- FindStat

Identifier

St001259: 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] => 7

[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] => 9

[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] => 8

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

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

[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] => 10

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

[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] => 11

[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] => 10

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

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

[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] => 12

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

[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] => 10

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

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

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

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

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

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

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

[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] => 13

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

[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] => 10

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

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

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

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

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

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

[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] => 13

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

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

[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] => 13

[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] => 12

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

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

[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] => 14

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

[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] => 12

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

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

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

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

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

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

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

[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] => 15

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

[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] => 12

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

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

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

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

[1,0,1,1,1,0,1,0,0,0,1,0] => 16

[1,0,1,1,1,0,1,0,0,1,0,0] => 16

[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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$F_{1} = q^{2}$

$F_{2} = q^{3} + q^{4}$

$F_{3} = q^{4} + q^{5} + 2\ q^{6} + q^{7}$

$F_{4} = q^{5} + q^{6} + 2\ q^{7} + 5\ q^{8} + 2\ q^{9} + 3\ q^{10}$

$F_{5} = q^{6} + q^{7} + 2\ q^{8} + 5\ q^{9} + 10\ q^{10} + 7\ q^{11} + 6\ q^{12} + 7\ q^{13} + 3\ q^{14}$

$F_{6} = q^{7} + q^{8} + 2\ q^{9} + 5\ q^{10} + 10\ q^{11} + 22\ q^{12} + 17\ q^{13} + 19\ q^{14} + 19\ q^{15} + 15\ q^{16} + 11\ q^{17} + 8\ q^{18} + 2\ q^{19}$

Description

The vector space dimension of the double dual of D(A) in the corresponding Nakayama algebra.

Code

DeclareOperation("doubledualda",[IsList]);

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

local A,CoRegA,U;

A:=LIST[1];
CoRegA:=DirectSumOfQPAModules(IndecInjectiveModules(A));
U:=StarOfModule(StarOfModule(CoRegA));
return(Dimension(U));
end);

Created

Sep 15, 2018 at 15:32 by Rene Marczinzik

Updated

Sep 20, 2018 at 09:41 by Rene Marczinzik