Identifier
- St001291: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[1,0]=>1
[1,0,1,0]=>2
[1,1,0,0]=>1
[1,0,1,0,1,0]=>3
[1,0,1,1,0,0]=>2
[1,1,0,0,1,0]=>3
[1,1,0,1,0,0]=>2
[1,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,0]=>4
[1,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,0]=>4
[1,1,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,0,1,0]=>4
[1,1,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,0]=>5
[1,0,1,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,0,1,0]=>5
[1,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,1,0,0,1,0,1,0]=>5
[1,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,0]=>5
[1,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,1,1,0,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,0,0,0]=>3
[1,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,0]=>5
[1,1,0,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,1,0,0,1,0]=>5
[1,1,0,0,1,1,0,1,0,0]=>4
[1,1,0,0,1,1,1,0,0,0]=>3
[1,1,0,1,0,0,1,0,1,0]=>5
[1,1,0,1,0,0,1,1,0,0]=>4
[1,1,0,1,0,1,0,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,0]=>4
[1,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,0,0,1,0]=>5
[1,1,0,1,1,0,0,1,0,0]=>4
[1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0]=>5
[1,1,1,0,0,0,1,1,0,0]=>4
[1,1,1,0,0,1,0,0,1,0]=>5
[1,1,1,0,0,1,0,1,0,0]=>4
[1,1,1,0,0,1,1,0,0,0]=>3
[1,1,1,0,1,0,0,0,1,0]=>5
[1,1,1,0,1,0,0,1,0,0]=>4
[1,1,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,0,0,0,1,0]=>5
[1,1,1,1,0,0,0,1,0,0]=>4
[1,1,1,1,0,0,1,0,0,0]=>3
[1,1,1,1,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,0]=>1
[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]=>5
[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]=>5
[1,0,1,0,1,0,1,1,1,0,0,0]=>4
[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]=>5
[1,0,1,0,1,1,0,1,0,0,1,0]=>6
[1,0,1,0,1,1,0,1,0,1,0,0]=>5
[1,0,1,0,1,1,0,1,1,0,0,0]=>4
[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]=>5
[1,0,1,0,1,1,1,0,1,0,0,0]=>4
[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]=>6
[1,0,1,1,0,0,1,0,1,1,0,0]=>5
[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]=>5
[1,0,1,1,0,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,1,0,0,1,0,1,0]=>6
[1,0,1,1,0,1,0,0,1,1,0,0]=>5
[1,0,1,1,0,1,0,1,0,0,1,0]=>6
[1,0,1,1,0,1,0,1,0,1,0,0]=>5
[1,0,1,1,0,1,0,1,1,0,0,0]=>4
[1,0,1,1,0,1,1,0,0,0,1,0]=>6
[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]=>4
[1,0,1,1,0,1,1,1,0,0,0,0]=>3
[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]=>5
[1,0,1,1,1,0,0,1,0,0,1,0]=>6
[1,0,1,1,1,0,0,1,0,1,0,0]=>5
[1,0,1,1,1,0,0,1,1,0,0,0]=>4
[1,0,1,1,1,0,1,0,0,0,1,0]=>6
[1,0,1,1,1,0,1,0,0,1,0,0]=>5
[1,0,1,1,1,0,1,0,1,0,0,0]=>4
[1,0,1,1,1,0,1,1,0,0,0,0]=>3
[1,0,1,1,1,1,0,0,0,0,1,0]=>6
[1,0,1,1,1,1,0,0,0,1,0,0]=>5
[1,0,1,1,1,1,0,0,1,0,0,0]=>4
[1,0,1,1,1,1,0,1,0,0,0,0]=>3
[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]=>6
[1,1,0,0,1,0,1,0,1,1,0,0]=>5
[1,1,0,0,1,0,1,1,0,0,1,0]=>6
[1,1,0,0,1,0,1,1,0,1,0,0]=>5
[1,1,0,0,1,0,1,1,1,0,0,0]=>4
[1,1,0,0,1,1,0,0,1,0,1,0]=>6
[1,1,0,0,1,1,0,0,1,1,0,0]=>5
[1,1,0,0,1,1,0,1,0,0,1,0]=>6
[1,1,0,0,1,1,0,1,0,1,0,0]=>5
[1,1,0,0,1,1,0,1,1,0,0,0]=>4
[1,1,0,0,1,1,1,0,0,0,1,0]=>6
[1,1,0,0,1,1,1,0,0,1,0,0]=>5
[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]=>3
[1,1,0,1,0,0,1,0,1,0,1,0]=>6
[1,1,0,1,0,0,1,0,1,1,0,0]=>5
[1,1,0,1,0,0,1,1,0,0,1,0]=>6
[1,1,0,1,0,0,1,1,0,1,0,0]=>5
[1,1,0,1,0,0,1,1,1,0,0,0]=>4
[1,1,0,1,0,1,0,0,1,0,1,0]=>6
[1,1,0,1,0,1,0,0,1,1,0,0]=>5
[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[1,1,0,1,0,1,0,1,1,0,0,0]=>4
[1,1,0,1,0,1,1,0,0,0,1,0]=>6
[1,1,0,1,0,1,1,0,0,1,0,0]=>5
[1,1,0,1,0,1,1,0,1,0,0,0]=>4
[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]=>6
[1,1,0,1,1,0,0,0,1,1,0,0]=>5
[1,1,0,1,1,0,0,1,0,0,1,0]=>6
[1,1,0,1,1,0,0,1,0,1,0,0]=>5
[1,1,0,1,1,0,0,1,1,0,0,0]=>4
[1,1,0,1,1,0,1,0,0,0,1,0]=>6
[1,1,0,1,1,0,1,0,0,1,0,0]=>5
[1,1,0,1,1,0,1,0,1,0,0,0]=>4
[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]=>6
[1,1,0,1,1,1,0,0,0,1,0,0]=>5
[1,1,0,1,1,1,0,0,1,0,0,0]=>4
[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]=>2
[1,1,1,0,0,0,1,0,1,0,1,0]=>6
[1,1,1,0,0,0,1,0,1,1,0,0]=>5
[1,1,1,0,0,0,1,1,0,0,1,0]=>6
[1,1,1,0,0,0,1,1,0,1,0,0]=>5
[1,1,1,0,0,0,1,1,1,0,0,0]=>4
[1,1,1,0,0,1,0,0,1,0,1,0]=>6
[1,1,1,0,0,1,0,0,1,1,0,0]=>5
[1,1,1,0,0,1,0,1,0,0,1,0]=>6
[1,1,1,0,0,1,0,1,0,1,0,0]=>5
[1,1,1,0,0,1,0,1,1,0,0,0]=>4
[1,1,1,0,0,1,1,0,0,0,1,0]=>6
[1,1,1,0,0,1,1,0,0,1,0,0]=>5
[1,1,1,0,0,1,1,0,1,0,0,0]=>4
[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]=>6
[1,1,1,0,1,0,0,0,1,1,0,0]=>5
[1,1,1,0,1,0,0,1,0,0,1,0]=>6
[1,1,1,0,1,0,0,1,0,1,0,0]=>5
[1,1,1,0,1,0,0,1,1,0,0,0]=>4
[1,1,1,0,1,0,1,0,0,0,1,0]=>6
[1,1,1,0,1,0,1,0,0,1,0,0]=>5
[1,1,1,0,1,0,1,0,1,0,0,0]=>4
[1,1,1,0,1,0,1,1,0,0,0,0]=>3
[1,1,1,0,1,1,0,0,0,0,1,0]=>6
[1,1,1,0,1,1,0,0,0,1,0,0]=>5
[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]=>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]=>6
[1,1,1,1,0,0,0,0,1,1,0,0]=>5
[1,1,1,1,0,0,0,1,0,0,1,0]=>6
[1,1,1,1,0,0,0,1,0,1,0,0]=>5
[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[1,1,1,1,0,0,1,0,0,0,1,0]=>6
[1,1,1,1,0,0,1,0,0,1,0,0]=>5
[1,1,1,1,0,0,1,0,1,0,0,0]=>4
[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]=>6
[1,1,1,1,0,1,0,0,0,1,0,0]=>5
[1,1,1,1,0,1,0,0,1,0,0,0]=>4
[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]=>2
[1,1,1,1,1,0,0,0,0,0,1,0]=>6
[1,1,1,1,1,0,0,0,0,1,0,0]=>5
[1,1,1,1,1,0,0,0,1,0,0,0]=>4
[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]=>1
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Description
The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path.
Let $A$ be the Nakayama algebra associated to a Dyck path as given in DyckPaths/NakayamaAlgebras. This statistics is the number of indecomposable summands of $D(A) \otimes D(A)$, where $D(A)$ is the natural dual of $A$.
Let $A$ be the Nakayama algebra associated to a Dyck path as given in DyckPaths/NakayamaAlgebras. This statistics is the number of indecomposable summands of $D(A) \otimes D(A)$, where $D(A)$ is the natural dual of $A$.
Code
DeclareOperation("iterateddatest2", [IsList]);
InstallMethod(iterateddatest2, "for a representation of a quiver", [IsList],0,function(L)
local A,RegA,J,simA,U,projA,UU,CoRegA,W,WW,WW2,UU2;
A:=L[1];
CoRegA:=DirectSumOfQPAModules(IndecInjectiveModules(A));
W:=NakayamaFunctorOfModule(CoRegA);
UU:=DecomposeModule(W);
return(Size(UU));
end
);
Created
Nov 16, 2018 at 09:01 by Rene Marczinzik
Updated
Nov 16, 2018 at 10:21 by Christian Stump
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