Identifier
- St001021: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[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]=>1
[1,1,1,0,0,0]=>0
[1,0,1,0,1,0,1,0]=>0
[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]=>2
[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]=>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]=>0
[1,1,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,0,0]=>2
[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]=>0
[1,0,1,0,1,1,0,0,1,0]=>0
[1,0,1,0,1,1,0,1,0,0]=>3
[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]=>2
[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]=>0
[1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,0]=>4
[1,0,1,1,1,1,0,0,0,0]=>0
[1,1,0,0,1,0,1,0,1,0]=>0
[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]=>2
[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]=>1
[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]=>1
[1,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,0,0,0,0]=>1
[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]=>1
[1,1,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,0,1,1,0,0,0]=>1
[1,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,0,0,0,1,0]=>0
[1,1,1,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,0,0,0]=>3
[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]=>0
[1,0,1,0,1,0,1,1,0,0,1,0]=>0
[1,0,1,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,0,1,1,1,0,0,0]=>0
[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]=>3
[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]=>0
[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]=>6
[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]=>0
[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]=>2
[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]=>2
[1,0,1,1,0,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,1,0,1,0,0]=>0
[1,0,1,1,0,1,0,1,1,0,0,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,0]=>2
[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]=>2
[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]=>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]=>4
[1,0,1,1,1,0,1,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,0,1,1,1,0,1,1,0,0,0,0]=>4
[1,0,1,1,1,1,0,0,0,0,1,0]=>0
[1,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,0]=>6
[1,0,1,1,1,1,1,0,0,0,0,0]=>0
[1,1,0,0,1,0,1,0,1,0,1,0]=>0
[1,1,0,0,1,0,1,0,1,1,0,0]=>0
[1,1,0,0,1,0,1,1,0,0,1,0]=>0
[1,1,0,0,1,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,0,1,1,1,0,0,0]=>0
[1,1,0,0,1,1,0,0,1,0,1,0]=>0
[1,1,0,0,1,1,0,0,1,1,0,0]=>0
[1,1,0,0,1,1,0,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,0,1,1,0,0,0]=>2
[1,1,0,0,1,1,1,0,0,0,1,0]=>0
[1,1,0,0,1,1,1,0,0,1,0,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,0]=>4
[1,1,0,0,1,1,1,1,0,0,0,0]=>0
[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,1,0,0]=>4
[1,1,0,1,0,0,1,1,1,0,0,0]=>1
[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,0]=>0
[1,1,0,1,0,1,0,1,0,1,0,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,0]=>0
[1,1,0,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,0,1,1,0,0,1,0,0]=>4
[1,1,0,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,0,1,1,1,0,0,0,0]=>1
[1,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,0,1,1,0,0]=>1
[1,1,0,1,1,0,0,1,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,1,0,1,0,0,0]=>2
[1,1,0,1,1,0,1,1,0,0,0,0]=>3
[1,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,1,0,1,1,1,0,0,1,0,0,0]=>5
[1,1,0,1,1,1,0,1,0,0,0,0]=>5
[1,1,0,1,1,1,1,0,0,0,0,0]=>1
[1,1,1,0,0,0,1,0,1,0,1,0]=>0
[1,1,1,0,0,0,1,0,1,1,0,0]=>0
[1,1,1,0,0,0,1,1,0,0,1,0]=>0
[1,1,1,0,0,0,1,1,0,1,0,0]=>2
[1,1,1,0,0,0,1,1,1,0,0,0]=>0
[1,1,1,0,0,1,0,0,1,0,1,0]=>1
[1,1,1,0,0,1,0,0,1,1,0,0]=>1
[1,1,1,0,0,1,0,1,0,0,1,0]=>1
[1,1,1,0,0,1,0,1,0,1,0,0]=>0
[1,1,1,0,0,1,0,1,1,0,0,0]=>1
[1,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,1,1,0,0,1,0,0]=>3
[1,1,1,0,0,1,1,0,1,0,0,0]=>3
[1,1,1,0,0,1,1,1,0,0,0,0]=>1
[1,1,1,0,1,0,0,0,1,0,1,0]=>2
[1,1,1,0,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,0,1,0,0]=>1
[1,1,1,0,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,0,1,1,0,0,0,0]=>2
[1,1,1,0,1,1,0,0,0,0,1,0]=>2
[1,1,1,0,1,1,0,0,0,1,0,0]=>4
[1,1,1,0,1,1,0,0,1,0,0,0]=>4
[1,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,1,1,0,1,1,1,0,0,0,0,0]=>2
[1,1,1,1,0,0,0,0,1,0,1,0]=>0
[1,1,1,1,0,0,0,0,1,1,0,0]=>0
[1,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,0,1,0,0]=>1
[1,1,1,1,0,0,0,1,1,0,0,0]=>1
[1,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,1,1,1,0,0,1,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,1,0,0,0,0,1,0]=>3
[1,1,1,1,0,1,0,0,0,1,0,0]=>3
[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[1,1,1,1,0,1,1,0,0,0,0,0]=>3
[1,1,1,1,1,0,0,0,0,0,1,0]=>0
[1,1,1,1,1,0,0,0,0,1,0,0]=>1
[1,1,1,1,1,0,0,0,1,0,0,0]=>2
[1,1,1,1,1,0,0,1,0,0,0,0]=>3
[1,1,1,1,1,0,1,0,0,0,0,0]=>4
[1,1,1,1,1,1,0,0,0,0,0,0]=>0
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Description
Sum of the differences between projective and codominant dimension of the non-projective indecomposable injective modules in the Nakayama algebra corresponding to the Dyck path.
Code
DeclareOperation("difference", [IsList]);
InstallMethod(difference, "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:=Filtered(IndecInjectiveModules(A),x->IsProjectiveModule(x)=false);
temp2:=[];for i in R do Append(temp2,[ProjDimensionOfModule(i,1000)-DominantDimensionOfModule(DualOfModule(i),1000)]);od;
return(Sum(temp2));
end
);
Created
Oct 30, 2017 at 11:10 by Rene Marczinzik
Updated
Oct 30, 2017 at 11:10 by Rene Marczinzik
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