Identifier
Values
[1,0,1,0] => [1,1,0,1,0,0] => [1,1,0,0,1,0] => 0
[1,1,0,0] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => 0
[1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0] => 0
[1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [1,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => [1,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => 0
[1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => 0
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Description
The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$.
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
swap returns and last descent
Description
Return a Dyck path with number of returns and length of the last descent interchanged.
This is the specialisation of the map $\Phi$ in [1] to Dyck paths. It is characterised by the fact that the number of up steps before a down step that is neither a return nor part of the last descent is preserved.