Identifier
Identifier
  • St001231: Dyck paths ⟶ ℤ (values match St001234The number of indecomposable three dimensional modules with projective dimension one.)
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 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.
Actually the same statistics results for algebras with at most 7 simple modules when dropping the assumption that the module has projective dimension one. The author is not sure whether this holds in general.
Code

DeclareOperation("neighbortest",[IsList]);

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

local A,LL,LL2,U,simA;

A:=LIST[1];
simA:=Filtered(SimpleModules(A),x->IsProjectiveModule(x)=false and IsInjectiveModule(x)=false and ProjDimensionOfModule(x,30)<=1);
U:=Filtered(simA,x->ProjDimensionOfModule(x,30)=ProjDimensionOfModule(DTr(x),30) and ProjDimensionOfModule(x,30)=ProjDimensionOfModule(TrD(x),30));
return(Size(U));
end);


Created
Aug 08, 2018 at 13:01 by Rene Marczinzik
Updated
Aug 08, 2018 at 13:01 by Rene Marczinzik