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Identifier

St000969: Dyck paths ⟶ ℤ

Values

[1,0] => 2

[1,0,1,0] => 3

[1,1,0,0] => 2

[1,0,1,0,1,0] => 4

[1,0,1,1,0,0] => 3

[1,1,0,0,1,0] => 2

[1,1,0,1,0,0] => 3

[1,1,1,0,0,0] => 2

[1,0,1,0,1,0,1,0] => 5

[1,0,1,0,1,1,0,0] => 4

[1,0,1,1,0,0,1,0] => 3

[1,0,1,1,0,1,0,0] => 4

[1,0,1,1,1,0,0,0] => 3

[1,1,0,0,1,0,1,0] => 3

[1,1,0,0,1,1,0,0] => 2

[1,1,0,1,0,0,1,0] => 4

[1,1,0,1,0,1,0,0] => 4

[1,1,0,1,1,0,0,0] => 3

[1,1,1,0,0,0,1,0] => 2

[1,1,1,0,0,1,0,0] => 2

[1,1,1,0,1,0,0,0] => 3

[1,1,1,1,0,0,0,0] => 2

[1,0,1,0,1,0,1,0,1,0] => 6

[1,0,1,0,1,0,1,1,0,0] => 5

[1,0,1,0,1,1,0,0,1,0] => 4

[1,0,1,0,1,1,0,1,0,0] => 5

[1,0,1,0,1,1,1,0,0,0] => 4

[1,0,1,1,0,0,1,0,1,0] => 3

[1,0,1,1,0,0,1,1,0,0] => 3

[1,0,1,1,0,1,0,0,1,0] => 5

[1,0,1,1,0,1,0,1,0,0] => 5

[1,0,1,1,0,1,1,0,0,0] => 4

[1,0,1,1,1,0,0,0,1,0] => 3

[1,0,1,1,1,0,0,1,0,0] => 3

[1,0,1,1,1,0,1,0,0,0] => 4

[1,0,1,1,1,1,0,0,0,0] => 3

[1,1,0,0,1,0,1,0,1,0] => 4

[1,1,0,0,1,0,1,1,0,0] => 3

[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] => 2

[1,1,0,1,0,0,1,0,1,0] => 5

[1,1,0,1,0,0,1,1,0,0] => 4

[1,1,0,1,0,1,0,0,1,0] => 5

[1,1,0,1,0,1,0,1,0,0] => 4

[1,1,0,1,0,1,1,0,0,0] => 4

[1,1,0,1,1,0,0,0,1,0] => 3

[1,1,0,1,1,0,0,1,0,0] => 4

[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] => 3

[1,1,1,0,0,0,1,1,0,0] => 2

[1,1,1,0,0,1,0,0,1,0] => 3

[1,1,1,0,0,1,0,1,0,0] => 3

[1,1,1,0,0,1,1,0,0,0] => 2

[1,1,1,0,1,0,0,0,1,0] => 4

[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] => 3

[1,1,1,1,0,0,0,0,1,0] => 2

[1,1,1,1,0,0,0,1,0,0] => 2

[1,1,1,1,0,0,1,0,0,0] => 2

[1,1,1,1,0,1,0,0,0,0] => 3

[1,1,1,1,1,0,0,0,0,0] => 2

[1,0,1,0,1,0,1,0,1,0,1,0] => 7

[1,0,1,0,1,0,1,0,1,1,0,0] => 6

[1,0,1,0,1,0,1,1,0,0,1,0] => 5

[1,0,1,0,1,0,1,1,0,1,0,0] => 6

[1,0,1,0,1,0,1,1,1,0,0,0] => 5

[1,0,1,0,1,1,0,0,1,0,1,0] => 4

[1,0,1,0,1,1,0,0,1,1,0,0] => 4

[1,0,1,0,1,1,0,1,0,0,1,0] => 6

[1,0,1,0,1,1,0,1,0,1,0,0] => 6

[1,0,1,0,1,1,0,1,1,0,0,0] => 5

[1,0,1,0,1,1,1,0,0,0,1,0] => 4

[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] => 5

[1,0,1,0,1,1,1,1,0,0,0,0] => 4

[1,0,1,1,0,0,1,0,1,0,1,0] => 4

[1,0,1,1,0,0,1,0,1,1,0,0] => 3

[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] => 3

[1,0,1,1,0,0,1,1,1,0,0,0] => 3

[1,0,1,1,0,1,0,0,1,0,1,0] => 6

[1,0,1,1,0,1,0,0,1,1,0,0] => 5

[1,0,1,1,0,1,0,1,0,0,1,0] => 6

[1,0,1,1,0,1,0,1,0,1,0,0] => 5

[1,0,1,1,0,1,0,1,1,0,0,0] => 5

[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] => 5

[1,0,1,1,0,1,1,0,1,0,0,0] => 5

[1,0,1,1,0,1,1,1,0,0,0,0] => 4

[1,0,1,1,1,0,0,0,1,0,1,0] => 3

[1,0,1,1,1,0,0,0,1,1,0,0] => 3

[1,0,1,1,1,0,0,1,0,0,1,0] => 3

[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] => 3

[1,0,1,1,1,0,1,0,0,0,1,0] => 5

[1,0,1,1,1,0,1,0,0,1,0,0] => 5

[1,0,1,1,1,0,1,0,1,0,0,0] => 5

[1,0,1,1,1,0,1,1,0,0,0,0] => 4

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Description

We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n-1}]$ by adding $c_0$ to $c_{n-1}$. Then we calculate the global dimension of that CNakayama algebra.

Code

DeclareOperation("lnakintocnak",[IsList]);

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

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

L:=LIST[1];
T:=ShallowCopy(L);
n:=Size(L);
T[n]:=T[1]+1;

return(T);

end);

z:=8;R:=BuildSequencesLNak(z);temp:=[];for i in R do Append(temp,[[i,gldim(lnakintocnak([i]))]]);od;temp;

Created

Sep 03, 2017 at 14:54 by Rene Marczinzik

Updated

Sep 03, 2017 at 14:54 by Rene Marczinzik