- FindStat

Identifier

St001876: Lattices ⟶ ℤ (values match St001877Number of indecomposable injective modules with projective dimension 2.)

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
([(0,3),(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
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>1
([(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
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>1
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>2
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>1
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>2
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>1
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>0
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>1
([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)=>2
([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)=>2
([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)=>1
([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)=>2
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)=>3
([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)=>2
([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)=>3
([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)=>2
([(0,6),(2,7),(3,7),(4,1),(5,4),(6,2),(6,3),(7,5)],8)=>1
([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)=>1
([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)=>1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)=>0
([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)=>2
([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)=>0
([(0,5),(1,7),(2,7),(4,6),(5,4),(6,1),(6,2),(7,3)],8)=>1
([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)=>0
([(0,4),(0,5),(2,8),(3,8),(4,7),(5,7),(6,2),(6,3),(7,6),(8,1)],9)=>2
([(0,6),(1,8),(2,8),(3,7),(4,7),(6,1),(6,2),(7,5),(8,3),(8,4)],9)=>2
([(0,3),(0,4),(1,7),(2,7),(3,8),(4,8),(5,6),(6,1),(6,2),(8,5)],9)=>2
([(0,6),(2,8),(3,8),(4,7),(5,1),(6,4),(7,2),(7,3),(8,5)],9)=>1
([(0,2),(0,3),(2,8),(3,8),(4,6),(5,4),(6,1),(7,5),(8,7)],9)=>1
([(0,4),(0,5),(2,7),(3,7),(4,8),(5,8),(6,1),(7,6),(8,2),(8,3)],9)=>2
([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)=>3
([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)=>3
([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)=>3
([(0,6),(2,8),(3,7),(4,2),(4,7),(5,1),(6,3),(6,4),(7,8),(8,5)],9)=>2
([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)=>3
([(0,7),(2,8),(3,8),(4,5),(5,1),(6,4),(7,2),(7,3),(8,6)],9)=>1
([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)=>4
([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(8,5)],9)=>2
([(0,5),(2,8),(3,7),(4,2),(4,7),(5,6),(6,3),(6,4),(7,8),(8,1)],9)=>2
([(0,5),(1,8),(2,8),(3,7),(4,7),(5,6),(6,1),(6,2),(8,3),(8,4)],9)=>2
([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)=>3
([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)=>3
([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)=>0
([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)=>2
([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9)=>2
([(0,6),(1,8),(2,8),(3,5),(4,3),(5,7),(6,4),(7,1),(7,2)],9)=>1
([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)=>0
([(0,6),(2,8),(3,8),(4,1),(5,4),(6,7),(7,2),(7,3),(8,5)],9)=>1
([(0,6),(1,8),(2,8),(4,5),(5,7),(6,4),(7,1),(7,2),(8,3)],9)=>1
                    

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

Description

The number of 2-regular simple modules in the incidence algebra of the lattice.

Code


DeclareOperation("2regularsimples",[IsList]);

InstallMethod(2regularsimples, "for a representation of a quiver", [IsList],0,function(LIST)

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

A:=LIST[1];
simA:=SimpleModules(A);
RegA:=DirectSumOfQPAModules(IndecProjectiveModules(A));
W:=Filtered(simA,x->ProjDimensionOfModule(x,33)=2 and gradeofmodule([A,x])=2 and Size(ExtOverAlgebra(NthSyzygy(x,1),RegA)[2])=1);
return(Size(W));

end);

Created

Oct 03, 2020 at 18:31 by Rene Marczinzik

Updated

Oct 03, 2020 at 18:31 by Rene Marczinzik