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Identifier
Values
=>
Cc0005;cc-rep
[1,0]=>1 [1,0,1,0]=>1 [1,1,0,0]=>3 [1,0,1,0,1,0]=>1 [1,0,1,1,0,0]=>1 [1,1,0,0,1,0]=>1 [1,1,0,1,0,0]=>3 [1,1,1,0,0,0]=>6 [1,0,1,0,1,0,1,0]=>1 [1,0,1,0,1,1,0,0]=>1 [1,0,1,1,0,0,1,0]=>2 [1,0,1,1,0,1,0,0]=>3 [1,0,1,1,1,0,0,0]=>1 [1,1,0,0,1,0,1,0]=>1 [1,1,0,0,1,1,0,0]=>1 [1,1,0,1,0,0,1,0]=>3 [1,1,0,1,0,1,0,0]=>2 [1,1,0,1,1,0,0,0]=>3 [1,1,1,0,0,0,1,0]=>1 [1,1,1,0,0,1,0,0]=>3 [1,1,1,0,1,0,0,0]=>6 [1,1,1,1,0,0,0,0]=>10 [1,0,1,0,1,0,1,0,1,0]=>1 [1,0,1,0,1,0,1,1,0,0]=>1 [1,0,1,0,1,1,0,0,1,0]=>2 [1,0,1,0,1,1,0,1,0,0]=>3 [1,0,1,0,1,1,1,0,0,0]=>1 [1,0,1,1,0,0,1,0,1,0]=>2 [1,0,1,1,0,0,1,1,0,0]=>2 [1,0,1,1,0,1,0,0,1,0]=>3 [1,0,1,1,0,1,0,1,0,0]=>2 [1,0,1,1,0,1,1,0,0,0]=>3 [1,0,1,1,1,0,0,0,1,0]=>2 [1,0,1,1,1,0,0,1,0,0]=>4 [1,0,1,1,1,0,1,0,0,0]=>6 [1,0,1,1,1,1,0,0,0,0]=>1 [1,1,0,0,1,0,1,0,1,0]=>1 [1,1,0,0,1,0,1,1,0,0]=>1 [1,1,0,0,1,1,0,0,1,0]=>2 [1,1,0,0,1,1,0,1,0,0]=>3 [1,1,0,0,1,1,1,0,0,0]=>1 [1,1,0,1,0,0,1,0,1,0]=>3 [1,1,0,1,0,0,1,1,0,0]=>3 [1,1,0,1,0,1,0,0,1,0]=>2 [1,1,0,1,0,1,0,1,0,0]=>3 [1,1,0,1,0,1,1,0,0,0]=>2 [1,1,0,1,1,0,0,0,1,0]=>4 [1,1,0,1,1,0,0,1,0,0]=>6 [1,1,0,1,1,0,1,0,0,0]=>4 [1,1,0,1,1,1,0,0,0,0]=>3 [1,1,1,0,0,0,1,0,1,0]=>1 [1,1,1,0,0,0,1,1,0,0]=>1 [1,1,1,0,0,1,0,0,1,0]=>3 [1,1,1,0,0,1,0,1,0,0]=>2 [1,1,1,0,0,1,1,0,0,0]=>3 [1,1,1,0,1,0,0,0,1,0]=>6 [1,1,1,0,1,0,0,1,0,0]=>4 [1,1,1,0,1,0,1,0,0,0]=>4 [1,1,1,0,1,1,0,0,0,0]=>6 [1,1,1,1,0,0,0,0,1,0]=>1 [1,1,1,1,0,0,0,1,0,0]=>3 [1,1,1,1,0,0,1,0,0,0]=>6 [1,1,1,1,0,1,0,0,0,0]=>10 [1,1,1,1,1,0,0,0,0,0]=>15 [1,0,1,0,1,0,1,0,1,0,1,0]=>1 [1,0,1,0,1,0,1,0,1,1,0,0]=>1 [1,0,1,0,1,0,1,1,0,0,1,0]=>2 [1,0,1,0,1,0,1,1,0,1,0,0]=>3 [1,0,1,0,1,0,1,1,1,0,0,0]=>1 [1,0,1,0,1,1,0,0,1,0,1,0]=>2 [1,0,1,0,1,1,0,0,1,1,0,0]=>2 [1,0,1,0,1,1,0,1,0,0,1,0]=>3 [1,0,1,0,1,1,0,1,0,1,0,0]=>2 [1,0,1,0,1,1,0,1,1,0,0,0]=>3 [1,0,1,0,1,1,1,0,0,0,1,0]=>2 [1,0,1,0,1,1,1,0,0,1,0,0]=>4 [1,0,1,0,1,1,1,0,1,0,0,0]=>6 [1,0,1,0,1,1,1,1,0,0,0,0]=>1 [1,0,1,1,0,0,1,0,1,0,1,0]=>2 [1,0,1,1,0,0,1,0,1,1,0,0]=>2 [1,0,1,1,0,0,1,1,0,0,1,0]=>3 [1,0,1,1,0,0,1,1,0,1,0,0]=>4 [1,0,1,1,0,0,1,1,1,0,0,0]=>2 [1,0,1,1,0,1,0,0,1,0,1,0]=>3 [1,0,1,1,0,1,0,0,1,1,0,0]=>3 [1,0,1,1,0,1,0,1,0,0,1,0]=>2 [1,0,1,1,0,1,0,1,0,1,0,0]=>3 [1,0,1,1,0,1,0,1,1,0,0,0]=>2 [1,0,1,1,0,1,1,0,0,0,1,0]=>4 [1,0,1,1,0,1,1,0,0,1,0,0]=>6 [1,0,1,1,0,1,1,0,1,0,0,0]=>4 [1,0,1,1,0,1,1,1,0,0,0,0]=>3 [1,0,1,1,1,0,0,0,1,0,1,0]=>2 [1,0,1,1,1,0,0,0,1,1,0,0]=>2 [1,0,1,1,1,0,0,1,0,0,1,0]=>4 [1,0,1,1,1,0,0,1,0,1,0,0]=>3 [1,0,1,1,1,0,0,1,1,0,0,0]=>4 [1,0,1,1,1,0,1,0,0,0,1,0]=>6 [1,0,1,1,1,0,1,0,0,1,0,0]=>4 [1,0,1,1,1,0,1,0,1,0,0,0]=>4 [1,0,1,1,1,0,1,1,0,0,0,0]=>6 [1,0,1,1,1,1,0,0,0,0,1,0]=>2 [1,0,1,1,1,1,0,0,0,1,0,0]=>4 [1,0,1,1,1,1,0,0,1,0,0,0]=>7 [1,0,1,1,1,1,0,1,0,0,0,0]=>10 [1,0,1,1,1,1,1,0,0,0,0,0]=>1 [1,1,0,0,1,0,1,0,1,0,1,0]=>1 [1,1,0,0,1,0,1,0,1,1,0,0]=>1 [1,1,0,0,1,0,1,1,0,0,1,0]=>2 [1,1,0,0,1,0,1,1,0,1,0,0]=>3 [1,1,0,0,1,0,1,1,1,0,0,0]=>1 [1,1,0,0,1,1,0,0,1,0,1,0]=>2 [1,1,0,0,1,1,0,0,1,1,0,0]=>2 [1,1,0,0,1,1,0,1,0,0,1,0]=>3 [1,1,0,0,1,1,0,1,0,1,0,0]=>2 [1,1,0,0,1,1,0,1,1,0,0,0]=>3 [1,1,0,0,1,1,1,0,0,0,1,0]=>2 [1,1,0,0,1,1,1,0,0,1,0,0]=>4 [1,1,0,0,1,1,1,0,1,0,0,0]=>6 [1,1,0,0,1,1,1,1,0,0,0,0]=>1 [1,1,0,1,0,0,1,0,1,0,1,0]=>3 [1,1,0,1,0,0,1,0,1,1,0,0]=>3 [1,1,0,1,0,0,1,1,0,0,1,0]=>4 [1,1,0,1,0,0,1,1,0,1,0,0]=>6 [1,1,0,1,0,0,1,1,1,0,0,0]=>3 [1,1,0,1,0,1,0,0,1,0,1,0]=>2 [1,1,0,1,0,1,0,0,1,1,0,0]=>2 [1,1,0,1,0,1,0,1,0,0,1,0]=>3 [1,1,0,1,0,1,0,1,0,1,0,0]=>3 [1,1,0,1,0,1,0,1,1,0,0,0]=>3 [1,1,0,1,0,1,1,0,0,0,1,0]=>3 [1,1,0,1,0,1,1,0,0,1,0,0]=>4 [1,1,0,1,0,1,1,0,1,0,0,0]=>5 [1,1,0,1,0,1,1,1,0,0,0,0]=>2 [1,1,0,1,1,0,0,0,1,0,1,0]=>4 [1,1,0,1,1,0,0,0,1,1,0,0]=>4 [1,1,0,1,1,0,0,1,0,0,1,0]=>6 [1,1,0,1,1,0,0,1,0,1,0,0]=>4 [1,1,0,1,1,0,0,1,1,0,0,0]=>6 [1,1,0,1,1,0,1,0,0,0,1,0]=>4 [1,1,0,1,1,0,1,0,0,1,0,0]=>3 [1,1,0,1,1,0,1,0,1,0,0,0]=>6 [1,1,0,1,1,0,1,1,0,0,0,0]=>4 [1,1,0,1,1,1,0,0,0,0,1,0]=>4 [1,1,0,1,1,1,0,0,0,1,0,0]=>6 [1,1,0,1,1,1,0,0,1,0,0,0]=>10 [1,1,0,1,1,1,0,1,0,0,0,0]=>7 [1,1,0,1,1,1,1,0,0,0,0,0]=>3 [1,1,1,0,0,0,1,0,1,0,1,0]=>1 [1,1,1,0,0,0,1,0,1,1,0,0]=>1 [1,1,1,0,0,0,1,1,0,0,1,0]=>2 [1,1,1,0,0,0,1,1,0,1,0,0]=>3 [1,1,1,0,0,0,1,1,1,0,0,0]=>1 [1,1,1,0,0,1,0,0,1,0,1,0]=>3 [1,1,1,0,0,1,0,0,1,1,0,0]=>3 [1,1,1,0,0,1,0,1,0,0,1,0]=>2 [1,1,1,0,0,1,0,1,0,1,0,0]=>3 [1,1,1,0,0,1,0,1,1,0,0,0]=>2 [1,1,1,0,0,1,1,0,0,0,1,0]=>4 [1,1,1,0,0,1,1,0,0,1,0,0]=>6 [1,1,1,0,0,1,1,0,1,0,0,0]=>4 [1,1,1,0,0,1,1,1,0,0,0,0]=>3 [1,1,1,0,1,0,0,0,1,0,1,0]=>6 [1,1,1,0,1,0,0,0,1,1,0,0]=>6 [1,1,1,0,1,0,0,1,0,0,1,0]=>4 [1,1,1,0,1,0,0,1,0,1,0,0]=>5 [1,1,1,0,1,0,0,1,1,0,0,0]=>4 [1,1,1,0,1,0,1,0,0,0,1,0]=>4 [1,1,1,0,1,0,1,0,0,1,0,0]=>6 [1,1,1,0,1,0,1,0,1,0,0,0]=>4 [1,1,1,0,1,0,1,1,0,0,0,0]=>4 [1,1,1,0,1,1,0,0,0,0,1,0]=>7 [1,1,1,0,1,1,0,0,0,1,0,0]=>10 [1,1,1,0,1,1,0,0,1,0,0,0]=>7 [1,1,1,0,1,1,0,1,0,0,0,0]=>6 [1,1,1,0,1,1,1,0,0,0,0,0]=>6 [1,1,1,1,0,0,0,0,1,0,1,0]=>1 [1,1,1,1,0,0,0,0,1,1,0,0]=>1 [1,1,1,1,0,0,0,1,0,0,1,0]=>3 [1,1,1,1,0,0,0,1,0,1,0,0]=>2 [1,1,1,1,0,0,0,1,1,0,0,0]=>3 [1,1,1,1,0,0,1,0,0,0,1,0]=>6 [1,1,1,1,0,0,1,0,0,1,0,0]=>4 [1,1,1,1,0,0,1,0,1,0,0,0]=>4 [1,1,1,1,0,0,1,1,0,0,0,0]=>6 [1,1,1,1,0,1,0,0,0,0,1,0]=>10 [1,1,1,1,0,1,0,0,0,1,0,0]=>7 [1,1,1,1,0,1,0,0,1,0,0,0]=>6 [1,1,1,1,0,1,0,1,0,0,0,0]=>7 [1,1,1,1,0,1,1,0,0,0,0,0]=>10 [1,1,1,1,1,0,0,0,0,0,1,0]=>1 [1,1,1,1,1,0,0,0,0,1,0,0]=>3 [1,1,1,1,1,0,0,0,1,0,0,0]=>6 [1,1,1,1,1,0,0,1,0,0,0,0]=>10 [1,1,1,1,1,0,1,0,0,0,0,0]=>15 [1,1,1,1,1,1,0,0,0,0,0,0]=>21
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Description
The sum of the dimensions of $\operatorname{Ext}^i(D(A),A)$ for $i=1,\ldots,g$, where $g$ is the global dimension of the linear Nakayama algebra corresponding to a Dyck path.
The correspondence between linear Nakayama algebras and Dyck paths is explained on the Nakayama algebras page.
Code
DeclareOperation("dimextgldim2",[IsList]);

InstallMethod(dimextgldim2, "for a representation of a quiver", [IsList],0,function(LIST)

local M, n, f, N, i, h;

L:=LIST[1];

A:=NakayamaAlgebra(L,GF(3));
g:=gldim(L);
projA:=IndecProjectiveModules(A);RegA:=DirectSumOfQPAModules(projA);injA:=IndecInjectiveModules(A);CoRegA:=DirectSumOfQPAModules(injA);
temp2:=[];
for i in [2..g] do Append(temp2,[Size(ExtOverAlgebra(NthSyzygy(CoRegA,i-1),RegA)[2])]);od;
t:=Sum(temp2);



return(t);

end);
Created
Aug 31, 2017 at 11:17 by Rene Marczinzik
Updated
Mar 11, 2026 at 18:23 by Nupur Jain