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Identifier
Values
[1,0] => 2
[1,0,1,0] => 2
[1,1,0,0] => 5
[1,0,1,0,1,0] => 2
[1,0,1,1,0,0] => 4
[1,1,0,0,1,0] => 5
[1,1,0,1,0,0] => 5
[1,1,1,0,0,0] => 14
[1,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,0] => 10
[1,1,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,0] => 10
[1,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,0,0,0] => 10
[1,1,1,0,0,0,1,0] => 14
[1,1,1,0,0,1,0,0] => 14
[1,1,1,0,1,0,0,0] => 14
[1,1,1,1,0,0,0,0] => 42
[1,0,1,0,1,0,1,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,0] => 8
[1,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,0,0,0] => 8
[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] => 28
[1,1,0,0,1,0,1,0,1,0] => 5
[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] => 25
[1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,1,0,0] => 10
[1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,0] => 5
[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] => 25
[1,1,1,0,0,0,1,0,1,0] => 14
[1,1,1,0,0,0,1,1,0,0] => 28
[1,1,1,0,0,1,0,0,1,0] => 14
[1,1,1,0,0,1,0,1,0,0] => 14
[1,1,1,0,0,1,1,0,0,0] => 28
[1,1,1,0,1,0,0,0,1,0] => 14
[1,1,1,0,1,0,0,1,0,0] => 14
[1,1,1,0,1,0,1,0,0,0] => 14
[1,1,1,0,1,1,0,0,0,0] => 28
[1,1,1,1,0,0,0,0,1,0] => 42
[1,1,1,1,0,0,0,1,0,0] => 42
[1,1,1,1,0,0,1,0,0,0] => 42
[1,1,1,1,0,1,0,0,0,0] => 42
[1,1,1,1,1,0,0,0,0,0] => 132
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Description
Number of tilting modules of the corresponding LNakayama algebra, where a tilting module is a generalised tilting module of projective dimension 1.
References
[1] https://en.wikipedia.org/wiki/Tilting_theory
Code
DeclareOperation("TiltingModulesProjDim1",[IsList]);

InstallMethod(TiltingModulesProjDim1, "for a representation of a quiver", [IsList],0,function(LIST)

local M, n, f, N, i, h;

u:=LIST[1];
A:=NakayamaAlgebra(GF(3),u);
L:=ARQuiver([A,1000])[2];
LL:=Filtered(L,x->(IsProjectiveModule(x)=false or IsInjectiveModule(x)=false));
LL2:=Filtered(LL,x->ProjDimensionOfModule(x,100)<=1);
r:=Size(SimpleModules(A))-(Size(L)-Size(LL));
subsets1:=Combinations([1..Length(LL2)],r);subsets2:=List(subsets1,x->LL2{x});
W:=Filtered(subsets2,x->N_RigidModule(DirectSumOfQPAModules(x),1)=true);




return([u,Size(W)]);

end);
Created
Aug 25, 2017 at 11:15 by Rene Marczinzik
Updated
Aug 25, 2017 at 11:15 by Rene Marczinzik