- FindStat

Identifier

St001200: Dyck paths ⟶ ℤ

Values

=>
                            Cc0005;cc-rep
                            
                            
                            

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

search for individual values

searching the database for the individual values of this statistic

Description

The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.

Code

DeclareOperation("numbersimplesprojdimatmostkeAe",[IsList]);

InstallMethod(numbersimplesprojdimatmostkeAe, "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,W,simB;

A:=LIST[1];
k:=LIST[2];
projA:=IndecProjectiveModules(A);priA:=DirectSumOfQPAModules(Filtered(projA,x->IsInjectiveModule(x)=true));
B:=EndOfModuleAsQuiverAlgebra(priA)[3];
simB:=SimpleModules(B);
W:=Filtered(simB,x->ProjDimensionOfModule(x,30)<=k);
return(Size(W));
end);

Created

May 14, 2018 at 11:30 by Rene Marczinzik

Updated

May 14, 2018 at 11:30 by Rene Marczinzik