Identifier
- St001227: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[1,0]=>0
[1,0,1,0]=>1
[1,1,0,0]=>0
[1,0,1,0,1,0]=>2
[1,0,1,1,0,0]=>2
[1,1,0,0,1,0]=>1
[1,1,0,1,0,0]=>1
[1,1,1,0,0,0]=>0
[1,0,1,0,1,0,1,0]=>3
[1,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,0,1,0]=>3
[1,0,1,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,0]=>3
[1,1,0,0,1,0,1,0]=>2
[1,1,0,0,1,1,0,0]=>2
[1,1,0,1,0,0,1,0]=>2
[1,1,0,1,0,1,0,0]=>2
[1,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,1,0,0]=>1
[1,1,1,0,1,0,0,0]=>1
[1,1,1,1,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0]=>4
[1,0,1,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,0,1,0]=>4
[1,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,1,1,0,0,0]=>4
[1,0,1,1,0,0,1,0,1,0]=>4
[1,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,1,0,1,1,0,0,0]=>4
[1,0,1,1,1,0,0,0,1,0]=>4
[1,0,1,1,1,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,0,0,0]=>4
[1,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,1,0,0,1,0]=>3
[1,1,0,0,1,1,0,1,0,0]=>3
[1,1,0,0,1,1,1,0,0,0]=>3
[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]=>3
[1,1,0,1,0,1,0,1,0,0]=>3
[1,1,0,1,0,1,1,0,0,0]=>3
[1,1,0,1,1,0,0,0,1,0]=>3
[1,1,0,1,1,0,0,1,0,0]=>3
[1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,0,0,0,0]=>3
[1,1,1,0,0,0,1,0,1,0]=>2
[1,1,1,0,0,0,1,1,0,0]=>2
[1,1,1,0,0,1,0,0,1,0]=>2
[1,1,1,0,0,1,0,1,0,0]=>2
[1,1,1,0,0,1,1,0,0,0]=>2
[1,1,1,0,1,0,0,0,1,0]=>2
[1,1,1,0,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,1,0,0,0]=>2
[1,1,1,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,0,0]=>1
[1,1,1,1,0,0,1,0,0,0]=>1
[1,1,1,1,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0]=>5
[1,0,1,0,1,0,1,0,1,1,0,0]=>5
[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]=>5
[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]=>5
[1,0,1,0,1,1,0,0,1,1,0,0]=>5
[1,0,1,0,1,1,0,1,0,0,1,0]=>5
[1,0,1,0,1,1,0,1,0,1,0,0]=>5
[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]=>5
[1,0,1,0,1,1,1,0,0,1,0,0]=>5
[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]=>5
[1,0,1,1,0,0,1,0,1,0,1,0]=>5
[1,0,1,1,0,0,1,0,1,1,0,0]=>5
[1,0,1,1,0,0,1,1,0,0,1,0]=>5
[1,0,1,1,0,0,1,1,0,1,0,0]=>5
[1,0,1,1,0,0,1,1,1,0,0,0]=>5
[1,0,1,1,0,1,0,0,1,0,1,0]=>5
[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]=>5
[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]=>5
[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]=>5
[1,0,1,1,1,0,0,0,1,0,1,0]=>5
[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[1,0,1,1,1,0,0,1,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,0,1,0,0]=>5
[1,0,1,1,1,0,0,1,1,0,0,0]=>5
[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]=>5
[1,0,1,1,1,1,0,0,0,0,1,0]=>5
[1,0,1,1,1,1,0,0,0,1,0,0]=>5
[1,0,1,1,1,1,0,0,1,0,0,0]=>5
[1,0,1,1,1,1,0,1,0,0,0,0]=>5
[1,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,1,0,0,1,0,1,0,1,0,1,0]=>4
[1,1,0,0,1,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,0,1,1,0,0,1,0]=>4
[1,1,0,0,1,0,1,1,0,1,0,0]=>4
[1,1,0,0,1,0,1,1,1,0,0,0]=>4
[1,1,0,0,1,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,0,0,1,1,0,0]=>4
[1,1,0,0,1,1,0,1,0,0,1,0]=>4
[1,1,0,0,1,1,0,1,0,1,0,0]=>4
[1,1,0,0,1,1,0,1,1,0,0,0]=>4
[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[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]=>4
[1,1,0,0,1,1,1,1,0,0,0,0]=>4
[1,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,0,1,0,1,1,0,0]=>4
[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]=>4
[1,1,0,1,0,0,1,1,1,0,0,0]=>4
[1,1,0,1,0,1,0,0,1,0,1,0]=>4
[1,1,0,1,0,1,0,0,1,1,0,0]=>4
[1,1,0,1,0,1,0,1,0,0,1,0]=>4
[1,1,0,1,0,1,0,1,0,1,0,0]=>4
[1,1,0,1,0,1,0,1,1,0,0,0]=>4
[1,1,0,1,0,1,1,0,0,0,1,0]=>4
[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]=>4
[1,1,0,1,0,1,1,1,0,0,0,0]=>4
[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]=>4
[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]=>4
[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]=>4
[1,1,0,1,1,0,1,0,1,0,0,0]=>4
[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]=>4
[1,1,0,1,1,1,0,0,1,0,0,0]=>4
[1,1,0,1,1,1,0,1,0,0,0,0]=>4
[1,1,0,1,1,1,1,0,0,0,0,0]=>4
[1,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,1,0,0,0,1,0,1,1,0,0]=>3
[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[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]=>3
[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]=>3
[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]=>3
[1,1,1,0,0,1,1,0,0,0,1,0]=>3
[1,1,1,0,0,1,1,0,0,1,0,0]=>3
[1,1,1,0,0,1,1,0,1,0,0,0]=>3
[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]=>3
[1,1,1,0,1,0,0,0,1,1,0,0]=>3
[1,1,1,0,1,0,0,1,0,0,1,0]=>3
[1,1,1,0,1,0,0,1,0,1,0,0]=>3
[1,1,1,0,1,0,0,1,1,0,0,0]=>3
[1,1,1,0,1,0,1,0,0,0,1,0]=>3
[1,1,1,0,1,0,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,1,0,1,1,0,0,0,0]=>3
[1,1,1,0,1,1,0,0,0,0,1,0]=>3
[1,1,1,0,1,1,0,0,0,1,0,0]=>3
[1,1,1,0,1,1,0,0,1,0,0,0]=>3
[1,1,1,0,1,1,0,1,0,0,0,0]=>3
[1,1,1,0,1,1,1,0,0,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,0,1,0]=>2
[1,1,1,1,0,0,0,0,1,1,0,0]=>2
[1,1,1,1,0,0,0,1,0,0,1,0]=>2
[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]=>2
[1,1,1,1,0,0,1,0,0,0,1,0]=>2
[1,1,1,1,0,0,1,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,1,0,0,0,0,1,0]=>2
[1,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,1,0,0,1,0,0,0]=>2
[1,1,1,1,0,1,0,1,0,0,0,0]=>2
[1,1,1,1,0,1,1,0,0,0,0,0]=>2
[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]=>1
[1,1,1,1,1,0,0,0,1,0,0,0]=>1
[1,1,1,1,1,0,0,1,0,0,0,0]=>1
[1,1,1,1,1,0,1,0,0,0,0,0]=>1
[1,1,1,1,1,1,0,0,0,0,0,0]=>0
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Description
The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra.
Code
DeclareOperation("extsocrad", [IsList]);
InstallMethod(extsocrad, "for a representation of a quiver", [IsList],0,function(L)
local A,RegA,J,simA,U,projA,UU,g;
A:=L[1];
RegA:=DirectSumOfQPAModules(IndecProjectiveModules(A));
U:=SocleOfModule(RegA);
J:=RadicalOfModule(RegA);
return(Size(ExtOverAlgebra(NthSyzygy(U,0),J)[2]));
end
);
Created
Jul 18, 2018 at 20:01 by Rene Marczinzik
Updated
Jul 18, 2018 at 20:01 by Rene Marczinzik
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