- FindStat

Identifier

St001213: Dyck paths ⟶ ℤ

Values

[1,0] => 2

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

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

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

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

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

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

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

[1,0,1,0,1,0,1,0] => 8

[1,0,1,0,1,1,0,0] => 7

[1,0,1,1,0,0,1,0] => 7

[1,0,1,1,0,1,0,0] => 8

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

[1,1,0,0,1,0,1,0] => 7

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

[1,1,0,1,0,0,1,0] => 8

[1,1,0,1,0,1,0,0] => 9

[1,1,0,1,1,0,0,0] => 7

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

[1,1,1,0,0,1,0,0] => 7

[1,1,1,0,1,0,0,0] => 8

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

[1,0,1,0,1,0,1,0,1,0] => 10

[1,0,1,0,1,0,1,1,0,0] => 9

[1,0,1,0,1,1,0,0,1,0] => 9

[1,0,1,0,1,1,0,1,0,0] => 10

[1,0,1,0,1,1,1,0,0,0] => 8

[1,0,1,1,0,0,1,0,1,0] => 9

[1,0,1,1,0,0,1,1,0,0] => 8

[1,0,1,1,0,1,0,0,1,0] => 10

[1,0,1,1,0,1,0,1,0,0] => 11

[1,0,1,1,0,1,1,0,0,0] => 9

[1,0,1,1,1,0,0,0,1,0] => 8

[1,0,1,1,1,0,0,1,0,0] => 9

[1,0,1,1,1,0,1,0,0,0] => 10

[1,0,1,1,1,1,0,0,0,0] => 7

[1,1,0,0,1,0,1,0,1,0] => 9

[1,1,0,0,1,0,1,1,0,0] => 8

[1,1,0,0,1,1,0,0,1,0] => 8

[1,1,0,0,1,1,0,1,0,0] => 9

[1,1,0,0,1,1,1,0,0,0] => 7

[1,1,0,1,0,0,1,0,1,0] => 10

[1,1,0,1,0,0,1,1,0,0] => 9

[1,1,0,1,0,1,0,0,1,0] => 11

[1,1,0,1,0,1,0,1,0,0] => 12

[1,1,0,1,0,1,1,0,0,0] => 10

[1,1,0,1,1,0,0,0,1,0] => 9

[1,1,0,1,1,0,0,1,0,0] => 10

[1,1,0,1,1,0,1,0,0,0] => 11

[1,1,0,1,1,1,0,0,0,0] => 8

[1,1,1,0,0,0,1,0,1,0] => 8

[1,1,1,0,0,0,1,1,0,0] => 7

[1,1,1,0,0,1,0,0,1,0] => 9

[1,1,1,0,0,1,0,1,0,0] => 10

[1,1,1,0,0,1,1,0,0,0] => 8

[1,1,1,0,1,0,0,0,1,0] => 10

[1,1,1,0,1,0,0,1,0,0] => 11

[1,1,1,0,1,0,1,0,0,0] => 12

[1,1,1,0,1,1,0,0,0,0] => 9

[1,1,1,1,0,0,0,0,1,0] => 7

[1,1,1,1,0,0,0,1,0,0] => 8

[1,1,1,1,0,0,1,0,0,0] => 9

[1,1,1,1,0,1,0,0,0,0] => 10

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

[1,0,1,0,1,0,1,0,1,0,1,0] => 12

[1,0,1,0,1,0,1,0,1,1,0,0] => 11

[1,0,1,0,1,0,1,1,0,0,1,0] => 11

[1,0,1,0,1,0,1,1,0,1,0,0] => 12

[1,0,1,0,1,0,1,1,1,0,0,0] => 10

[1,0,1,0,1,1,0,0,1,0,1,0] => 11

[1,0,1,0,1,1,0,0,1,1,0,0] => 10

[1,0,1,0,1,1,0,1,0,0,1,0] => 12

[1,0,1,0,1,1,0,1,0,1,0,0] => 13

[1,0,1,0,1,1,0,1,1,0,0,0] => 11

[1,0,1,0,1,1,1,0,0,0,1,0] => 10

[1,0,1,0,1,1,1,0,0,1,0,0] => 11

[1,0,1,0,1,1,1,0,1,0,0,0] => 12

[1,0,1,0,1,1,1,1,0,0,0,0] => 9

[1,0,1,1,0,0,1,0,1,0,1,0] => 11

[1,0,1,1,0,0,1,0,1,1,0,0] => 10

[1,0,1,1,0,0,1,1,0,0,1,0] => 10

[1,0,1,1,0,0,1,1,0,1,0,0] => 11

[1,0,1,1,0,0,1,1,1,0,0,0] => 9

[1,0,1,1,0,1,0,0,1,0,1,0] => 12

[1,0,1,1,0,1,0,0,1,1,0,0] => 11

[1,0,1,1,0,1,0,1,0,0,1,0] => 13

[1,0,1,1,0,1,0,1,0,1,0,0] => 14

[1,0,1,1,0,1,0,1,1,0,0,0] => 12

[1,0,1,1,0,1,1,0,0,0,1,0] => 11

[1,0,1,1,0,1,1,0,0,1,0,0] => 12

[1,0,1,1,0,1,1,0,1,0,0,0] => 13

[1,0,1,1,0,1,1,1,0,0,0,0] => 10

[1,0,1,1,1,0,0,0,1,0,1,0] => 10

[1,0,1,1,1,0,0,0,1,1,0,0] => 9

[1,0,1,1,1,0,0,1,0,0,1,0] => 11

[1,0,1,1,1,0,0,1,0,1,0,0] => 12

[1,0,1,1,1,0,0,1,1,0,0,0] => 10

[1,0,1,1,1,0,1,0,0,0,1,0] => 12

[1,0,1,1,1,0,1,0,0,1,0,0] => 13

[1,0,1,1,1,0,1,0,1,0,0,0] => 14

[1,0,1,1,1,0,1,1,0,0,0,0] => 11

>>> Load all 196 entries. <<<

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Description

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

Code

DeclareOperation("Ext1countall",[IsList]);

InstallMethod(Ext1countall, "for a representation of a quiver", [IsList],0,function(LIST)

local A,simA,RegA,U,L;
A:=LIST[1];
L:=ARQuiver([A,1000])[2];
RegA:=DirectSumOfQPAModules(IndecProjectiveModules(A));
U:=Filtered(L,x->Size(ExtOverAlgebra(NthSyzygy(x,0),RegA)[2])=0);
return(Size(U));

end);

Created

Jun 20, 2018 at 16:24 by Rene Marczinzik

Updated

Jun 20, 2018 at 16:24 by Rene Marczinzik