- FindStat

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Identifier

St001211: Dyck paths ⟶ ℤ

Values

[1,0] => 2

[1,0,1,0] => 2

[1,1,0,0] => 3

[1,0,1,0,1,0] => 3

[1,0,1,1,0,0] => 3

[1,1,0,0,1,0] => 3

[1,1,0,1,0,0] => 3

[1,1,1,0,0,0] => 4

[1,0,1,0,1,0,1,0] => 4

[1,0,1,0,1,1,0,0] => 4

[1,0,1,1,0,0,1,0] => 3

[1,0,1,1,0,1,0,0] => 3

[1,0,1,1,1,0,0,0] => 4

[1,1,0,0,1,0,1,0] => 4

[1,1,0,0,1,1,0,0] => 4

[1,1,0,1,0,0,1,0] => 4

[1,1,0,1,0,1,0,0] => 4

[1,1,0,1,1,0,0,0] => 4

[1,1,1,0,0,0,1,0] => 4

[1,1,1,0,0,1,0,0] => 4

[1,1,1,0,1,0,0,0] => 4

[1,1,1,1,0,0,0,0] => 5

[1,0,1,0,1,0,1,0,1,0] => 5

[1,0,1,0,1,0,1,1,0,0] => 5

[1,0,1,0,1,1,0,0,1,0] => 4

[1,0,1,0,1,1,0,1,0,0] => 4

[1,0,1,0,1,1,1,0,0,0] => 5

[1,0,1,1,0,0,1,0,1,0] => 4

[1,0,1,1,0,0,1,1,0,0] => 4

[1,0,1,1,0,1,0,0,1,0] => 4

[1,0,1,1,0,1,0,1,0,0] => 4

[1,0,1,1,0,1,1,0,0,0] => 4

[1,0,1,1,1,0,0,0,1,0] => 4

[1,0,1,1,1,0,0,1,0,0] => 4

[1,0,1,1,1,0,1,0,0,0] => 4

[1,0,1,1,1,1,0,0,0,0] => 5

[1,1,0,0,1,0,1,0,1,0] => 5

[1,1,0,0,1,0,1,1,0,0] => 5

[1,1,0,0,1,1,0,0,1,0] => 4

[1,1,0,0,1,1,0,1,0,0] => 4

[1,1,0,0,1,1,1,0,0,0] => 5

[1,1,0,1,0,0,1,0,1,0] => 5

[1,1,0,1,0,0,1,1,0,0] => 5

[1,1,0,1,0,1,0,0,1,0] => 5

[1,1,0,1,0,1,0,1,0,0] => 5

[1,1,0,1,0,1,1,0,0,0] => 5

[1,1,0,1,1,0,0,0,1,0] => 4

[1,1,0,1,1,0,0,1,0,0] => 4

[1,1,0,1,1,0,1,0,0,0] => 4

[1,1,0,1,1,1,0,0,0,0] => 5

[1,1,1,0,0,0,1,0,1,0] => 5

[1,1,1,0,0,0,1,1,0,0] => 5

[1,1,1,0,0,1,0,0,1,0] => 5

[1,1,1,0,0,1,0,1,0,0] => 5

[1,1,1,0,0,1,1,0,0,0] => 5

[1,1,1,0,1,0,0,0,1,0] => 5

[1,1,1,0,1,0,0,1,0,0] => 5

[1,1,1,0,1,0,1,0,0,0] => 5

[1,1,1,0,1,1,0,0,0,0] => 5

[1,1,1,1,0,0,0,0,1,0] => 5

[1,1,1,1,0,0,0,1,0,0] => 5

[1,1,1,1,0,0,1,0,0,0] => 5

[1,1,1,1,0,1,0,0,0,0] => 5

[1,1,1,1,1,0,0,0,0,0] => 6

[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] => 6

[1,0,1,0,1,0,1,1,0,0,1,0] => 5

[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] => 5

[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] => 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] => 5

[1,0,1,0,1,1,1,0,0,0,1,0] => 5

[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] => 5

[1,0,1,0,1,1,1,1,0,0,0,0] => 6

[1,0,1,1,0,0,1,0,1,0,1,0] => 5

[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] => 4

[1,0,1,1,0,0,1,1,0,1,0,0] => 4

[1,0,1,1,0,0,1,1,1,0,0,0] => 5

[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] => 5

[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] => 5

[1,0,1,1,0,1,0,1,1,0,0,0] => 5

[1,0,1,1,0,1,1,0,0,0,1,0] => 4

[1,0,1,1,0,1,1,0,0,1,0,0] => 4

[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] => 5

[1,0,1,1,1,0,0,0,1,0,1,0] => 5

[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] => 5

[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] => 5

[1,0,1,1,1,0,1,0,0,0,1,0] => 5

[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] => 5

[1,0,1,1,1,0,1,1,0,0,0,0] => 5

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Description

The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module.

Code

DeclareOperation("Ext2count",[IsList]);

InstallMethod(Ext2count, "for a representation of a quiver", [IsList],0,function(LIST)

local A,simA,RegA,U;
A:=LIST[1];
simA:=SimpleModules(A);
RegA:=DirectSumOfQPAModules(IndecProjectiveModules(A));
U:=Filtered(simA,x->Size(ExtOverAlgebra(NthSyzygy(x,1),RegA)[2])=0);
return(Size(U));

end);

Created

Jun 20, 2018 at 15:37 by Rene Marczinzik

Updated

Jun 20, 2018 at 15:37 by Rene Marczinzik