- FindStat

Identifier

St001170: Dyck paths ⟶ ℤ

Values

[1,0] => 1

[1,0,1,0] => 2

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

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

[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] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => 6

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

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

[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] => 6

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

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

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

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

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

[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] => 6

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

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

[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] => 6

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

[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] => 6

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

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

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

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

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

[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] => 6

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

[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] => 6

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

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

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

>>> Load all 196 entries. <<<

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Description

Number of indecomposable injective modules whose socle has projective dimension at most g-1 when g denotes the global dimension in the corresponding Nakayama algebra.

References

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

Code

DeclareOperation("numberindinjwithpdsocleatmostgldimminusone",[IsList]);

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

local A,g,projA,UU,priA,injA;

A:=LIST[1];
g:=GlobalDimensionOfAlgebra(A,100);
injA:=IndecInjectiveModules(A);UU:=Filtered(injA,x->ProjDimensionOfModule(SocleOfModule(x),30)<=g-1);
return(Size(UU));
end);

Created

Apr 29, 2018 at 14:14 by Rene Marczinzik

Updated

May 02, 2018 at 11:34 by Rene Marczinzik