- FindStat

Identifier

St001195: Dyck paths ⟶ ℤ

Values

=>
                            Cc0005;cc-rep
                            
                            
                            

                        [1,0,1,0,1,0]=>0
[1,0,1,1,0,0]=>1
[1,1,0,0,1,0]=>0
[1,1,0,1,0,0]=>1
[1,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,1,0,0]=>1
[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]=>1
[1,1,0,0,1,0,1,0]=>0
[1,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,0]=>0
[1,1,0,1,0,1,0,0]=>1
[1,1,0,1,1,0,0,0]=>1
[1,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,0,1,1,0,0]=>1
[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]=>1
[1,0,1,1,0,0,1,0,1,0]=>0
[1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,0]=>0
[1,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0]=>0
[1,1,0,0,1,0,1,1,0,0]=>1
[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]=>1
[1,1,0,1,0,0,1,0,1,0]=>0
[1,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,0,1,0]=>0
[1,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,0]=>1
[1,1,0,1,1,0,1,0,0,0]=>1
[1,1,0,1,1,1,0,0,0,0]=>1
[1,1,1,0,0,0,1,0,1,0]=>1
[1,1,1,0,0,0,1,1,0,0]=>1
[1,1,1,0,0,1,0,0,1,0]=>0
[1,1,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,0,0]=>1
[1,1,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,0,0]=>1
[1,1,1,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,0]=>1
                    

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Description

The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$.

Code

DeclareOperation("gldimAAfAA",[IsList]);

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

local A,k,injA,RegA,temp,CoRegA,priA,U,UU,g,g2,B,T,TT;

A:=LIST[1];
projA:=IndecProjectiveModules(A);priA:=DirectSumOfQPAModules(Filtered(projA,x->IsInjectiveModule(x)=true));RegA:=DirectSumOfQPAModules(projA);
T:=DualOfModule(priA);TT:=StarOfModule(T);
U:=TraceOfModule(TT,RegA);UU:=CoKernel(U);
B:=EndOfModuleAsQuiverAlgebra(UU)[3];
g:=GlobalDimensionOfAlgebra(B,30);
return(g);
end);

Created

May 14, 2018 at 10:36 by Rene Marczinzik

Updated

May 14, 2018 at 10:36 by Rene Marczinzik