:=IndecInjectiveModules(A);
W:=Filtered(injA,x->IsEvenInt(ProjDimensionOfModule(x,33))=true);
return(Size(W));
end
);
Created
Dec 16, 2019 at 14:09 by Rene Marczinzik
Updated
Dec 16, 2019 at 14:09 by Rene Marczinzik