- FindStat

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Identifier

St001166: Dyck paths ⟶ ℤ

Values

[1,0] => 2

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

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

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

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

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

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

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

[1,0,1,0,1,0,1,0] => 5

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

[1,0,1,1,0,0,1,0] => 5

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,0,0,0,0] => 5

[1,0,1,0,1,0,1,0,1,0] => 6

[1,0,1,0,1,0,1,1,0,0] => 5

[1,0,1,0,1,1,0,0,1,0] => 5

[1,0,1,0,1,1,0,1,0,0] => 5

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

[1,0,1,1,0,0,1,0,1,0] => 5

[1,0,1,1,0,0,1,1,0,0] => 5

[1,0,1,1,0,1,0,0,1,0] => 5

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

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

[1,0,1,1,1,0,0,0,1,0] => 5

[1,0,1,1,1,0,0,1,0,0] => 5

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

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

[1,1,0,0,1,0,1,0,1,0] => 5

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

[1,1,0,0,1,1,0,0,1,0] => 5

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

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

[1,1,0,1,0,0,1,0,1,0] => 5

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

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

[1,1,0,1,0,1,0,1,0,0] => 6

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

[1,1,0,1,1,0,0,0,1,0] => 5

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

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

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

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

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

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

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

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

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

[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] => 3

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

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

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

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

[1,1,1,1,1,0,0,0,0,0] => 6

[1,0,1,0,1,0,1,0,1,0,1,0] => 7

[1,0,1,0,1,0,1,0,1,1,0,0] => 6

[1,0,1,0,1,0,1,1,0,0,1,0] => 6

[1,0,1,0,1,0,1,1,0,1,0,0] => 6

[1,0,1,0,1,0,1,1,1,0,0,0] => 5

[1,0,1,0,1,1,0,0,1,0,1,0] => 7

[1,0,1,0,1,1,0,0,1,1,0,0] => 5

[1,0,1,0,1,1,0,1,0,0,1,0] => 6

[1,0,1,0,1,1,0,1,0,1,0,0] => 5

[1,0,1,0,1,1,0,1,1,0,0,0] => 5

[1,0,1,0,1,1,1,0,0,0,1,0] => 5

[1,0,1,0,1,1,1,0,0,1,0,0] => 5

[1,0,1,0,1,1,1,0,1,0,0,0] => 5

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

[1,0,1,1,0,0,1,0,1,0,1,0] => 6

[1,0,1,1,0,0,1,0,1,1,0,0] => 5

[1,0,1,1,0,0,1,1,0,0,1,0] => 7

[1,0,1,1,0,0,1,1,0,1,0,0] => 5

[1,0,1,1,0,0,1,1,1,0,0,0] => 5

[1,0,1,1,0,1,0,0,1,0,1,0] => 6

[1,0,1,1,0,1,0,0,1,1,0,0] => 5

[1,0,1,1,0,1,0,1,0,0,1,0] => 5

[1,0,1,1,0,1,0,1,0,1,0,0] => 6

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

[1,0,1,1,0,1,1,0,0,0,1,0] => 5

[1,0,1,1,0,1,1,0,0,1,0,0] => 5

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

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

[1,0,1,1,1,0,0,0,1,0,1,0] => 5

[1,0,1,1,1,0,0,0,1,1,0,0] => 5

[1,0,1,1,1,0,0,1,0,0,1,0] => 5

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

[1,0,1,1,1,0,0,1,1,0,0,0] => 5

[1,0,1,1,1,0,1,0,0,0,1,0] => 5

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

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

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

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Description

Number of indecomposable projective non-injective modules with dominant dimension equal to the global dimension plus the number of indecomposable projective injective modules in the corresponding Nakayama algebra.

References

[1] Marczinzik, René Upper bounds for the dominant dimension of Nakayama and related algebras. zbMATH:06820683

Code

DeclareOperation("numberprojnoninjdomdimequalgldimplusprojinj",[IsList]);

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

local A,g,projA,UU,priA;

A:=LIST[1];
g:=GlobalDimensionOfAlgebra(A,100);
projA:=IndecProjectiveModules(A);priA:=Filtered(projA,x->IsInjectiveModule(x)=true);
UU:=Filtered(projA,x->DominantDimensionOfModule(x,100)=g);
return(Size(UU)+Size(priA));
end);

Created

Apr 29, 2018 at 13:31 by Rene Marczinzik

Updated

Apr 29, 2018 at 13:31 by Rene Marczinzik