Identifier
- St001138: Dyck paths ⟶ ℤ
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
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