Identifier
Identifier
  • St001234: Dyck paths ⟶ ℤ (values match St001231The number of simple modules that are non-projective and non-injective with the property that they have projective dimension equal to one and that also the Auslander-Reiten translates of the module and the inverse Auslander-Reiten translate of the module have the same projective dimension.)
Values
[1,0] generating graphics... => 0
[1,0,1,0] generating graphics... => 0
[1,1,0,0] generating graphics... => 0
[1,0,1,0,1,0] generating graphics... => 0
[1,0,1,1,0,0] generating graphics... => 0
[1,1,0,0,1,0] generating graphics... => 0
[1,1,0,1,0,0] generating graphics... => 0
[1,1,1,0,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,0] generating graphics... => 0
[1,0,1,0,1,1,0,0] generating graphics... => 0
[1,0,1,1,0,0,1,0] generating graphics... => 0
[1,0,1,1,0,1,0,0] generating graphics... => 0
[1,0,1,1,1,0,0,0] generating graphics... => 0
[1,1,0,0,1,0,1,0] generating graphics... => 0
[1,1,0,0,1,1,0,0] generating graphics... => 0
[1,1,0,1,0,0,1,0] generating graphics... => 0
[1,1,0,1,0,1,0,0] generating graphics... => 0
[1,1,0,1,1,0,0,0] generating graphics... => 0
[1,1,1,0,0,0,1,0] generating graphics... => 1
[1,1,1,0,0,1,0,0] generating graphics... => 1
[1,1,1,0,1,0,0,0] generating graphics... => 1
[1,1,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,0,1,0,1,0,1,0] generating graphics... => 0
[1,0,1,0,1,0,1,1,0,0] generating graphics... => 0
[1,0,1,0,1,1,0,0,1,0] generating graphics... => 0
[1,0,1,0,1,1,0,1,0,0] generating graphics... => 0
[1,0,1,0,1,1,1,0,0,0] generating graphics... => 0
[1,0,1,1,0,0,1,0,1,0] generating graphics... => 0
[1,0,1,1,0,0,1,1,0,0] generating graphics... => 0
[1,0,1,1,0,1,0,0,1,0] generating graphics... => 0
[1,0,1,1,0,1,0,1,0,0] generating graphics... => 0
[1,0,1,1,0,1,1,0,0,0] generating graphics... => 0
[1,0,1,1,1,0,0,0,1,0] generating graphics... => 0
[1,0,1,1,1,0,0,1,0,0] generating graphics... => 0
[1,0,1,1,1,0,1,0,0,0] generating graphics... => 0
[1,0,1,1,1,1,0,0,0,0] generating graphics... => 1
[1,1,0,0,1,0,1,0,1,0] generating graphics... => 0
[1,1,0,0,1,0,1,1,0,0] generating graphics... => 0
[1,1,0,0,1,1,0,0,1,0] generating graphics... => 0
[1,1,0,0,1,1,0,1,0,0] generating graphics... => 0
[1,1,0,0,1,1,1,0,0,0] generating graphics... => 0
[1,1,0,1,0,0,1,0,1,0] generating graphics... => 0
[1,1,0,1,0,0,1,1,0,0] generating graphics... => 0
[1,1,0,1,0,1,0,0,1,0] generating graphics... => 0
[1,1,0,1,0,1,0,1,0,0] generating graphics... => 0
[1,1,0,1,0,1,1,0,0,0] generating graphics... => 0
[1,1,0,1,1,0,0,0,1,0] generating graphics... => 0
[1,1,0,1,1,0,0,1,0,0] generating graphics... => 0
[1,1,0,1,1,0,1,0,0,0] generating graphics... => 0
[1,1,0,1,1,1,0,0,0,0] generating graphics... => 0
[1,1,1,0,0,0,1,0,1,0] generating graphics... => 1
[1,1,1,0,0,0,1,1,0,0] generating graphics... => 1
[1,1,1,0,0,1,0,0,1,0] generating graphics... => 1
[1,1,1,0,0,1,0,1,0,0] generating graphics... => 1
[1,1,1,0,0,1,1,0,0,0] generating graphics... => 1
[1,1,1,0,1,0,0,0,1,0] generating graphics... => 1
[1,1,1,0,1,0,0,1,0,0] generating graphics... => 1
[1,1,1,0,1,0,1,0,0,0] generating graphics... => 1
[1,1,1,0,1,1,0,0,0,0] generating graphics... => 1
[1,1,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,0,0] generating graphics... => 3
[1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 0
[1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 0
[1,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 0
[1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 0
[1,0,1,0,1,0,1,1,1,0,0,0] generating graphics... => 0
[1,0,1,0,1,1,0,0,1,0,1,0] generating graphics... => 0
[1,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 0
[1,0,1,0,1,1,0,1,0,0,1,0] generating graphics... => 0
[1,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 0
[1,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 0
[1,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 0
[1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 0
[1,0,1,0,1,1,1,0,1,0,0,0] generating graphics... => 0
[1,0,1,0,1,1,1,1,0,0,0,0] generating graphics... => 1
[1,0,1,1,0,0,1,0,1,0,1,0] generating graphics... => 0
[1,0,1,1,0,0,1,0,1,1,0,0] generating graphics... => 0
[1,0,1,1,0,0,1,1,0,0,1,0] generating graphics... => 0
[1,0,1,1,0,0,1,1,0,1,0,0] generating graphics... => 0
[1,0,1,1,0,0,1,1,1,0,0,0] generating graphics... => 0
[1,0,1,1,0,1,0,0,1,0,1,0] generating graphics... => 0
[1,0,1,1,0,1,0,0,1,1,0,0] generating graphics... => 0
[1,0,1,1,0,1,0,1,0,0,1,0] generating graphics... => 0
[1,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 0
[1,0,1,1,0,1,0,1,1,0,0,0] generating graphics... => 0
[1,0,1,1,0,1,1,0,0,0,1,0] generating graphics... => 0
[1,0,1,1,0,1,1,0,0,1,0,0] generating graphics... => 0
[1,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 0
[1,0,1,1,0,1,1,1,0,0,0,0] generating graphics... => 0
[1,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 0
[1,0,1,1,1,0,0,0,1,1,0,0] generating graphics... => 0
[1,0,1,1,1,0,0,1,0,0,1,0] generating graphics... => 0
[1,0,1,1,1,0,0,1,0,1,0,0] generating graphics... => 0
[1,0,1,1,1,0,0,1,1,0,0,0] generating graphics... => 0
[1,0,1,1,1,0,1,0,0,0,1,0] generating graphics... => 0
[1,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 0
[1,0,1,1,1,0,1,0,1,0,0,0] generating graphics... => 0
[1,0,1,1,1,0,1,1,0,0,0,0] generating graphics... => 0
[1,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 1
[1,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 1
[1,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 1
[1,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 1
[1,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,0,1,0,1,0] generating graphics... => 0
[1,1,0,0,1,0,1,0,1,1,0,0] generating graphics... => 0
[1,1,0,0,1,0,1,1,0,0,1,0] generating graphics... => 0
[1,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 0
[1,1,0,0,1,0,1,1,1,0,0,0] generating graphics... => 0
[1,1,0,0,1,1,0,0,1,0,1,0] generating graphics... => 0
[1,1,0,0,1,1,0,0,1,1,0,0] generating graphics... => 0
[1,1,0,0,1,1,0,1,0,0,1,0] generating graphics... => 0
[1,1,0,0,1,1,0,1,0,1,0,0] generating graphics... => 0
[1,1,0,0,1,1,0,1,1,0,0,0] generating graphics... => 0
[1,1,0,0,1,1,1,0,0,0,1,0] generating graphics... => 0
[1,1,0,0,1,1,1,0,0,1,0,0] generating graphics... => 0
[1,1,0,0,1,1,1,0,1,0,0,0] generating graphics... => 0
[1,1,0,0,1,1,1,1,0,0,0,0] generating graphics... => 1
[1,1,0,1,0,0,1,0,1,0,1,0] generating graphics... => 0
[1,1,0,1,0,0,1,0,1,1,0,0] generating graphics... => 0
[1,1,0,1,0,0,1,1,0,0,1,0] generating graphics... => 0
[1,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 0
[1,1,0,1,0,0,1,1,1,0,0,0] generating graphics... => 0
[1,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 0
[1,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 0
[1,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 0
[1,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 0
[1,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 0
[1,1,0,1,0,1,1,0,0,0,1,0] generating graphics... => 0
[1,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 0
[1,1,0,1,0,1,1,0,1,0,0,0] generating graphics... => 0
[1,1,0,1,0,1,1,1,0,0,0,0] generating graphics... => 0
[1,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 0
[1,1,0,1,1,0,0,0,1,1,0,0] generating graphics... => 0
[1,1,0,1,1,0,0,1,0,0,1,0] generating graphics... => 0
[1,1,0,1,1,0,0,1,0,1,0,0] generating graphics... => 0
[1,1,0,1,1,0,0,1,1,0,0,0] generating graphics... => 0
[1,1,0,1,1,0,1,0,0,0,1,0] generating graphics... => 0
[1,1,0,1,1,0,1,0,0,1,0,0] generating graphics... => 0
[1,1,0,1,1,0,1,0,1,0,0,0] generating graphics... => 0
[1,1,0,1,1,0,1,1,0,0,0,0] generating graphics... => 0
[1,1,0,1,1,1,0,0,0,0,1,0] generating graphics... => 0
[1,1,0,1,1,1,0,0,0,1,0,0] generating graphics... => 0
[1,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 0
[1,1,0,1,1,1,0,1,0,0,0,0] generating graphics... => 0
[1,1,0,1,1,1,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 1
[1,1,1,0,0,0,1,0,1,1,0,0] generating graphics... => 1
[1,1,1,0,0,0,1,1,0,0,1,0] generating graphics... => 1
[1,1,1,0,0,0,1,1,0,1,0,0] generating graphics... => 1
[1,1,1,0,0,0,1,1,1,0,0,0] generating graphics... => 1
[1,1,1,0,0,1,0,0,1,0,1,0] generating graphics... => 1
[1,1,1,0,0,1,0,0,1,1,0,0] generating graphics... => 1
[1,1,1,0,0,1,0,1,0,0,1,0] generating graphics... => 1
[1,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 1
[1,1,1,0,0,1,0,1,1,0,0,0] generating graphics... => 1
[1,1,1,0,0,1,1,0,0,0,1,0] generating graphics... => 1
[1,1,1,0,0,1,1,0,0,1,0,0] generating graphics... => 1
[1,1,1,0,0,1,1,0,1,0,0,0] generating graphics... => 1
[1,1,1,0,0,1,1,1,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,0,0,0,1,0,1,0] generating graphics... => 1
[1,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 1
[1,1,1,0,1,0,0,1,0,0,1,0] generating graphics... => 1
[1,1,1,0,1,0,0,1,0,1,0,0] generating graphics... => 1
[1,1,1,0,1,0,0,1,1,0,0,0] generating graphics... => 1
[1,1,1,0,1,0,1,0,0,0,1,0] generating graphics... => 1
[1,1,1,0,1,0,1,0,0,1,0,0] generating graphics... => 1
[1,1,1,0,1,0,1,0,1,0,0,0] generating graphics... => 1
[1,1,1,0,1,0,1,1,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 1
[1,1,1,0,1,1,0,0,0,1,0,0] generating graphics... => 1
[1,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 1
[1,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 1
[1,1,1,0,1,1,1,0,0,0,0,0] generating graphics... => 1
[1,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,1,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,0,1,0,1,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,1,1,0,0,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,1,0,0,0] generating graphics... => 2
[1,1,1,1,0,0,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,1,0,0,0,0] generating graphics... => 2
[1,1,1,1,0,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 3
[1,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 3
[1,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 3
[1,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 4
click to show generating function       
Description
The number of indecomposable three dimensional modules with projective dimension one.
It return zero when there are no such modules.
Code

DeclareOperation("3dimproj",[IsList]);

InstallMethod(3dimproj, "for a representation of a quiver", [IsList],0,function(LIST)

local A,LL,LL2,U,simA;

A:=LIST[1];
LL:=ARQuiverNak([A]);
LL2:=Filtered(LL,x->Dimension(x)=3);
if Size(LL2)=0 then return(0);else
return(Size(Filtered(LL2,x->ProjDimensionOfModule(x,2)=1)));fi;
end);



Created
Aug 08, 2018 at 10:17 by Rene Marczinzik
Updated
Aug 08, 2018 at 10:17 by Rene Marczinzik