- FindStat

Identifier

St000951: Dyck paths ⟶ ℤ

Values

[1,0] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,1,1,1,0,0,0,0,0] => 15

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

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

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

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

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

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

[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] => 0

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

[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] => 4

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

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

[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] => 1

[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] => 2

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

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

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

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

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

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

[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] => 2

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

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

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

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

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

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

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

[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] => 0

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

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

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

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Description

The dimension of $Ext^{1}(D(A),A)$ of the corresponding LNakayama algebra.

Code

DeclareOperation("DimExt",[IsList]);

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

local M, n, f, N, i, h;

u:=LIST[1];
A:=NakayamaAlgebra(GF(3),u);
projA:=IndecProjectiveModules(A);RegA:=DirectSumOfQPAModules(projA);injA:=IndecInjectiveModules(A);CoRegA:=DirectSumOfQPAModules(injA);
r:=Size(ExtOverAlgebra(CoRegA,RegA)[2]);




return([u,r]);

end);

Created

Aug 25, 2017 at 13:03 by Rene Marczinzik

Updated

Aug 25, 2017 at 13:03 by Rene Marczinzik