Identifier
Identifier
Values
[1,0] generating graphics... => 3
[1,0,1,0] generating graphics... => 5
[1,1,0,0] generating graphics... => 6
[1,0,1,0,1,0] generating graphics... => 7
[1,0,1,1,0,0] generating graphics... => 8
[1,1,0,0,1,0] generating graphics... => 8
[1,1,0,1,0,0] generating graphics... => 9
[1,1,1,0,0,0] generating graphics... => 10
[1,0,1,0,1,0,1,0] generating graphics... => 8
[1,0,1,0,1,1,0,0] generating graphics... => 10
[1,0,1,1,0,0,1,0] generating graphics... => 9
[1,0,1,1,0,1,0,0] generating graphics... => 11
[1,0,1,1,1,0,0,0] generating graphics... => 12
[1,1,0,0,1,0,1,0] generating graphics... => 10
[1,1,0,0,1,1,0,0] generating graphics... => 11
[1,1,0,1,0,0,1,0] generating graphics... => 11
[1,1,0,1,0,1,0,0] generating graphics... => 12
[1,1,0,1,1,0,0,0] generating graphics... => 13
[1,1,1,0,0,0,1,0] generating graphics... => 12
[1,1,1,0,0,1,0,0] generating graphics... => 13
[1,1,1,0,1,0,0,0] generating graphics... => 14
[1,1,1,1,0,0,0,0] generating graphics... => 15
[1,0,1,0,1,0,1,0,1,0] generating graphics... => 9
[1,0,1,0,1,0,1,1,0,0] generating graphics... => 11
[1,0,1,0,1,1,0,0,1,0] generating graphics... => 11
[1,0,1,0,1,1,0,1,0,0] generating graphics... => 12
[1,0,1,0,1,1,1,0,0,0] generating graphics... => 14
[1,0,1,1,0,0,1,0,1,0] generating graphics... => 11
[1,0,1,1,0,0,1,1,0,0] generating graphics... => 12
[1,0,1,1,0,1,0,0,1,0] generating graphics... => 12
[1,0,1,1,0,1,0,1,0,0] generating graphics... => 12
[1,0,1,1,0,1,1,0,0,0] generating graphics... => 15
[1,0,1,1,1,0,0,0,1,0] generating graphics... => 13
[1,0,1,1,1,0,0,1,0,0] generating graphics... => 13
[1,0,1,1,1,0,1,0,0,0] generating graphics... => 16
[1,0,1,1,1,1,0,0,0,0] generating graphics... => 17
[1,1,0,0,1,0,1,0,1,0] generating graphics... => 11
[1,1,0,0,1,0,1,1,0,0] generating graphics... => 13
[1,1,0,0,1,1,0,0,1,0] generating graphics... => 12
[1,1,0,0,1,1,0,1,0,0] generating graphics... => 14
[1,1,0,0,1,1,1,0,0,0] generating graphics... => 15
[1,1,0,1,0,0,1,0,1,0] generating graphics... => 12
[1,1,0,1,0,0,1,1,0,0] generating graphics... => 14
[1,1,0,1,0,1,0,0,1,0] generating graphics... => 12
[1,1,0,1,0,1,0,1,0,0] generating graphics... => 14
[1,1,0,1,0,1,1,0,0,0] generating graphics... => 16
[1,1,0,1,1,0,0,0,1,0] generating graphics... => 13
[1,1,0,1,1,0,0,1,0,0] generating graphics... => 15
[1,1,0,1,1,0,1,0,0,0] generating graphics... => 17
[1,1,0,1,1,1,0,0,0,0] generating graphics... => 18
[1,1,1,0,0,0,1,0,1,0] generating graphics... => 14
[1,1,1,0,0,0,1,1,0,0] generating graphics... => 15
[1,1,1,0,0,1,0,0,1,0] generating graphics... => 15
[1,1,1,0,0,1,0,1,0,0] generating graphics... => 16
[1,1,1,0,0,1,1,0,0,0] generating graphics... => 17
[1,1,1,0,1,0,0,0,1,0] generating graphics... => 16
[1,1,1,0,1,0,0,1,0,0] generating graphics... => 17
[1,1,1,0,1,0,1,0,0,0] generating graphics... => 18
[1,1,1,0,1,1,0,0,0,0] generating graphics... => 19
[1,1,1,1,0,0,0,0,1,0] generating graphics... => 17
[1,1,1,1,0,0,0,1,0,0] generating graphics... => 18
[1,1,1,1,0,0,1,0,0,0] generating graphics... => 19
[1,1,1,1,0,1,0,0,0,0] generating graphics... => 20
[1,1,1,1,1,0,0,0,0,0] generating graphics... => 21
[1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 10
[1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 12
[1,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 12
[1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 13
[1,0,1,0,1,0,1,1,1,0,0,0] generating graphics... => 15
[1,0,1,0,1,1,0,0,1,0,1,0] generating graphics... => 13
[1,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 14
[1,0,1,0,1,1,0,1,0,0,1,0] generating graphics... => 13
[1,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 13
[1,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 16
[1,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 15
[1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 15
[1,0,1,0,1,1,1,0,1,0,0,0] generating graphics... => 17
[1,0,1,0,1,1,1,1,0,0,0,0] generating graphics... => 19
[1,0,1,1,0,0,1,0,1,0,1,0] generating graphics... => 12
[1,0,1,1,0,0,1,0,1,1,0,0] generating graphics... => 14
[1,0,1,1,0,0,1,1,0,0,1,0] generating graphics... => 13
[1,0,1,1,0,0,1,1,0,1,0,0] generating graphics... => 15
[1,0,1,1,0,0,1,1,1,0,0,0] generating graphics... => 16
[1,0,1,1,0,1,0,0,1,0,1,0] generating graphics... => 13
[1,0,1,1,0,1,0,0,1,1,0,0] generating graphics... => 15
[1,0,1,1,0,1,0,1,0,0,1,0] generating graphics... => 12
[1,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 14
[1,0,1,1,0,1,0,1,1,0,0,0] generating graphics... => 16
[1,0,1,1,0,1,1,0,0,0,1,0] generating graphics... => 15
[1,0,1,1,0,1,1,0,0,1,0,0] generating graphics... => 16
[1,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 17
[1,0,1,1,0,1,1,1,0,0,0,0] generating graphics... => 20
[1,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 15
[1,0,1,1,1,0,0,0,1,1,0,0] generating graphics... => 16
[1,0,1,1,1,0,0,1,0,0,1,0] generating graphics... => 15
[1,0,1,1,1,0,0,1,0,1,0,0] generating graphics... => 16
[1,0,1,1,1,0,0,1,1,0,0,0] generating graphics... => 17
[1,0,1,1,1,0,1,0,0,0,1,0] generating graphics... => 17
[1,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 17
[1,0,1,1,1,0,1,0,1,0,0,0] generating graphics... => 17
[1,0,1,1,1,0,1,1,0,0,0,0] generating graphics... => 21
[1,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 18
[1,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 18
[1,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 18
[1,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 22
[1,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 23
[1,1,0,0,1,0,1,0,1,0,1,0] generating graphics... => 12
[1,1,0,0,1,0,1,0,1,1,0,0] generating graphics... => 14
[1,1,0,0,1,0,1,1,0,0,1,0] generating graphics... => 14
[1,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 15
[1,1,0,0,1,0,1,1,1,0,0,0] generating graphics... => 17
[1,1,0,0,1,1,0,0,1,0,1,0] generating graphics... => 14
[1,1,0,0,1,1,0,0,1,1,0,0] generating graphics... => 15
[1,1,0,0,1,1,0,1,0,0,1,0] generating graphics... => 15
[1,1,0,0,1,1,0,1,0,1,0,0] generating graphics... => 15
[1,1,0,0,1,1,0,1,1,0,0,0] generating graphics... => 18
[1,1,0,0,1,1,1,0,0,0,1,0] generating graphics... => 16
[1,1,0,0,1,1,1,0,0,1,0,0] generating graphics... => 16
[1,1,0,0,1,1,1,0,1,0,0,0] generating graphics... => 19
[1,1,0,0,1,1,1,1,0,0,0,0] generating graphics... => 20
[1,1,0,1,0,0,1,0,1,0,1,0] generating graphics... => 13
[1,1,0,1,0,0,1,0,1,1,0,0] generating graphics... => 15
[1,1,0,1,0,0,1,1,0,0,1,0] generating graphics... => 15
[1,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 16
[1,1,0,1,0,0,1,1,1,0,0,0] generating graphics... => 18
[1,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 13
[1,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 15
[1,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 14
[1,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 15
[1,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 18
[1,1,0,1,0,1,1,0,0,0,1,0] generating graphics... => 16
[1,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 16
[1,1,0,1,0,1,1,0,1,0,0,0] generating graphics... => 19
[1,1,0,1,0,1,1,1,0,0,0,0] generating graphics... => 21
[1,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 15
[1,1,0,1,1,0,0,0,1,1,0,0] generating graphics... => 16
[1,1,0,1,1,0,0,1,0,0,1,0] generating graphics... => 16
[1,1,0,1,1,0,0,1,0,1,0,0] generating graphics... => 16
[1,1,0,1,1,0,0,1,1,0,0,0] generating graphics... => 19
[1,1,0,1,1,0,1,0,0,0,1,0] generating graphics... => 17
[1,1,0,1,1,0,1,0,0,1,0,0] generating graphics... => 16
[1,1,0,1,1,0,1,0,1,0,0,0] generating graphics... => 19
[1,1,0,1,1,0,1,1,0,0,0,0] generating graphics... => 22
[1,1,0,1,1,1,0,0,0,0,1,0] generating graphics... => 18
[1,1,0,1,1,1,0,0,0,1,0,0] generating graphics... => 17
[1,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 20
[1,1,0,1,1,1,0,1,0,0,0,0] generating graphics... => 23
[1,1,0,1,1,1,1,0,0,0,0,0] generating graphics... => 24
[1,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 15
[1,1,1,0,0,0,1,0,1,1,0,0] generating graphics... => 17
[1,1,1,0,0,0,1,1,0,0,1,0] generating graphics... => 16
[1,1,1,0,0,0,1,1,0,1,0,0] generating graphics... => 18
[1,1,1,0,0,0,1,1,1,0,0,0] generating graphics... => 19
[1,1,1,0,0,1,0,0,1,0,1,0] generating graphics... => 16
[1,1,1,0,0,1,0,0,1,1,0,0] generating graphics... => 18
[1,1,1,0,0,1,0,1,0,0,1,0] generating graphics... => 16
[1,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 18
[1,1,1,0,0,1,0,1,1,0,0,0] generating graphics... => 20
[1,1,1,0,0,1,1,0,0,0,1,0] generating graphics... => 17
[1,1,1,0,0,1,1,0,0,1,0,0] generating graphics... => 19
[1,1,1,0,0,1,1,0,1,0,0,0] generating graphics... => 21
[1,1,1,0,0,1,1,1,0,0,0,0] generating graphics... => 22
[1,1,1,0,1,0,0,0,1,0,1,0] generating graphics... => 17
[1,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 19
[1,1,1,0,1,0,0,1,0,0,1,0] generating graphics... => 17
[1,1,1,0,1,0,0,1,0,1,0,0] generating graphics... => 19
[1,1,1,0,1,0,0,1,1,0,0,0] generating graphics... => 21
[1,1,1,0,1,0,1,0,0,0,1,0] generating graphics... => 17
[1,1,1,0,1,0,1,0,0,1,0,0] generating graphics... => 19
[1,1,1,0,1,0,1,0,1,0,0,0] generating graphics... => 21
[1,1,1,0,1,0,1,1,0,0,0,0] generating graphics... => 23
[1,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 18
[1,1,1,0,1,1,0,0,0,1,0,0] generating graphics... => 20
[1,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 22
[1,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 24
[1,1,1,0,1,1,1,0,0,0,0,0] generating graphics... => 25
[1,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 19
[1,1,1,1,0,0,0,0,1,1,0,0] generating graphics... => 20
[1,1,1,1,0,0,0,1,0,0,1,0] generating graphics... => 20
[1,1,1,1,0,0,0,1,0,1,0,0] generating graphics... => 21
[1,1,1,1,0,0,0,1,1,0,0,0] generating graphics... => 22
[1,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 21
[1,1,1,1,0,0,1,0,0,1,0,0] generating graphics... => 22
[1,1,1,1,0,0,1,0,1,0,0,0] generating graphics... => 23
[1,1,1,1,0,0,1,1,0,0,0,0] generating graphics... => 24
[1,1,1,1,0,1,0,0,0,0,1,0] generating graphics... => 22
[1,1,1,1,0,1,0,0,0,1,0,0] generating graphics... => 23
[1,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 24
[1,1,1,1,0,1,0,1,0,0,0,0] generating graphics... => 25
[1,1,1,1,0,1,1,0,0,0,0,0] generating graphics... => 26
[1,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 23
[1,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 24
[1,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 25
[1,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 26
[1,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 27
[1,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 28
click to show generating function       
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