- FindStat

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Identifier

St001025: Dyck paths ⟶ ℤ

Values

[1,0] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

Number of simple modules with projective dimension 4 in the Nakayama algebra corresponding to the Dyck path.

Code

DeclareOperation("numberssimpprojdim4", [IsList]);

InstallMethod(numberssimpprojdim4, "for a representation of a quiver", [IsList],0,function(L)


local list, A,R,RR;


list:=L;

A:=NakayamaAlgebra(GF(3),list);
R:=SimpleModules(A);
RR:=Filtered(R,x->ProjDimensionOfModule(x,4)=4);
return(Size(RR));
end
);

Created

Oct 30, 2017 at 22:21 by Rene Marczinzik

Updated

Oct 30, 2017 at 22:21 by Rene Marczinzik