- FindStat

Identifier

St001228: Dyck paths ⟶ ℤ

Values

[1,0] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => 11

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

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

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

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

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

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

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

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

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

[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] => 12

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

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

[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] => 11

[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] => 13

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

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

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

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

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

[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] => 7

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 196 entries. <<<

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Description

The vector space dimension of the space of module homomorphisms between J and itself when J denotes the Jacobson radical of the corresponding Nakayama algebra.

Code

DeclareOperation("dimhomjj",[IsList]);

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

local A,simA,M,g,n,U,RegA,J;

A:=LIST[1];
RegA:=DirectSumOfQPAModules(IndecProjectiveModules(A));
J:=RadicalOfModule(RegA);

return(Size(HomOverAlgebra(J,J)));
end);

Created

Jul 19, 2018 at 23:34 by Rene Marczinzik

Updated

Jul 19, 2018 at 23:34 by Rene Marczinzik