Identifier
- St001873: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[1,0]=>0
[1,0,1,0]=>0
[1,1,0,0]=>1
[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]=>1
[1,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,0]=>2
[1,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,0]=>2
[1,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,0,0]=>2
[1,0,1,0,1,0,1,0,1,0]=>0
[1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0]=>2
[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]=>2
[1,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,0]=>1
[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]=>2
[1,1,0,1,0,1,1,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,0]=>2
[1,1,0,1,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0]=>1
[1,1,1,0,0,0,1,1,0,0]=>2
[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]=>2
[1,1,1,0,1,0,0,0,1,0]=>1
[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]=>2
[1,1,1,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,0]=>2
[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]=>1
[1,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,0]=>1
[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]=>2
[1,0,1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,1,0,0,0]=>1
[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]=>1
[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]=>2
[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]=>2
[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[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]=>2
[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]=>2
[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]=>1
[1,0,1,1,1,0,0,0,1,1,0,0]=>2
[1,0,1,1,1,0,0,1,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,1,1,0,0,0]=>2
[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
[1,0,1,1,1,1,0,0,0,0,1,0]=>2
[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[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]=>2
[1,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,0,1,1,0,0]=>2
[1,1,0,0,1,0,1,1,0,0,1,0]=>2
[1,1,0,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0,1,1,0,0]=>3
[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]=>3
[1,1,0,0,1,1,0,1,1,0,0,0]=>3
[1,1,0,0,1,1,1,0,0,0,1,0]=>2
[1,1,0,0,1,1,1,0,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,1,0,0,0]=>2
[1,1,0,0,1,1,1,1,0,0,0,0]=>3
[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]=>2
[1,1,0,1,0,0,1,1,0,0,1,0]=>2
[1,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,1,0,0,1,0,1,0]=>2
[1,1,0,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,0,1,1,0,0,0,1,0]=>2
[1,1,0,1,0,1,1,0,0,1,0,0]=>3
[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]=>3
[1,1,0,1,1,0,0,0,1,0,1,0]=>2
[1,1,0,1,1,0,0,0,1,1,0,0]=>3
[1,1,0,1,1,0,0,1,0,0,1,0]=>2
[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]=>2
[1,1,0,1,1,0,1,0,0,1,0,0]=>3
[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]=>2
[1,1,0,1,1,1,0,0,0,1,0,0]=>3
[1,1,0,1,1,1,0,0,1,0,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,0,0]=>3
[1,1,0,1,1,1,1,0,0,0,0,0]=>3
[1,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,1,1,0,0,0,1,0,1,1,0,0]=>2
[1,1,1,0,0,0,1,1,0,0,1,0]=>2
[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]=>2
[1,1,1,0,0,1,0,0,1,0,1,0]=>2
[1,1,1,0,0,1,0,0,1,1,0,0]=>3
[1,1,1,0,0,1,0,1,0,0,1,0]=>2
[1,1,1,0,0,1,0,1,0,1,0,0]=>3
[1,1,1,0,0,1,0,1,1,0,0,0]=>3
[1,1,1,0,0,1,1,0,0,0,1,0]=>2
[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]=>2
[1,1,1,0,0,1,1,1,0,0,0,0]=>3
[1,1,1,0,1,0,0,0,1,0,1,0]=>1
[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]=>2
[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]=>2
[1,1,1,0,1,0,1,0,1,0,0,0]=>3
[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]=>2
[1,1,1,0,1,1,0,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[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]=>2
[1,1,1,1,0,0,0,0,1,1,0,0]=>3
[1,1,1,1,0,0,0,1,0,0,1,0]=>2
[1,1,1,1,0,0,0,1,0,1,0,0]=>3
[1,1,1,1,0,0,0,1,1,0,0,0]=>3
[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]=>3
[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]=>3
[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[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]=>2
[1,1,1,1,1,0,0,0,0,1,0,0]=>3
[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]=>2
[1,1,1,1,1,1,0,0,0,0,0,0]=>3
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Description
For a Nakayama algebra corresponding to a Dyck path, we define the matrix C with entries the Hom-spaces between $e_i J$ and $e_j J$ (the radical of the indecomposable projective modules).
The statistic gives half of the rank of the matrix C^t-C.
The statistic gives half of the rank of the matrix C^t-C.
Code
DeclareOperation("radicalmathelp",[IsList]);
InstallMethod(radicalmathelp, "for a representation of a quiver", [IsList],0,function(LIST)
local A,projA,U,W,i,WW,injA,j,g,l,RegA,R,GG;
A:=LIST[1];
M:=LIST[2];
projA:=IndecProjectiveModules(A);
GG:=[];for i in projA do Append(GG,[RadicalOfModule(i)]);od;
W:=[];for i in GG do Append(W,[Size(HomOverAlgebra(i,M))]);od;
return(W);
end);
DeclareOperation("radicalmat",[IsList]);
InstallMethod(radicalmat, "for a representation of a quiver", [IsList],0,function(LIST)
local A,projA,U,W,i,WW,injA,j,g,l,RegA,R,GG;
A:=LIST[1];
g:=GlobalDimensionOfAlgebra(A,33);
projA:=IndecProjectiveModules(A);
GG:=[];for i in projA do Append(GG,[RadicalOfModule(i)]);od;
W:=[];for i in GG do Append(W,[radicalmathelp([A,i])]);od;
return(TransposedMat(W)-W);
end);
Created
Jan 05, 2020 at 16:56 by Rene Marczinzik
Updated
Jan 05, 2020 at 16:56 by Rene Marczinzik
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