Identifier
- St001264: 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]=>1
[1,1,0,0,1,0]=>0
[1,1,0,1,0,0]=>0
[1,1,1,0,0,0]=>0
[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]=>0
[1,0,1,1,0,1,0,0]=>0
[1,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,0]=>0
[1,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,0]=>0
[1,1,0,1,0,1,0,0]=>0
[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]=>0
[1,1,1,0,1,0,0,0]=>0
[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]=>1
[1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,1,0,1,0,0]=>0
[1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,0]=>0
[1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,0]=>0
[1,0,1,1,0,1,0,1,0,0]=>0
[1,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0]=>0
[1,0,1,1,1,0,0,1,0,0]=>0
[1,0,1,1,1,0,1,0,0,0]=>0
[1,0,1,1,1,1,0,0,0,0]=>3
[1,1,0,0,1,0,1,0,1,0]=>0
[1,1,0,0,1,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,0,1,0]=>0
[1,1,0,0,1,1,0,1,0,0]=>0
[1,1,0,0,1,1,1,0,0,0]=>2
[1,1,0,1,0,0,1,0,1,0]=>0
[1,1,0,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,1,0,0,1,0]=>0
[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]=>0
[1,1,0,1,1,0,0,1,0,0]=>0
[1,1,0,1,1,0,1,0,0,0]=>0
[1,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0]=>0
[1,1,1,0,0,0,1,1,0,0]=>1
[1,1,1,0,0,1,0,0,1,0]=>0
[1,1,1,0,0,1,0,1,0,0]=>0
[1,1,1,0,0,1,1,0,0,0]=>1
[1,1,1,0,1,0,0,0,1,0]=>0
[1,1,1,0,1,0,0,1,0,0]=>0
[1,1,1,0,1,0,1,0,0,0]=>0
[1,1,1,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,0,0,0,1,0]=>0
[1,1,1,1,0,0,0,1,0,0]=>0
[1,1,1,1,0,0,1,0,0,0]=>0
[1,1,1,1,0,1,0,0,0,0]=>0
[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]=>1
[1,0,1,0,1,0,1,1,0,0,1,0]=>2
[1,0,1,0,1,0,1,1,0,1,0,0]=>0
[1,0,1,0,1,0,1,1,1,0,0,0]=>2
[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]=>3
[1,0,1,0,1,1,0,1,0,0,1,0]=>0
[1,0,1,0,1,1,0,1,0,1,0,0]=>0
[1,0,1,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,0]=>3
[1,0,1,0,1,1,1,0,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,1,0,0,0]=>0
[1,0,1,0,1,1,1,1,0,0,0,0]=>3
[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]=>1
[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]=>0
[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]=>0
[1,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,0]=>0
[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,0]=>1
[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]=>0
[1,0,1,1,0,1,1,0,1,0,0,0]=>0
[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]=>1
[1,0,1,1,1,0,0,1,0,0,1,0]=>0
[1,0,1,1,1,0,0,1,0,1,0,0]=>0
[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]=>0
[1,0,1,1,1,0,1,0,0,1,0,0]=>0
[1,0,1,1,1,0,1,0,1,0,0,0]=>0
[1,0,1,1,1,0,1,1,0,0,0,0]=>1
[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]=>0
[1,0,1,1,1,1,0,0,1,0,0,0]=>0
[1,0,1,1,1,1,0,1,0,0,0,0]=>0
[1,0,1,1,1,1,1,0,0,0,0,0]=>4
[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]=>1
[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]=>0
[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]=>0
[1,1,0,0,1,1,0,0,1,1,0,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,0]=>0
[1,1,0,0,1,1,0,1,0,1,0,0]=>0
[1,1,0,0,1,1,0,1,1,0,0,0]=>1
[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]=>0
[1,1,0,0,1,1,1,0,1,0,0,0]=>0
[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]=>0
[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]=>2
[1,1,0,1,0,0,1,1,0,1,0,0]=>0
[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]=>0
[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]=>0
[1,1,0,1,0,1,0,1,1,0,0,0]=>1
[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]=>0
[1,1,0,1,0,1,1,0,1,0,0,0]=>0
[1,1,0,1,0,1,1,1,0,0,0,0]=>2
[1,1,0,1,1,0,0,0,1,0,1,0]=>0
[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]=>0
[1,1,0,1,1,0,0,1,0,1,0,0]=>0
[1,1,0,1,1,0,0,1,1,0,0,0]=>1
[1,1,0,1,1,0,1,0,0,0,1,0]=>0
[1,1,0,1,1,0,1,0,0,1,0,0]=>0
[1,1,0,1,1,0,1,0,1,0,0,0]=>0
[1,1,0,1,1,0,1,1,0,0,0,0]=>1
[1,1,0,1,1,1,0,0,0,0,1,0]=>0
[1,1,0,1,1,1,0,0,0,1,0,0]=>0
[1,1,0,1,1,1,0,0,1,0,0,0]=>0
[1,1,0,1,1,1,0,1,0,0,0,0]=>0
[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]=>0
[1,1,1,0,0,0,1,0,1,1,0,0]=>1
[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]=>0
[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]=>0
[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]=>0
[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]=>0
[1,1,1,0,0,1,1,0,0,1,0,0]=>0
[1,1,1,0,0,1,1,0,1,0,0,0]=>0
[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,1,0,0,0,1,0,1,0]=>0
[1,1,1,0,1,0,0,0,1,1,0,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,0]=>0
[1,1,1,0,1,0,0,1,0,1,0,0]=>0
[1,1,1,0,1,0,0,1,1,0,0,0]=>1
[1,1,1,0,1,0,1,0,0,0,1,0]=>0
[1,1,1,0,1,0,1,0,0,1,0,0]=>0
[1,1,1,0,1,0,1,0,1,0,0,0]=>0
[1,1,1,0,1,0,1,1,0,0,0,0]=>1
[1,1,1,0,1,1,0,0,0,0,1,0]=>0
[1,1,1,0,1,1,0,0,0,1,0,0]=>0
[1,1,1,0,1,1,0,0,1,0,0,0]=>0
[1,1,1,0,1,1,0,1,0,0,0,0]=>0
[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]=>1
[1,1,1,1,0,0,0,1,0,0,1,0]=>0
[1,1,1,1,0,0,0,1,0,1,0,0]=>0
[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]=>0
[1,1,1,1,0,0,1,0,0,1,0,0]=>0
[1,1,1,1,0,0,1,0,1,0,0,0]=>0
[1,1,1,1,0,0,1,1,0,0,0,0]=>1
[1,1,1,1,0,1,0,0,0,0,1,0]=>0
[1,1,1,1,0,1,0,0,0,1,0,0]=>0
[1,1,1,1,0,1,0,0,1,0,0,0]=>0
[1,1,1,1,0,1,0,1,0,0,0,0]=>0
[1,1,1,1,0,1,1,0,0,0,0,0]=>1
[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]=>0
[1,1,1,1,1,0,0,0,1,0,0,0]=>0
[1,1,1,1,1,0,0,1,0,0,0,0]=>0
[1,1,1,1,1,0,1,0,0,0,0,0]=>0
[1,1,1,1,1,1,0,0,0,0,0,0]=>0
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Description
The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra.
Code
DeclareOperation("smallestindexgldim", [IsList]);
InstallMethod(smallestindexgldim, "for a representation of a quiver", [IsList],0,function(L)
local AA,A,g,simA,n,U;
AA:=L[1];
A:=NakayamaAlgebra(AA,GF(3));
g:=gldim(AA);
simA:=SimpleModules(A);
n:=Size(simA);
U:=Filtered([1..n],x->ProjDimensionOfModule(simA[x],30)=g);
return(Minimum(U)-1);
end
);
Created
Sep 26, 2018 at 21:52 by Rene Marczinzik
Updated
Sep 26, 2018 at 21:52 by Rene Marczinzik
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