Identifier
- St001018: Dyck paths ⟶ ℤ
Values
[1,0] => 1
[1,0,1,0] => 2
[1,1,0,0] => 2
[1,0,1,0,1,0] => 3
[1,0,1,1,0,0] => 3
[1,1,0,0,1,0] => 3
[1,1,0,1,0,0] => 4
[1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,0,0,0] => 5
[1,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,0,0] => 5
[1,1,1,0,1,0,0,0] => 6
[1,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,0] => 5
[1,0,1,0,1,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,0] => 8
[1,0,1,0,1,1,1,0,0,0] => 5
[1,0,1,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,0] => 5
[1,0,1,1,0,1,0,0,1,0] => 7
[1,0,1,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,0,0] => 7
[1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,0] => 6
[1,0,1,1,1,0,1,0,0,0] => 9
[1,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,0,1,1,0,0] => 5
[1,1,0,0,1,1,0,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,0] => 7
[1,1,0,0,1,1,1,0,0,0] => 5
[1,1,0,1,0,0,1,0,1,0] => 6
[1,1,0,1,0,0,1,1,0,0] => 6
[1,1,0,1,0,1,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,1,1,0,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,0,0] => 8
[1,1,0,1,1,0,1,0,0,0] => 8
[1,1,0,1,1,1,0,0,0,0] => 6
[1,1,1,0,0,0,1,0,1,0] => 5
[1,1,1,0,0,0,1,1,0,0] => 5
[1,1,1,0,0,1,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,0,0] => 6
[1,1,1,0,0,1,1,0,0,0] => 6
[1,1,1,0,1,0,0,0,1,0] => 7
[1,1,1,0,1,0,0,1,0,0] => 7
[1,1,1,0,1,0,1,0,0,0] => 7
[1,1,1,0,1,1,0,0,0,0] => 7
[1,1,1,1,0,0,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,0] => 6
[1,1,1,1,0,0,1,0,0,0] => 7
[1,1,1,1,0,1,0,0,0,0] => 8
[1,1,1,1,1,0,0,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,0,1,0,1,0,1,1,0,1,0,0] => 10
[1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,0,1,1,0,0] => 6
[1,0,1,0,1,1,0,1,0,0,1,0] => 9
[1,0,1,0,1,1,0,1,0,1,0,0] => 7
[1,0,1,0,1,1,0,1,1,0,0,0] => 9
[1,0,1,0,1,1,1,0,0,0,1,0] => 6
[1,0,1,0,1,1,1,0,0,1,0,0] => 7
[1,0,1,0,1,1,1,0,1,0,0,0] => 12
[1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,0,1,0,1,1,0,0] => 6
[1,0,1,1,0,0,1,1,0,0,1,0] => 6
[1,0,1,1,0,0,1,1,0,1,0,0] => 8
[1,0,1,1,0,0,1,1,1,0,0,0] => 6
[1,0,1,1,0,1,0,0,1,0,1,0] => 8
[1,0,1,1,0,1,0,0,1,1,0,0] => 8
[1,0,1,1,0,1,0,1,0,0,1,0] => 7
[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] => 7
[1,0,1,1,0,1,1,0,0,0,1,0] => 8
[1,0,1,1,0,1,1,0,0,1,0,0] => 11
[1,0,1,1,0,1,1,0,1,0,0,0] => 10
[1,0,1,1,0,1,1,1,0,0,0,0] => 8
[1,0,1,1,1,0,0,0,1,0,1,0] => 6
[1,0,1,1,1,0,0,0,1,1,0,0] => 6
[1,0,1,1,1,0,0,1,0,0,1,0] => 7
[1,0,1,1,1,0,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,0,1,1,0,0,0] => 7
[1,0,1,1,1,0,1,0,0,0,1,0] => 10
[1,0,1,1,1,0,1,0,0,1,0,0] => 9
[1,0,1,1,1,0,1,0,1,0,0,0] => 8
[1,0,1,1,1,0,1,1,0,0,0,0] => 10
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Description
Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path.
Code
DeclareOperation("Sumprojdiminj", [IsList]);
InstallMethod(Sumprojdiminj, "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);
R:=IndecInjectiveModules(A);
temp2:=[];for i in R do Append(temp2,[ProjDimensionOfModule(i,1000)]);od;
return(Sum(temp2));
end
);
Created
Oct 30, 2017 at 10:52 by Rene Marczinzik
Updated
Oct 30, 2017 at 10:52 by Rene Marczinzik
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