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Identifier
Values
[1,0] => 3
[1,0,1,0] => 4
[1,1,0,0] => 6
[1,0,1,0,1,0] => 5
[1,0,1,1,0,0] => 6
[1,1,0,0,1,0] => 7
[1,1,0,1,0,0] => 7
[1,1,1,0,0,0] => 10
[1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,0] => 7
[1,0,1,1,0,0,1,0] => 7
[1,0,1,1,0,1,0,0] => 7
[1,0,1,1,1,0,0,0] => 9
[1,1,0,0,1,0,1,0] => 8
[1,1,0,0,1,1,0,0] => 9
[1,1,0,1,0,0,1,0] => 8
[1,1,0,1,0,1,0,0] => 8
[1,1,0,1,1,0,0,0] => 9
[1,1,1,0,0,0,1,0] => 11
[1,1,1,0,0,1,0,0] => 11
[1,1,1,0,1,0,0,0] => 11
[1,1,1,1,0,0,0,0] => 15
[1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,1,0,0] => 8
[1,0,1,0,1,1,0,0,1,0] => 8
[1,0,1,0,1,1,0,1,0,0] => 8
[1,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,1,0,0,1,0,1,0] => 8
[1,0,1,1,0,0,1,1,0,0] => 9
[1,0,1,1,0,1,0,0,1,0] => 8
[1,0,1,1,0,1,0,1,0,0] => 8
[1,0,1,1,0,1,1,0,0,0] => 9
[1,0,1,1,1,0,0,0,1,0] => 10
[1,0,1,1,1,0,0,1,0,0] => 10
[1,0,1,1,1,0,1,0,0,0] => 10
[1,0,1,1,1,1,0,0,0,0] => 13
[1,1,0,0,1,0,1,0,1,0] => 9
[1,1,0,0,1,0,1,1,0,0] => 10
[1,1,0,0,1,1,0,0,1,0] => 10
[1,1,0,0,1,1,0,1,0,0] => 10
[1,1,0,0,1,1,1,0,0,0] => 12
[1,1,0,1,0,0,1,0,1,0] => 9
[1,1,0,1,0,0,1,1,0,0] => 10
[1,1,0,1,0,1,0,0,1,0] => 9
[1,1,0,1,0,1,0,1,0,0] => 9
[1,1,0,1,0,1,1,0,0,0] => 10
[1,1,0,1,1,0,0,0,1,0] => 10
[1,1,0,1,1,0,0,1,0,0] => 10
[1,1,0,1,1,0,1,0,0,0] => 10
[1,1,0,1,1,1,0,0,0,0] => 12
[1,1,1,0,0,0,1,0,1,0] => 12
[1,1,1,0,0,0,1,1,0,0] => 13
[1,1,1,0,0,1,0,0,1,0] => 12
[1,1,1,0,0,1,0,1,0,0] => 12
[1,1,1,0,0,1,1,0,0,0] => 13
[1,1,1,0,1,0,0,0,1,0] => 12
[1,1,1,0,1,0,0,1,0,0] => 12
[1,1,1,0,1,0,1,0,0,0] => 12
[1,1,1,0,1,1,0,0,0,0] => 13
[1,1,1,1,0,0,0,0,1,0] => 16
[1,1,1,1,0,0,0,1,0,0] => 16
[1,1,1,1,0,0,1,0,0,0] => 16
[1,1,1,1,0,1,0,0,0,0] => 16
[1,1,1,1,1,0,0,0,0,0] => 21
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Description
The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path.
Code
DeclareOperation("numbersprojdim1", [IsList]);

InstallMethod(numbersprojdim1, "for a representation of a quiver", [IsList],0,function(L)


local list, n, temp1, Liste_d, j, i, k, r, kk;


list:=L;

A:=NakayamaAlgebra(GF(3),list);
L:=ARQuiver([A,1000])[2];
LL:=Filtered(L,x->ProjDimensionOfModule(x,1)<=1);
return(Size(LL));
end
);
Created
Oct 27, 2017 at 20:35 by Rene Marczinzik
Updated
Oct 27, 2017 at 20:35 by Rene Marczinzik