Identifier
- St001278: 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]=>1
[1,1,0,0,1,0]=>1
[1,1,0,1,0,0]=>2
[1,1,1,0,0,0]=>0
[1,0,1,0,1,0,1,0]=>3
[1,0,1,0,1,1,0,0]=>2
[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]=>2
[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]=>4
[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]=>2
[1,1,1,0,1,0,0,0]=>3
[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]=>3
[1,0,1,0,1,1,0,0,1,0]=>3
[1,0,1,0,1,1,0,1,0,0]=>4
[1,0,1,0,1,1,1,0,0,0]=>2
[1,0,1,1,0,0,1,0,1,0]=>3
[1,0,1,1,0,0,1,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,0]=>4
[1,0,1,1,0,1,0,1,0,0]=>5
[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]=>3
[1,0,1,1,1,0,1,0,0,0]=>4
[1,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0]=>3
[1,1,0,0,1,0,1,1,0,0]=>2
[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]=>4
[1,1,0,1,0,0,1,1,0,0]=>3
[1,1,0,1,0,1,0,0,1,0]=>5
[1,1,0,1,0,1,0,1,0,0]=>6
[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]=>5
[1,1,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,0,0,1,0,1,0]=>2
[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]=>4
[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]=>5
[1,1,1,0,1,0,1,0,0,0]=>6
[1,1,1,0,1,1,0,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,0,0,0]=>3
[1,1,1,1,0,1,0,0,0,0]=>4
[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]=>4
[1,0,1,0,1,0,1,1,0,0,1,0]=>4
[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]=>3
[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]=>3
[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]=>6
[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]=>3
[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]=>2
[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]=>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]=>5
[1,0,1,1,0,1,0,0,1,1,0,0]=>4
[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]=>7
[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]=>6
[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]=>3
[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]=>5
[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]=>6
[1,0,1,1,1,0,1,0,1,0,0,0]=>7
[1,0,1,1,1,0,1,1,0,0,0,0]=>4
[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]=>3
[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]=>5
[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]=>4
[1,1,0,0,1,0,1,0,1,1,0,0]=>3
[1,1,0,0,1,0,1,1,0,0,1,0]=>3
[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]=>2
[1,1,0,0,1,1,0,0,1,0,1,0]=>3
[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]=>4
[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]=>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]=>3
[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]=>1
[1,1,0,1,0,0,1,0,1,0,1,0]=>5
[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]=>5
[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]=>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]=>7
[1,1,0,1,0,1,0,1,0,1,0,0]=>8
[1,1,0,1,0,1,0,1,1,0,0,0]=>6
[1,1,0,1,0,1,1,0,0,0,1,0]=>5
[1,1,0,1,0,1,1,0,0,1,0,0]=>6
[1,1,0,1,0,1,1,0,1,0,0,0]=>7
[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]=>3
[1,1,0,1,1,0,0,1,0,0,1,0]=>5
[1,1,0,1,1,0,0,1,0,1,0,0]=>6
[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]=>7
[1,1,0,1,1,0,1,0,1,0,0,0]=>8
[1,1,0,1,1,0,1,1,0,0,0,0]=>5
[1,1,0,1,1,1,0,0,0,0,1,0]=>3
[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]=>5
[1,1,0,1,1,1,0,1,0,0,0,0]=>6
[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]=>3
[1,1,1,0,0,0,1,0,1,1,0,0]=>2
[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]=>4
[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]=>5
[1,1,1,0,0,1,0,1,0,1,0,0]=>6
[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]=>3
[1,1,1,0,0,1,1,0,0,1,0,0]=>4
[1,1,1,0,0,1,1,0,1,0,0,0]=>5
[1,1,1,0,0,1,1,1,0,0,0,0]=>2
[1,1,1,0,1,0,0,0,1,0,1,0]=>5
[1,1,1,0,1,0,0,0,1,1,0,0]=>4
[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]=>7
[1,1,1,0,1,0,0,1,1,0,0,0]=>5
[1,1,1,0,1,0,1,0,0,0,1,0]=>7
[1,1,1,0,1,0,1,0,0,1,0,0]=>8
[1,1,1,0,1,0,1,0,1,0,0,0]=>9
[1,1,1,0,1,0,1,1,0,0,0,0]=>6
[1,1,1,0,1,1,0,0,0,0,1,0]=>4
[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]=>6
[1,1,1,0,1,1,0,1,0,0,0,0]=>7
[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]=>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]=>4
[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]=>4
[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]=>6
[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]=>5
[1,1,1,1,0,1,0,0,0,1,0,0]=>6
[1,1,1,1,0,1,0,0,1,0,0,0]=>7
[1,1,1,1,0,1,0,1,0,0,0,0]=>8
[1,1,1,1,0,1,1,0,0,0,0,0]=>4
[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]=>2
[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[1,1,1,1,1,0,0,1,0,0,0,0]=>4
[1,1,1,1,1,0,1,0,0,0,0,0]=>5
[1,1,1,1,1,1,0,0,0,0,0,0]=>0
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Description
The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra.
The statistic is also equal to the number of non-projective torsionless indecomposable modules in the corresponding Nakayama algebra.
See theorem 5.8. in the reference for a motivation.
The statistic is also equal to the number of non-projective torsionless indecomposable modules in the corresponding Nakayama algebra.
See theorem 5.8. in the reference for a motivation.
References
[1] Iyama, O., Solberg, Øyvind Auslander-Gorenstein algebras and precluster tilting. zbMATH:06833443
Code
DeclareOperation("highertaufixall",[IsList]);
InstallMethod(highertaufixall, "for a representation of a quiver", [IsList],0,function(LIST)
local A,RegA,CoRegA,t,simA,U,L;
A:=LIST[1];
t:=LIST[2];
L:=ARQuiverNak([A]);
U:=Filtered(L,x-> IsomorphicModules(highertauinverse([DTr(NthSyzygy(x,t)),t]),x)=true);
return(Size(U));
end);
Created
Oct 20, 2018 at 20:09 by Rene Marczinzik
Updated
Nov 26, 2018 at 21:48 by Rene Marczinzik
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