Identifier
- St001291: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[1,0]=>1
[1,0,1,0]=>2
[1,1,0,0]=>1
[1,0,1,0,1,0]=>3
[1,0,1,1,0,0]=>2
[1,1,0,0,1,0]=>3
[1,1,0,1,0,0]=>2
[1,1,1,0,0,0]=>1
[1,0,1,0,1,0,1,0]=>4
[1,0,1,0,1,1,0,0]=>3
[1,0,1,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,0]=>3
[1,0,1,1,1,0,0,0]=>2
[1,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,0,1,0]=>4
[1,1,0,1,0,1,0,0]=>3
[1,1,0,1,1,0,0,0]=>2
[1,1,1,0,0,0,1,0]=>4
[1,1,1,0,0,1,0,0]=>3
[1,1,1,0,1,0,0,0]=>2
[1,1,1,1,0,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,0]=>5
[1,0,1,0,1,0,1,1,0,0]=>4
[1,0,1,0,1,1,0,0,1,0]=>5
[1,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,1,1,0,0,0]=>3
[1,0,1,1,0,0,1,0,1,0]=>5
[1,0,1,1,0,0,1,1,0,0]=>4
[1,0,1,1,0,1,0,0,1,0]=>5
[1,0,1,1,0,1,0,1,0,0]=>4
[1,0,1,1,0,1,1,0,0,0]=>3
[1,0,1,1,1,0,0,0,1,0]=>5
[1,0,1,1,1,0,0,1,0,0]=>4
[1,0,1,1,1,0,1,0,0,0]=>3
[1,0,1,1,1,1,0,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,0]=>5
[1,1,0,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,1,0,0,1,0]=>5
[1,1,0,0,1,1,0,1,0,0]=>4
[1,1,0,0,1,1,1,0,0,0]=>3
[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]=>3
[1,1,0,1,1,0,0,0,1,0]=>5
[1,1,0,1,1,0,0,1,0,0]=>4
[1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0]=>5
[1,1,1,0,0,0,1,1,0,0]=>4
[1,1,1,0,0,1,0,0,1,0]=>5
[1,1,1,0,0,1,0,1,0,0]=>4
[1,1,1,0,0,1,1,0,0,0]=>3
[1,1,1,0,1,0,0,0,1,0]=>5
[1,1,1,0,1,0,0,1,0,0]=>4
[1,1,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,1,1,0,0,0,0]=>2
[1,1,1,1,0,0,0,0,1,0]=>5
[1,1,1,1,0,0,0,1,0,0]=>4
[1,1,1,1,0,0,1,0,0,0]=>3
[1,1,1,1,0,1,0,0,0,0]=>2
[1,1,1,1,1,0,0,0,0,0]=>1
[1,0,1,0,1,0,1,0,1,0,1,0]=>6
[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]=>6
[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]=>4
[1,0,1,0,1,1,0,0,1,0,1,0]=>6
[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]=>6
[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]=>4
[1,0,1,0,1,1,1,0,0,0,1,0]=>6
[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]=>4
[1,0,1,0,1,1,1,1,0,0,0,0]=>3
[1,0,1,1,0,0,1,0,1,0,1,0]=>6
[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]=>6
[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]=>4
[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]=>4
[1,0,1,1,0,1,1,0,0,0,1,0]=>6
[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]=>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]=>6
[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]=>6
[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]=>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]=>5
[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]=>3
[1,0,1,1,1,1,0,0,0,0,1,0]=>6
[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]=>4
[1,0,1,1,1,1,0,1,0,0,0,0]=>3
[1,0,1,1,1,1,1,0,0,0,0,0]=>2
[1,1,0,0,1,0,1,0,1,0,1,0]=>6
[1,1,0,0,1,0,1,0,1,1,0,0]=>5
[1,1,0,0,1,0,1,1,0,0,1,0]=>6
[1,1,0,0,1,0,1,1,0,1,0,0]=>5
[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]=>6
[1,1,0,0,1,1,0,0,1,1,0,0]=>5
[1,1,0,0,1,1,0,1,0,0,1,0]=>6
[1,1,0,0,1,1,0,1,0,1,0,0]=>5
[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]=>6
[1,1,0,0,1,1,1,0,0,1,0,0]=>5
[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]=>3
[1,1,0,1,0,0,1,0,1,0,1,0]=>6
[1,1,0,1,0,0,1,0,1,1,0,0]=>5
[1,1,0,1,0,0,1,1,0,0,1,0]=>6
[1,1,0,1,0,0,1,1,0,1,0,0]=>5
[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]=>6
[1,1,0,1,0,1,0,0,1,1,0,0]=>5
[1,1,0,1,0,1,0,1,0,0,1,0]=>6
[1,1,0,1,0,1,0,1,0,1,0,0]=>5
[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]=>6
[1,1,0,1,0,1,1,0,0,1,0,0]=>5
[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]=>3
[1,1,0,1,1,0,0,0,1,0,1,0]=>6
[1,1,0,1,1,0,0,0,1,1,0,0]=>5
[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]=>5
[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]=>6
[1,1,0,1,1,0,1,0,0,1,0,0]=>5
[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]=>3
[1,1,0,1,1,1,0,0,0,0,1,0]=>6
[1,1,0,1,1,1,0,0,0,1,0,0]=>5
[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]=>3
[1,1,0,1,1,1,1,0,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0,1,0]=>6
[1,1,1,0,0,0,1,0,1,1,0,0]=>5
[1,1,1,0,0,0,1,1,0,0,1,0]=>6
[1,1,1,0,0,0,1,1,0,1,0,0]=>5
[1,1,1,0,0,0,1,1,1,0,0,0]=>4
[1,1,1,0,0,1,0,0,1,0,1,0]=>6
[1,1,1,0,0,1,0,0,1,1,0,0]=>5
[1,1,1,0,0,1,0,1,0,0,1,0]=>6
[1,1,1,0,0,1,0,1,0,1,0,0]=>5
[1,1,1,0,0,1,0,1,1,0,0,0]=>4
[1,1,1,0,0,1,1,0,0,0,1,0]=>6
[1,1,1,0,0,1,1,0,0,1,0,0]=>5
[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]=>5
[1,1,1,0,1,0,0,1,0,0,1,0]=>6
[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]=>6
[1,1,1,0,1,0,1,0,0,1,0,0]=>5
[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]=>3
[1,1,1,0,1,1,0,0,0,0,1,0]=>6
[1,1,1,0,1,1,0,0,0,1,0,0]=>5
[1,1,1,0,1,1,0,0,1,0,0,0]=>4
[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]=>2
[1,1,1,1,0,0,0,0,1,0,1,0]=>6
[1,1,1,1,0,0,0,0,1,1,0,0]=>5
[1,1,1,1,0,0,0,1,0,0,1,0]=>6
[1,1,1,1,0,0,0,1,0,1,0,0]=>5
[1,1,1,1,0,0,0,1,1,0,0,0]=>4
[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]=>5
[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]=>3
[1,1,1,1,0,1,0,0,0,0,1,0]=>6
[1,1,1,1,0,1,0,0,0,1,0,0]=>5
[1,1,1,1,0,1,0,0,1,0,0,0]=>4
[1,1,1,1,0,1,0,1,0,0,0,0]=>3
[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]=>6
[1,1,1,1,1,0,0,0,0,1,0,0]=>5
[1,1,1,1,1,0,0,0,1,0,0,0]=>4
[1,1,1,1,1,0,0,1,0,0,0,0]=>3
[1,1,1,1,1,0,1,0,0,0,0,0]=>2
[1,1,1,1,1,1,0,0,0,0,0,0]=>1
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Description
The number of indecomposable summands of $D(A)\otimes D(A)$ of the linear Nakayama algebra $A$ corresponding to a Dyck path.
Here, $D(A)$ is the natural dual of $A$.
The correspondence between linear Nakayama algebras and Dyck paths is explained on the Nakayama algebras page.
Here, $D(A)$ is the natural dual of $A$.
The correspondence between linear Nakayama algebras and Dyck paths is explained on the Nakayama algebras page.
Code
gap('LoadPackage("QPA");')
import tempfile as _tf, os as _os
_gap_code = r"""
DeclareOperation("iterateddatest2", [IsList]);
InstallMethod(iterateddatest2, "for a representation of a quiver", [IsList],0,function(L)
local A, CoRegA, UU, W;
A := L[1];
CoRegA := DirectSumOfQPAModules(IndecInjectiveModules(A));
W := NakayamaFunctorOfModule(CoRegA);
UU := DecomposeModule(W);
return(Size(UU));
end
);
"""
with _tf.NamedTemporaryFile(mode="w", suffix=".g", delete=False, dir="/tmp") as _f:
_f.write('LoadPackage("QPA");;\n')
_f.write(_gap_code)
_tmp = _f.name
gap.eval('Read("' + _tmp + '");')
_os.unlink(_tmp)
def kupisch(D):
DR = D.reverse()
H = DR.heights()
return [1 + H[i] for i, s in enumerate(DR) if s == 0] + [1]
def statistic(D):
K = kupisch(D)
A = gap.NakayamaAlgebra(gap.GF(3), K)
return ZZ(gap.iterateddatest2([A]))
Created
Nov 16, 2018 at 09:01 by Rene Marczinzik
Updated
Mar 13, 2026 at 15:06 by Nupur Jain
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