Identifier
Values
=>
Cc0005;cc-rep
[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 [1,0,1,1,1,1,0,0,0,0,1,0]=>18 [1,0,1,1,1,1,0,0,0,1,0,0]=>18 [1,0,1,1,1,1,0,0,1,0,0,0]=>18 [1,0,1,1,1,1,0,1,0,0,0,0]=>22 [1,0,1,1,1,1,1,0,0,0,0,0]=>23 [1,1,0,0,1,0,1,0,1,0,1,0]=>12 [1,1,0,0,1,0,1,0,1,1,0,0]=>14 [1,1,0,0,1,0,1,1,0,0,1,0]=>14 [1,1,0,0,1,0,1,1,0,1,0,0]=>15 [1,1,0,0,1,0,1,1,1,0,0,0]=>17 [1,1,0,0,1,1,0,0,1,0,1,0]=>14 [1,1,0,0,1,1,0,0,1,1,0,0]=>15 [1,1,0,0,1,1,0,1,0,0,1,0]=>15 [1,1,0,0,1,1,0,1,0,1,0,0]=>15 [1,1,0,0,1,1,0,1,1,0,0,0]=>18 [1,1,0,0,1,1,1,0,0,0,1,0]=>16 [1,1,0,0,1,1,1,0,0,1,0,0]=>16 [1,1,0,0,1,1,1,0,1,0,0,0]=>19 [1,1,0,0,1,1,1,1,0,0,0,0]=>20 [1,1,0,1,0,0,1,0,1,0,1,0]=>13 [1,1,0,1,0,0,1,0,1,1,0,0]=>15 [1,1,0,1,0,0,1,1,0,0,1,0]=>15 [1,1,0,1,0,0,1,1,0,1,0,0]=>16 [1,1,0,1,0,0,1,1,1,0,0,0]=>18 [1,1,0,1,0,1,0,0,1,0,1,0]=>13 [1,1,0,1,0,1,0,0,1,1,0,0]=>15 [1,1,0,1,0,1,0,1,0,0,1,0]=>14 [1,1,0,1,0,1,0,1,0,1,0,0]=>15 [1,1,0,1,0,1,0,1,1,0,0,0]=>18 [1,1,0,1,0,1,1,0,0,0,1,0]=>16 [1,1,0,1,0,1,1,0,0,1,0,0]=>16 [1,1,0,1,0,1,1,0,1,0,0,0]=>19 [1,1,0,1,0,1,1,1,0,0,0,0]=>21 [1,1,0,1,1,0,0,0,1,0,1,0]=>15 [1,1,0,1,1,0,0,0,1,1,0,0]=>16 [1,1,0,1,1,0,0,1,0,0,1,0]=>16 [1,1,0,1,1,0,0,1,0,1,0,0]=>16 [1,1,0,1,1,0,0,1,1,0,0,0]=>19 [1,1,0,1,1,0,1,0,0,0,1,0]=>17 [1,1,0,1,1,0,1,0,0,1,0,0]=>16 [1,1,0,1,1,0,1,0,1,0,0,0]=>19 [1,1,0,1,1,0,1,1,0,0,0,0]=>22 [1,1,0,1,1,1,0,0,0,0,1,0]=>18 [1,1,0,1,1,1,0,0,0,1,0,0]=>17 [1,1,0,1,1,1,0,0,1,0,0,0]=>20 [1,1,0,1,1,1,0,1,0,0,0,0]=>23 [1,1,0,1,1,1,1,0,0,0,0,0]=>24 [1,1,1,0,0,0,1,0,1,0,1,0]=>15 [1,1,1,0,0,0,1,0,1,1,0,0]=>17 [1,1,1,0,0,0,1,1,0,0,1,0]=>16 [1,1,1,0,0,0,1,1,0,1,0,0]=>18 [1,1,1,0,0,0,1,1,1,0,0,0]=>19 [1,1,1,0,0,1,0,0,1,0,1,0]=>16 [1,1,1,0,0,1,0,0,1,1,0,0]=>18 [1,1,1,0,0,1,0,1,0,0,1,0]=>16 [1,1,1,0,0,1,0,1,0,1,0,0]=>18 [1,1,1,0,0,1,0,1,1,0,0,0]=>20 [1,1,1,0,0,1,1,0,0,0,1,0]=>17 [1,1,1,0,0,1,1,0,0,1,0,0]=>19 [1,1,1,0,0,1,1,0,1,0,0,0]=>21 [1,1,1,0,0,1,1,1,0,0,0,0]=>22 [1,1,1,0,1,0,0,0,1,0,1,0]=>17 [1,1,1,0,1,0,0,0,1,1,0,0]=>19 [1,1,1,0,1,0,0,1,0,0,1,0]=>17 [1,1,1,0,1,0,0,1,0,1,0,0]=>19 [1,1,1,0,1,0,0,1,1,0,0,0]=>21 [1,1,1,0,1,0,1,0,0,0,1,0]=>17 [1,1,1,0,1,0,1,0,0,1,0,0]=>19 [1,1,1,0,1,0,1,0,1,0,0,0]=>21 [1,1,1,0,1,0,1,1,0,0,0,0]=>23 [1,1,1,0,1,1,0,0,0,0,1,0]=>18 [1,1,1,0,1,1,0,0,0,1,0,0]=>20 [1,1,1,0,1,1,0,0,1,0,0,0]=>22 [1,1,1,0,1,1,0,1,0,0,0,0]=>24 [1,1,1,0,1,1,1,0,0,0,0,0]=>25 [1,1,1,1,0,0,0,0,1,0,1,0]=>19 [1,1,1,1,0,0,0,0,1,1,0,0]=>20 [1,1,1,1,0,0,0,1,0,0,1,0]=>20 [1,1,1,1,0,0,0,1,0,1,0,0]=>21 [1,1,1,1,0,0,0,1,1,0,0,0]=>22 [1,1,1,1,0,0,1,0,0,0,1,0]=>21 [1,1,1,1,0,0,1,0,0,1,0,0]=>22 [1,1,1,1,0,0,1,0,1,0,0,0]=>23 [1,1,1,1,0,0,1,1,0,0,0,0]=>24 [1,1,1,1,0,1,0,0,0,0,1,0]=>22 [1,1,1,1,0,1,0,0,0,1,0,0]=>23 [1,1,1,1,0,1,0,0,1,0,0,0]=>24 [1,1,1,1,0,1,0,1,0,0,0,0]=>25 [1,1,1,1,0,1,1,0,0,0,0,0]=>26 [1,1,1,1,1,0,0,0,0,0,1,0]=>23 [1,1,1,1,1,0,0,0,0,1,0,0]=>24 [1,1,1,1,1,0,0,0,1,0,0,0]=>25 [1,1,1,1,1,0,0,1,0,0,0,0]=>26 [1,1,1,1,1,0,1,0,0,0,0,0]=>27 [1,1,1,1,1,1,0,0,0,0,0,0]=>28
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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