- FindStat

Identifier

St001138: Dyck paths ⟶ ℤ

Values

[1,0] => 3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,0,1,1,1,1,0,0,0,0] => 17

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

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

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

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

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

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

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

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

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

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

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

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

[1,1,0,1,1,0,1,0,0,0] => 17

[1,1,0,1,1,1,0,0,0,0] => 18

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

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

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

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

[1,1,1,0,0,1,1,0,0,0] => 17

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

[1,1,1,0,1,0,0,1,0,0] => 17

[1,1,1,0,1,0,1,0,0,0] => 18

[1,1,1,0,1,1,0,0,0,0] => 19

[1,1,1,1,0,0,0,0,1,0] => 17

[1,1,1,1,0,0,0,1,0,0] => 18

[1,1,1,1,0,0,1,0,0,0] => 19

[1,1,1,1,0,1,0,0,0,0] => 20

[1,1,1,1,1,0,0,0,0,0] => 21

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

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

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

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

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

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

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

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

[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] => 16

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

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

[1,0,1,0,1,1,1,0,1,0,0,0] => 17

[1,0,1,0,1,1,1,1,0,0,0,0] => 19

[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] => 14

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

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

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

[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] => 15

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

[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] => 16

[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] => 16

[1,0,1,1,0,1,1,0,1,0,0,0] => 17

[1,0,1,1,0,1,1,1,0,0,0,0] => 20

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

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

[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] => 16

[1,0,1,1,1,0,0,1,1,0,0,0] => 17

[1,0,1,1,1,0,1,0,0,0,1,0] => 17

[1,0,1,1,1,0,1,0,0,1,0,0] => 17

[1,0,1,1,1,0,1,0,1,0,0,0] => 17

[1,0,1,1,1,0,1,1,0,0,0,0] => 21

>>> Load all 196 entries. <<<

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Description

The number of indecomposable modules with projective dimension or injective dimension at most one in the corresponding Nakayama algebra.

References

[1] Marczinzik, René Upper bounds for the dominant dimension of Nakayama and related algebras. zbMATH:06820683

Code

DeclareOperation("numberofmoduleswithprojinjdimlessorequal1",[IsList]);

InstallMethod(numberofmoduleswithprojinjdimlessorequal1, "for a representation of a quiver", [IsList],0,function(LIST)

local M, n, f, N, i, h,A,g,r,L,LL,subsets1,subsets2,W,simA,G1,G2,G3,g1,g2,g3,WU,O,OF,RegA,LU;

LU:=LIST[1];
A:=NakayamaAlgebra(LU,GF(3));
L:=ARQuiver([A,1000])[2];
LL:=Filtered(L,x->ProjDimensionOfModule(x,30)<=1 or InjDimensionOfModule(x,30)<=1);
return(Size(LL));

end);

Created

Apr 09, 2018 at 14:03 by Rene Marczinzik

Updated

May 02, 2018 at 12:35 by Rene Marczinzik