Identifier
- St001169: Dyck paths ⟶ ℤ (values match St000015The number of peaks of a Dyck path., St000053The number of valleys of the Dyck path., St001068Number of torsionless simple modules in the corresponding Nakayama algebra.)
Values
=>
Cc0005;cc-rep
[1,0]=>0
[1,0,1,0]=>1
[1,1,0,0]=>0
[1,0,1,0,1,0]=>2
[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]=>0
[1,0,1,0,1,0,1,0]=>3
[1,0,1,0,1,1,0,0]=>2
[1,0,1,1,0,0,1,0]=>2
[1,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0]=>1
[1,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,0]=>2
[1,1,0,1,1,0,0,0]=>1
[1,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0]=>4
[1,0,1,0,1,0,1,1,0,0]=>3
[1,0,1,0,1,1,0,0,1,0]=>3
[1,0,1,0,1,1,0,1,0,0]=>3
[1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,0]=>3
[1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,0,0]=>2
[1,0,1,1,1,0,0,0,1,0]=>2
[1,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,0]=>2
[1,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0]=>3
[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]=>1
[1,1,0,1,0,0,1,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,0]=>2
[1,1,0,1,0,1,0,0,1,0]=>3
[1,1,0,1,0,1,0,1,0,0]=>3
[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]=>1
[1,1,1,0,0,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,1,0,0]=>1
[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]=>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]=>1
[1,1,1,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0]=>5
[1,0,1,0,1,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,0,1,1,0,0,1,0]=>4
[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]=>3
[1,0,1,0,1,1,0,0,1,0,1,0]=>4
[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]=>4
[1,0,1,0,1,1,0,1,0,1,0,0]=>4
[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]=>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]=>3
[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]=>4
[1,0,1,1,0,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,0,1,1,0,0,1,0]=>3
[1,0,1,1,0,0,1,1,0,1,0,0]=>3
[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]=>4
[1,0,1,1,0,1,0,0,1,1,0,0]=>3
[1,0,1,1,0,1,0,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,1,0,1,0,0]=>4
[1,0,1,1,0,1,0,1,1,0,0,0]=>3
[1,0,1,1,0,1,1,0,0,0,1,0]=>3
[1,0,1,1,0,1,1,0,0,1,0,0]=>3
[1,0,1,1,0,1,1,0,1,0,0,0]=>3
[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]=>3
[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]=>3
[1,0,1,1,1,0,0,1,0,1,0,0]=>3
[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]=>3
[1,0,1,1,1,0,1,0,0,1,0,0]=>3
[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]=>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]=>1
[1,1,0,0,1,0,1,0,1,0,1,0]=>4
[1,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,0,1,0]=>3
[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]=>2
[1,1,0,0,1,1,0,0,1,0,1,0]=>3
[1,1,0,0,1,1,0,0,1,1,0,0]=>2
[1,1,0,0,1,1,0,1,0,0,1,0]=>3
[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]=>2
[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]=>2
[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]=>1
[1,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,1,0,0,1,1,0,1,0,0]=>3
[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]=>4
[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]=>4
[1,1,0,1,0,1,0,1,0,1,0,0]=>4
[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]=>3
[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]=>3
[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]=>3
[1,1,0,1,1,0,0,0,1,1,0,0]=>2
[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]=>2
[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]=>3
[1,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,1,0,1,1,0,0,0,0]=>2
[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]=>2
[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]=>2
[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]=>3
[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]=>1
[1,1,1,0,0,1,0,0,1,0,1,0]=>3
[1,1,1,0,0,1,0,0,1,1,0,0]=>2
[1,1,1,0,0,1,0,1,0,0,1,0]=>3
[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]=>2
[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]=>2
[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]=>1
[1,1,1,0,1,0,0,0,1,0,1,0]=>3
[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]=>3
[1,1,1,0,1,0,0,1,0,1,0,0]=>3
[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]=>3
[1,1,1,0,1,0,1,0,0,1,0,0]=>3
[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]=>2
[1,1,1,0,1,1,1,0,0,0,0,0]=>1
[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]=>1
[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]=>2
[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]=>1
[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]=>2
[1,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,0,0,0]=>2
[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]=>1
[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]=>1
[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,0]=>0
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Description
Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra.
References
[1] Marczinzik, René Upper bounds for the dominant dimension of Nakayama and related algebras. zbMATH:06820683
Code
DeclareOperation("numbersimplespdatleast2",[IsList]);
InstallMethod(numbersimplespdatleast2, "for a representation of a quiver", [IsList],0,function(LIST)
local A,L,LL,tut,simA,g,i,tut2,UU;
A:=LIST[1];
simA:=SimpleModules(A);
UU:=Filtered(simA,x->ProjDimensionOfModule(x,30)>=2);
return(Size(UU));
end);
Created
Apr 28, 2018 at 11:24 by Rene Marczinzik
Updated
Apr 28, 2018 at 11:24 by Rene Marczinzik
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