Identifier
Identifier
  • St001206: Dyck paths ⟶ ℤ (values match St001198The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.)
Values
[1,0,1,0] generating graphics... => 2
[1,0,1,0,1,0] generating graphics... => 2
[1,0,1,1,0,0] generating graphics... => 2
[1,1,0,0,1,0] generating graphics... => 2
[1,1,0,1,0,0] generating graphics... => 2
[1,0,1,0,1,0,1,0] generating graphics... => 2
[1,0,1,0,1,1,0,0] generating graphics... => 2
[1,0,1,1,0,0,1,0] generating graphics... => 2
[1,0,1,1,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,1,0,0,1,0] generating graphics... => 2
[1,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,0] generating graphics... => 2
[1,0,1,0,1,0,1,0,1,0] generating graphics... => 2
[1,0,1,0,1,0,1,1,0,0] generating graphics... => 2
[1,0,1,0,1,1,0,0,1,0] generating graphics... => 2
[1,0,1,0,1,1,0,1,0,0] generating graphics... => 2
[1,0,1,0,1,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,0,0,1,0,1,0] generating graphics... => 2
[1,0,1,1,0,0,1,1,0,0] generating graphics... => 2
[1,0,1,1,0,1,0,0,1,0] generating graphics... => 2
[1,0,1,1,0,1,0,1,0,0] generating graphics... => 3
[1,0,1,1,0,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,0,1,0] generating graphics... => 2
[1,0,1,1,1,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,0,1,0] generating graphics... => 2
[1,1,0,0,1,0,1,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,0,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,0,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,0,1,0,0,1,0,1,0] generating graphics... => 2
[1,1,0,1,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,1,0,1,0,0,1,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,0,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,0,1,0] generating graphics... => 2
[1,1,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,0,1,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,0,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,0,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,0,0] generating graphics... => 2
[1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 2
[1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 2
[1,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 2
[1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 2
[1,0,1,0,1,0,1,1,1,0,0,0] generating graphics... => 2
[1,0,1,0,1,1,0,0,1,0,1,0] generating graphics... => 2
[1,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 2
[1,0,1,0,1,1,0,1,0,0,1,0] generating graphics... => 2
[1,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 3
[1,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 2
[1,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 2
[1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 2
[1,0,1,0,1,1,1,0,1,0,0,0] generating graphics... => 2
[1,0,1,0,1,1,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,0,0,1,0,1,0,1,0] generating graphics... => 2
[1,0,1,1,0,0,1,0,1,1,0,0] generating graphics... => 2
[1,0,1,1,0,0,1,1,0,0,1,0] generating graphics... => 2
[1,0,1,1,0,0,1,1,0,1,0,0] generating graphics... => 2
[1,0,1,1,0,0,1,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,0,1,0,0,1,0,1,0] generating graphics... => 2
[1,0,1,1,0,1,0,0,1,1,0,0] generating graphics... => 2
[1,0,1,1,0,1,0,1,0,0,1,0] generating graphics... => 3
[1,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,0,1,1,0,1,0,1,1,0,0,0] generating graphics... => 3
[1,0,1,1,0,1,1,0,0,0,1,0] generating graphics... => 2
[1,0,1,1,0,1,1,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,0,1,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 2
[1,0,1,1,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,0,1,1,1,0,0,1,0,0,1,0] generating graphics... => 2
[1,0,1,1,1,0,0,1,0,1,0,0] generating graphics... => 3
[1,0,1,1,1,0,0,1,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,0,1,0,0,0,1,0] generating graphics... => 2
[1,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 3
[1,0,1,1,1,0,1,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,0,1,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 2
[1,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,0,1,0,1,0] generating graphics... => 2
[1,1,0,0,1,0,1,0,1,1,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,1,0,0,1,0] generating graphics... => 2
[1,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 2
[1,1,0,0,1,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,0,0,1,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,0,1,0,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,0,1,1,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,0,1,0,0,0] generating graphics... => 2
[1,1,0,0,1,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,0,1,0,0,1,0,1,0,1,0] generating graphics... => 2
[1,1,0,1,0,0,1,0,1,1,0,0] generating graphics... => 2
[1,1,0,1,0,0,1,1,0,0,1,0] generating graphics... => 2
[1,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,0,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 3
[1,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,0,1,0,1,1,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 3
[1,1,0,1,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,0,1,0,1,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 2
[1,1,0,1,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,0,1,1,0,0,1,0,0,1,0] generating graphics... => 2
[1,1,0,1,1,0,0,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,0,1,1,0,0,0] generating graphics... => 2
[1,1,0,1,1,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,0,1,1,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,0,1,1,0,1,0,1,0,0,0] generating graphics... => 3
[1,1,0,1,1,0,1,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,0,1,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 2
[1,1,0,1,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,1,0,1,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 2
[1,1,1,0,0,0,1,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,1,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,0,1,1,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,0,1,1,1,0,0,0] generating graphics... => 2
[1,1,1,0,0,1,0,0,1,0,1,0] generating graphics... => 2
[1,1,1,0,0,1,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,0,1,0,1,0,0,1,0] generating graphics... => 3
[1,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,0,1,1,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,0,1,0,1,0] generating graphics... => 2
[1,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,1,0,0,1,0] generating graphics... => 3
[1,1,1,0,1,0,0,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,1,0,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,0,1,0,0,0,1,0] generating graphics... => 3
[1,1,1,0,1,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,0,1,0,1,0,1,0,0,0] generating graphics... => 4
[1,1,1,0,1,0,1,1,0,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,0,1,1,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 3
[1,1,1,0,1,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,0,0,1,1,0,0] generating graphics... => 2
[1,1,1,1,0,0,0,1,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,0,1,0,1,0,0] generating graphics... => 3
[1,1,1,1,0,0,0,1,1,0,0,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,0,0,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,0,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,0,1,0,0] generating graphics... => 3
[1,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,0,1,0,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,1,0,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 2
[1,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 2
[1,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 2
Description
The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$.
Code
DeclareOperation("heighteAe",[IsList]);

InstallMethod(heighteAe, "for a representation of a quiver", [IsList],0,function(LIST)

local A,k,injA,RegA,temp,CoRegA,priA,U,UU,g,g2,B,T,TT,projB,priB,projA;

A:=LIST[1];
projA:=IndecProjectiveModules(A);priA:=DirectSumOfQPAModules(Filtered(projA,x->IsInjectiveModule(x)=true));
B:=EndOfModuleAsQuiverAlgebra(priA)[3];
projB:=IndecProjectiveModules(B);
T:=[];for i in projB do Append(T,[Dimension(i)]);od;
return(Maximum(T));
end);

Created
May 14, 2018 at 13:14 by Rene Marczinzik
Updated
May 14, 2018 at 13:14 by Rene Marczinzik