Identifier
Identifier
  • St001224: Dyck paths ⟶ ℤ (values match St000024The number of double up and double down steps of a Dyck path., St000443The number of long tunnels of a Dyck path., St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path., St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra.)
Values
[1,0] generating graphics... => 1
[1,0,1,0] generating graphics... => 1
[1,1,0,0] generating graphics... => 2
[1,0,1,0,1,0] generating graphics... => 1
[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
[1,1,1,0,0,0] generating graphics... => 3
[1,0,1,0,1,0,1,0] generating graphics... => 1
[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... => 3
[1,1,0,0,1,0,1,0] generating graphics... => 2
[1,1,0,0,1,1,0,0] generating graphics... => 3
[1,1,0,1,0,0,1,0] generating graphics... => 2
[1,1,0,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,0,1,0] generating graphics... => 3
[1,1,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,0,0,0] generating graphics... => 4
[1,0,1,0,1,0,1,0,1,0] generating graphics... => 1
[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... => 3
[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... => 3
[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... => 2
[1,0,1,1,0,1,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,0,0,0,1,0] generating graphics... => 3
[1,0,1,1,1,0,0,1,0,0] generating graphics... => 3
[1,0,1,1,1,0,1,0,0,0] generating graphics... => 3
[1,0,1,1,1,1,0,0,0,0] generating graphics... => 4
[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... => 3
[1,1,0,0,1,1,0,0,1,0] generating graphics... => 3
[1,1,0,0,1,1,0,1,0,0] generating graphics... => 3
[1,1,0,0,1,1,1,0,0,0] generating graphics... => 4
[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... => 3
[1,1,0,1,0,1,0,0,1,0] generating graphics... => 2
[1,1,0,1,0,1,0,1,0,0] generating graphics... => 2
[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... => 3
[1,1,0,1,1,0,0,1,0,0] generating graphics... => 3
[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... => 4
[1,1,1,0,0,0,1,0,1,0] generating graphics... => 3
[1,1,1,0,0,0,1,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,0,0,1,0] generating graphics... => 3
[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... => 4
[1,1,1,0,1,0,0,0,1,0] generating graphics... => 3
[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... => 4
[1,1,1,1,0,0,0,0,1,0] generating graphics... => 4
[1,1,1,1,0,0,0,1,0,0] generating graphics... => 4
[1,1,1,1,0,0,1,0,0,0] generating graphics... => 4
[1,1,1,1,0,1,0,0,0,0] generating graphics... => 4
[1,1,1,1,1,0,0,0,0,0] generating graphics... => 5
[1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 1
[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... => 3
[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... => 3
[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... => 2
[1,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 3
[1,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 3
[1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 3
[1,0,1,0,1,1,1,0,1,0,0,0] generating graphics... => 3
[1,0,1,0,1,1,1,1,0,0,0,0] generating graphics... => 4
[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... => 3
[1,0,1,1,0,0,1,1,0,0,1,0] generating graphics... => 3
[1,0,1,1,0,0,1,1,0,1,0,0] generating graphics... => 3
[1,0,1,1,0,0,1,1,1,0,0,0] generating graphics... => 4
[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... => 3
[1,0,1,1,0,1,0,1,0,0,1,0] generating graphics... => 2
[1,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 2
[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... => 3
[1,0,1,1,0,1,1,0,0,1,0,0] generating graphics... => 3
[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... => 4
[1,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 3
[1,0,1,1,1,0,0,0,1,1,0,0] generating graphics... => 4
[1,0,1,1,1,0,0,1,0,0,1,0] generating graphics... => 3
[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... => 4
[1,0,1,1,1,0,1,0,0,0,1,0] generating graphics... => 3
[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... => 4
[1,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 4
[1,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 4
[1,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 4
[1,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 4
[1,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 5
[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... => 3
[1,1,0,0,1,0,1,1,0,0,1,0] generating graphics... => 3
[1,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 3
[1,1,0,0,1,0,1,1,1,0,0,0] generating graphics... => 4
[1,1,0,0,1,1,0,0,1,0,1,0] generating graphics... => 3
[1,1,0,0,1,1,0,0,1,1,0,0] generating graphics... => 4
[1,1,0,0,1,1,0,1,0,0,1,0] generating graphics... => 3
[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... => 4
[1,1,0,0,1,1,1,0,0,0,1,0] generating graphics... => 4
[1,1,0,0,1,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,0,0,1,1,1,0,1,0,0,0] generating graphics... => 4
[1,1,0,0,1,1,1,1,0,0,0,0] generating graphics... => 5
[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... => 3
[1,1,0,1,0,0,1,1,0,0,1,0] generating graphics... => 3
[1,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 3
[1,1,0,1,0,0,1,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 2
[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... => 2
[1,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 2
[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... => 4
[1,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 3
[1,1,0,1,1,0,0,0,1,1,0,0] generating graphics... => 4
[1,1,0,1,1,0,0,1,0,0,1,0] generating graphics... => 3
[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... => 4
[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... => 4
[1,1,0,1,1,1,0,0,0,0,1,0] generating graphics... => 4
[1,1,0,1,1,1,0,0,0,1,0,0] generating graphics... => 4
[1,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,1,0,1,0,0,0,0] generating graphics... => 4
[1,1,0,1,1,1,1,0,0,0,0,0] generating graphics... => 5
[1,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 3
[1,1,1,0,0,0,1,0,1,1,0,0] generating graphics... => 4
[1,1,1,0,0,0,1,1,0,0,1,0] generating graphics... => 4
[1,1,1,0,0,0,1,1,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,0,1,1,1,0,0,0] generating graphics... => 5
[1,1,1,0,0,1,0,0,1,0,1,0] generating graphics... => 3
[1,1,1,0,0,1,0,0,1,1,0,0] generating graphics... => 4
[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... => 4
[1,1,1,0,0,1,1,0,0,0,1,0] generating graphics... => 4
[1,1,1,0,0,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,0,0,1,1,0,1,0,0,0] generating graphics... => 4
[1,1,1,0,0,1,1,1,0,0,0,0] generating graphics... => 5
[1,1,1,0,1,0,0,0,1,0,1,0] generating graphics... => 3
[1,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 4
[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... => 4
[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... => 3
[1,1,1,0,1,0,1,1,0,0,0,0] generating graphics... => 4
[1,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 4
[1,1,1,0,1,1,0,0,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 4
[1,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 4
[1,1,1,0,1,1,1,0,0,0,0,0] generating graphics... => 5
[1,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 4
[1,1,1,1,0,0,0,0,1,1,0,0] generating graphics... => 5
[1,1,1,1,0,0,0,1,0,0,1,0] generating graphics... => 4
[1,1,1,1,0,0,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,1,0,0,0,1,1,0,0,0] generating graphics... => 5
[1,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 4
[1,1,1,1,0,0,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,1,0,0,1,0,1,0,0,0] generating graphics... => 4
[1,1,1,1,0,0,1,1,0,0,0,0] generating graphics... => 5
[1,1,1,1,0,1,0,0,0,0,1,0] generating graphics... => 4
[1,1,1,1,0,1,0,0,0,1,0,0] generating graphics... => 4
[1,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 4
[1,1,1,1,0,1,0,1,0,0,0,0] generating graphics... => 4
[1,1,1,1,0,1,1,0,0,0,0,0] generating graphics... => 5
[1,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 5
[1,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 5
[1,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 5
[1,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 5
[1,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 5
[1,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 6
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Description
Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. Then the statistic gives the vector space dimension of the first Ext-group between X and the regular module.
Code

DeclareOperation("ext1sim",[IsList]);

InstallMethod(ext1sim, "for a representation of a quiver", [IsList],0,function(LIST)

local A,N,RegA,g,temmi,UT,M,L,U,simA;

A:=LIST[1];
simA:=SimpleModules(A);N:=DirectSumOfQPAModules(simA);
RegA:=DirectSumOfQPAModules(IndecProjectiveModules(A));
return(Size(ExtOverAlgebra(NthSyzygy(N,0),RegA)[2]));
end);

Created
Jun 20, 2018 at 22:27 by Rene Marczinzik
Updated
Jun 20, 2018 at 22:27 by Rene Marczinzik