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Identifier
Values
([(0,2),(2,1)],3) => 2
([(0,1),(0,2),(1,3),(2,3)],4) => 4
([(0,3),(2,1),(3,2)],4) => 3
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 9
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 5
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 6
([(0,4),(2,3),(3,1),(4,2)],5) => 4
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 5
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 16
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => 10
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => 10
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => 8
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => 10
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => 10
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) => 12
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 7
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => 7
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => 8
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 6
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 6
([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 6
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => 7
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 25
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7) => 17
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 17
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 18
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => 11
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7) => 11
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7) => 11
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7) => 15
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7) => 17
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7) => 10
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7) => 11
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7) => 12
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) => 9
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7) => 16
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 8
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7) => 12
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7) => 17
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 7
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7) => 20
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7) => 13
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7) => 13
([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7) => 14
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7) => 12
([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7) => 15
([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7) => 13
([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7) => 13
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7) => 11
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 8
([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) => 9
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7) => 11
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 7
([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) => 9
([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) => 9
([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) => 9
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 8
([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7) => 11
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => 8
([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) => 9
([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) => 10
([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7) => 13
([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7) => 12
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => 8
([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7) => 11
([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7) => 11
([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) => 10
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7) => 13
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => 8
([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) => 9
([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7) => 11
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 7
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => 7
([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) => 9
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Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Code
DeclareOperation("daP1top",[IsList]);

InstallMethod(daP1top, "for a representation of a quiver", [IsList],0,function(LIST)

local A,L,LL,M,B,n,T,D,injA,W,simA,S,P,projA,R,RegA,CoRegA;

A:=LIST[1];
CoRegA:=DirectSumOfQPAModules(IndecInjectiveModules(A));
T:=TopOfModule(NthSyzygy(CoRegA,1));
return(Dimension(T));

end);
Created
Oct 03, 2020 at 20:51 by Rene Marczinzik
Updated
Oct 03, 2020 at 20:51 by Rene Marczinzik