- FindStat

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Identifier

St001026: 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] => 1

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

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

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

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

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

[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] => 1

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

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

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

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

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

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

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

[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] => 0

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

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

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

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

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

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

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

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

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

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

[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] => 1

[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] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => 1

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

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

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

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

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

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

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

[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] => 0

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

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

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

[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] => 0

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

[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] => 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] => 2

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

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

[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] => 2

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

[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] => 1

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

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

[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] => 1

[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] => 1

[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] => 2

[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] => 2

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

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

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

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

[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] => 2

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

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

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Description

The maximum of the projective dimensions of the indecomposable non-projective injective modules minus the minimum in the Nakayama algebra corresponding to the Dyck path.

Code

DeclareOperation("indecinjmaxmin", [IsList]);

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


local list, A,R,temp3,x,i;


list:=L;

A:=NakayamaAlgebra(GF(3),list);
R:=IndecInjectiveModules(A);RR:=Filtered(R,x->IsProjectiveModule(x)=false);
temp3:=[];for i in RR do Append(temp3,[ProjDimensionOfModule(i,30)]);od;
return([Maximum(temp3)-Minimum(temp3)]);
end
);

Created

Oct 31, 2017 at 06:57 by Rene Marczinzik

Updated

Oct 31, 2017 at 06:57 by Rene Marczinzik