- FindStat

Identifier

St001003: Dyck paths ⟶ ℤ

Values

=>
                            Cc0005;cc-rep
                            
                            
                            

                        [1,0]=>3
[1,0,1,0]=>4
[1,1,0,0]=>6
[1,0,1,0,1,0]=>5
[1,0,1,1,0,0]=>6
[1,1,0,0,1,0]=>7
[1,1,0,1,0,0]=>7
[1,1,1,0,0,0]=>10
[1,0,1,0,1,0,1,0]=>6
[1,0,1,0,1,1,0,0]=>7
[1,0,1,1,0,0,1,0]=>7
[1,0,1,1,0,1,0,0]=>7
[1,0,1,1,1,0,0,0]=>9
[1,1,0,0,1,0,1,0]=>8
[1,1,0,0,1,1,0,0]=>9
[1,1,0,1,0,0,1,0]=>8
[1,1,0,1,0,1,0,0]=>8
[1,1,0,1,1,0,0,0]=>9
[1,1,1,0,0,0,1,0]=>11
[1,1,1,0,0,1,0,0]=>11
[1,1,1,0,1,0,0,0]=>11
[1,1,1,1,0,0,0,0]=>15
[1,0,1,0,1,0,1,0,1,0]=>7
[1,0,1,0,1,0,1,1,0,0]=>8
[1,0,1,0,1,1,0,0,1,0]=>8
[1,0,1,0,1,1,0,1,0,0]=>8
[1,0,1,0,1,1,1,0,0,0]=>10
[1,0,1,1,0,0,1,0,1,0]=>8
[1,0,1,1,0,0,1,1,0,0]=>9
[1,0,1,1,0,1,0,0,1,0]=>8
[1,0,1,1,0,1,0,1,0,0]=>8
[1,0,1,1,0,1,1,0,0,0]=>9
[1,0,1,1,1,0,0,0,1,0]=>10
[1,0,1,1,1,0,0,1,0,0]=>10
[1,0,1,1,1,0,1,0,0,0]=>10
[1,0,1,1,1,1,0,0,0,0]=>13
[1,1,0,0,1,0,1,0,1,0]=>9
[1,1,0,0,1,0,1,1,0,0]=>10
[1,1,0,0,1,1,0,0,1,0]=>10
[1,1,0,0,1,1,0,1,0,0]=>10
[1,1,0,0,1,1,1,0,0,0]=>12
[1,1,0,1,0,0,1,0,1,0]=>9
[1,1,0,1,0,0,1,1,0,0]=>10
[1,1,0,1,0,1,0,0,1,0]=>9
[1,1,0,1,0,1,0,1,0,0]=>9
[1,1,0,1,0,1,1,0,0,0]=>10
[1,1,0,1,1,0,0,0,1,0]=>10
[1,1,0,1,1,0,0,1,0,0]=>10
[1,1,0,1,1,0,1,0,0,0]=>10
[1,1,0,1,1,1,0,0,0,0]=>12
[1,1,1,0,0,0,1,0,1,0]=>12
[1,1,1,0,0,0,1,1,0,0]=>13
[1,1,1,0,0,1,0,0,1,0]=>12
[1,1,1,0,0,1,0,1,0,0]=>12
[1,1,1,0,0,1,1,0,0,0]=>13
[1,1,1,0,1,0,0,0,1,0]=>12
[1,1,1,0,1,0,0,1,0,0]=>12
[1,1,1,0,1,0,1,0,0,0]=>12
[1,1,1,0,1,1,0,0,0,0]=>13
[1,1,1,1,0,0,0,0,1,0]=>16
[1,1,1,1,0,0,0,1,0,0]=>16
[1,1,1,1,0,0,1,0,0,0]=>16
[1,1,1,1,0,1,0,0,0,0]=>16
[1,1,1,1,1,0,0,0,0,0]=>21
                    

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Description

The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path.

Code


DeclareOperation("numbersprojdim1", [IsList]);

InstallMethod(numbersprojdim1, "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);
L:=ARQuiver([A,1000])[2];
LL:=Filtered(L,x->ProjDimensionOfModule(x,1)<=1);
return(Size(LL));
end
);

Created

Oct 27, 2017 at 20:35 by Rene Marczinzik

Updated

Oct 27, 2017 at 20:35 by Rene Marczinzik