- FindStat

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Identifier

St000998: Dyck paths ⟶ ℤ

Values

[1,0] => 2

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

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

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

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

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

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

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

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

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

[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] => 5

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

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

[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] => 5

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

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

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

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

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

[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] => 6

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

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

[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] => 6

[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] => 6

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

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

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

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

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

[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] => 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] => 4

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

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

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

[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] => 4

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

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

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

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

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

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

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

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

[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] => 7

[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] => 7

[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] => 7

[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] => 7

[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] => 7

[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] => 7

[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] => 7

[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] => 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] => 5

[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] => 7

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

[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] => 6

[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] => 5

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

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

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Description

Number of indecomposable projective modules with injective dimension smaller than or equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path.

Code

DeclareOperation("numbersprojinjequaldomdim", [IsList]);

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


local list, n, temp1, Liste_d, j, i, k, r, kk;


list:=L;

A:=NakayamaAlgebra(GF(3),list);
g:=gldim(list);
R:=IndecProjectiveModules(A);
RR:=Filtered(R,x->InjDimensionOfModule(x,g)<=DominantDimensionOfModule(x,g));
return(Size(RR));
end
);

Created

Oct 27, 2017 at 21:37 by Rene Marczinzik

Updated

Oct 27, 2017 at 21:37 by Rene Marczinzik