edit this statistic or download as text // json
Identifier
Values
=>
Cc0005;cc-rep
[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
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
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