- FindStat

Identifier

St001314: Dyck paths ⟶ ℤ

Values

=>
                            Cc0005;cc-rep
                            
                            
                            

                        [1,0]=>0
[1,0,1,0]=>0
[1,1,0,0]=>0
[1,0,1,0,1,0]=>0
[1,0,1,1,0,0]=>0
[1,1,0,0,1,0]=>0
[1,1,0,1,0,0]=>1
[1,1,1,0,0,0]=>0
[1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,1,0,0]=>0
[1,0,1,1,0,0,1,0]=>0
[1,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,0]=>0
[1,1,0,0,1,0,1,0]=>0
[1,1,0,0,1,1,0,0]=>0
[1,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,0]=>2
[1,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,0,1,0]=>0
[1,1,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,0,1,1,0,0]=>0
[1,0,1,0,1,1,0,0,1,0]=>0
[1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,0]=>0
[1,0,1,1,0,0,1,0,1,0]=>0
[1,0,1,1,0,0,1,1,0,0]=>0
[1,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,0]=>0
[1,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0]=>0
[1,1,0,0,1,0,1,0,1,0]=>0
[1,1,0,0,1,0,1,1,0,0]=>0
[1,1,0,0,1,1,0,0,1,0]=>0
[1,1,0,0,1,1,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,0,0]=>0
[1,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,0,0,1,0]=>2
[1,1,0,1,1,0,0,1,0,0]=>4
[1,1,0,1,1,0,1,0,0,0]=>5
[1,1,0,1,1,1,0,0,0,0]=>3
[1,1,1,0,0,0,1,0,1,0]=>0
[1,1,1,0,0,0,1,1,0,0]=>0
[1,1,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,1,0,0,0]=>4
[1,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,0,0]=>5
[1,1,1,0,1,0,1,0,0,0]=>6
[1,1,1,0,1,1,0,0,0,0]=>5
[1,1,1,1,0,0,0,0,1,0]=>0
[1,1,1,1,0,0,0,1,0,0]=>3
[1,1,1,1,0,0,1,0,0,0]=>5
[1,1,1,1,0,1,0,0,0,0]=>3
[1,1,1,1,1,0,0,0,0,0]=>0
                    

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Description

The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra.

Code


DeclareOperation("TiltingModulesnosim",[IsList]);

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

local A,g,L,LL,r,subsets1,subsets2,W,projA,prinjA,WW,priA,i;

A:=LIST[1];
g:=GlobalDimensionOfAlgebra(A,30);
L:=Filtered(ARQuiverNak([A]),x->Dimension(x)>1);
LL:=Filtered(L,x->(IsProjectiveModule(x)=false or IsInjectiveModule(x)=false));
r:=Size(SimpleModules(A))-(Size(L)-Size(LL));
subsets1:=Combinations([1..Length(LL)],r);subsets2:=List(subsets1,x->LL{x});
W:=Filtered(subsets2,x->N_RigidModule(DirectSumOfQPAModules(x),g)=true);
projA:=IndecProjectiveModules(A);prinjA:=Filtered(projA,x->IsInjectiveModule(x)=true);priA:=DirectSumOfQPAModules(prinjA);
WW:=[];for i in W do Append(WW,[DirectSumOfQPAModules([priA,DirectSumOfQPAModules(i)])]);od;


return(WW);

end);

Created

Dec 02, 2018 at 23:25 by Rene Marczinzik

Updated

Dec 02, 2018 at 23:25 by Rene Marczinzik