- FindStat

Identifier

St001295: Dyck paths ⟶ ℤ (values match St000012The area of a Dyck path.)

Values

[1,0] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => 5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => 1

[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] => 2

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

[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] => 2

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

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

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

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

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

[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] => 1

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

[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] => 3

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

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

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

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

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

[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] => 5

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

[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] => 3

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

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

[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] => 6

[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] => 6

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

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

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Description

Gives the vector space dimension of the homomorphism space between J^2 and J^2.

Code

DeclareOperation("hom1rads2", [IsList]);

InstallMethod(hom1rads2, "for a representation of a quiver", [IsList],0,function(L)


local A,RegA,J1,J2,J3;



A:=L[1];
RegA:=DirectSumOfQPAModules(IndecProjectiveModules(A));
J1:=RadicalOfModule(RegA);
J2:=RadicalOfModule(J1);
return(Size(HomOverAlgebra(J2,J2)));
end
);

Created

Jul 20, 2018 at 18:31 by Rene Marczinzik

Updated

Jul 20, 2018 at 18:31 by Rene Marczinzik