- FindStat

Identifier

St001182: Dyck paths ⟶ ℤ

Values

[1,0] => 1

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

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

[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] => 1

[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] => 5

[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] => 1

[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] => 6

[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] => 6

[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] => 6

[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] => 6

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

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

[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] => 5

[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] => 5

[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] => 5

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

[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] => 1

[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] => 7

[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] => 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] => 7

[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] => 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] => 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] => 7

[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] => 7

[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] => 5

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

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

[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] => 5

[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] => 4

[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] => 7

[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] => 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] => 4

>>> Load all 196 entries. <<<

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Description

Number of indecomposable injective modules with codominant dimension at least two in the corresponding Nakayama algebra.

Code

DeclareOperation("numberindinjwithcodomdimatleastk",[IsList]);

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

local A,k,simA,WW,injA;

A:=LIST[1];
k:=LIST[2];
injA:=IndecInjectiveModules(A);
WW:=Filtered(injA,x->DominantDimensionOfModule(DualOfModule(x),30)>=k);
return(Size(WW));
end);

Created

May 12, 2018 at 00:23 by Rene Marczinzik

Updated

May 12, 2018 at 09:11 by Rene Marczinzik