Identifier
- St001023: Dyck paths ⟶ ℤ
Values
[1,0] => 2
[1,0,1,0] => 3
[1,1,0,0] => 3
[1,0,1,0,1,0] => 4
[1,0,1,1,0,0] => 4
[1,1,0,0,1,0] => 4
[1,1,0,1,0,0] => 4
[1,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,0] => 5
[1,0,1,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,0] => 5
[1,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,0] => 5
[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] => 5
[1,1,1,0,0,1,0,0] => 5
[1,1,1,0,1,0,0,0] => 5
[1,1,1,1,0,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,0,1,1,0,0] => 5
[1,0,1,0,1,1,0,0,1,0] => 6
[1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,1,0,0,1,0,1,0] => 6
[1,0,1,1,0,0,1,1,0,0] => 6
[1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,1,0,1,1,0,0,0] => 6
[1,0,1,1,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,0,1,0,0] => 6
[1,0,1,1,1,0,1,0,0,0] => 6
[1,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,0,1,1,0,0] => 6
[1,1,0,0,1,1,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,0] => 6
[1,1,0,0,1,1,1,0,0,0] => 6
[1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,1,0,0] => 6
[1,1,0,1,0,1,0,0,1,0] => 5
[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] => 6
[1,1,0,1,1,0,1,0,0,0] => 6
[1,1,0,1,1,1,0,0,0,0] => 6
[1,1,1,0,0,0,1,0,1,0] => 6
[1,1,1,0,0,0,1,1,0,0] => 6
[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] => 6
[1,1,1,0,1,0,0,1,0,0] => 6
[1,1,1,0,1,0,1,0,0,0] => 6
[1,1,1,0,1,1,0,0,0,0] => 6
[1,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,1,0,0,0,1,0,0] => 6
[1,1,1,1,0,0,1,0,0,0] => 6
[1,1,1,1,0,1,0,0,0,0] => 6
[1,1,1,1,1,0,0,0,0,0] => 6
[1,0,1,0,1,0,1,0,1,0,1,0] => 4
[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] => 6
[1,0,1,0,1,1,0,0,1,0,1,0] => 7
[1,0,1,0,1,1,0,0,1,1,0,0] => 7
[1,0,1,0,1,1,0,1,0,0,1,0] => 5
[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] => 6
[1,0,1,0,1,1,1,0,0,0,1,0] => 7
[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] => 6
[1,0,1,0,1,1,1,1,0,0,0,0] => 7
[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] => 7
[1,0,1,1,0,0,1,1,0,0,1,0] => 7
[1,0,1,1,0,0,1,1,0,1,0,0] => 7
[1,0,1,1,0,0,1,1,1,0,0,0] => 7
[1,0,1,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,0,1,1,0,0] => 6
[1,0,1,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,1,0,0,0,1,0] => 7
[1,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,0,0,0] => 7
[1,0,1,1,1,0,0,0,1,0,1,0] => 7
[1,0,1,1,1,0,0,0,1,1,0,0] => 7
[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] => 6
[1,0,1,1,1,0,1,0,0,1,0,0] => 6
[1,0,1,1,1,0,1,0,1,0,0,0] => 6
[1,0,1,1,1,0,1,1,0,0,0,0] => 7
>>> Load all 196 entries. <<<
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Description
Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path.
Code
DeclareOperation("numberssimpprojdimatmost3", [IsList]);
InstallMethod(numberssimpprojdimatmost3, "for a representation of a quiver", [IsList],0,function(L)
local list, A,R,RR;
list:=L;
A:=NakayamaAlgebra(GF(3),list);
R:=SimpleModules(A);
RR:=Filtered(R,x->ProjDimensionOfModule(x,3)<=3);
return(Size(RR));
end
);
Created
Oct 30, 2017 at 21:48 by Rene Marczinzik
Updated
Oct 30, 2017 at 21:48 by Rene Marczinzik
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