- FindStat

Identifier

St001877: Lattices ⟶ ℤ (values match St001876The number of 2-regular simple modules in the incidence algebra of the lattice.)

Values

=>
                            Cc0029;cc-rep
                            
                            
                            

                        ([(0,2),(2,1)],3)=>0
([(0,1),(0,2),(1,3),(2,3)],4)=>1
([(0,3),(2,1),(3,2)],4)=>0
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>4
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>1
([(0,4),(2,3),(3,1),(4,2)],5)=>0
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)=>5
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)=>5
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>4
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>4
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>2
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>3
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)=>4
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)=>4
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>3
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>0
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>6
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)=>6
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)=>6
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)=>5
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)=>5
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)=>5
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)=>4
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)=>4
([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>5
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>4
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>4
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>1
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>3
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>2
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)=>6
([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>5
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)=>4
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>6
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)=>5
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>2
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>5
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)=>4
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)=>5
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)=>5
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)=>4
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>1
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)=>4
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)=>5
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)=>5
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)=>6
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)=>6
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>3
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>3
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)=>5
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)=>5
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>3
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>4
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>2
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>4
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)=>4
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>3
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>4
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>1
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)=>5
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>2
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>4
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>2
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>3
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>0
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>3
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>3
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>1
                    

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Description

Number of indecomposable injective modules with projective dimension 2.

Code


DeclareOperation("indinjprojdim2",[IsList]);

InstallMethod(indinjprojdim2, "for a representation of a quiver", [IsList],0,function(LIST)

local A,L,LL,M,B,n,T,D,injA,W,simA;

A:=LIST[1];
injA:=IndecInjectiveModules(A);
W:=Filtered(injA,x->ProjDimensionOfModule(x,33)=2);
return(Size(W));

end);

Created

Oct 03, 2020 at 20:07 by Rene Marczinzik

Updated

Oct 03, 2020 at 20:07 by Rene Marczinzik