- FindStat

Identifier

St001165: Dyck paths ⟶ ℤ (values match St001471The magnitude of a Dyck path.)

Values

[1,0] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => 3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

Number of simple modules with even projective 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("numbersimpleswithevenprojdim",[IsList]);

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

local A,g,projA,UU,priA2,injA,simA;

A:=LIST[1];
simA:=SimpleModules(A);
UU:=Filtered(simA,x->IsEvenInt(ProjDimensionOfModule(x,100))=true);
return(Size(UU));
end);

Created

Apr 29, 2018 at 14:49 by Rene Marczinzik

Updated

Apr 29, 2018 at 14:49 by Rene Marczinzik