Identifier
-
Mp00028:
Dyck paths
—reverse⟶
Dyck paths
St001291: Dyck paths ⟶ ℤ
Values
[1,0] => [1,0] => 1
[1,0,1,0] => [1,0,1,0] => 2
[1,1,0,0] => [1,1,0,0] => 1
[1,0,1,0,1,0] => [1,0,1,0,1,0] => 3
[1,0,1,1,0,0] => [1,1,0,0,1,0] => 3
[1,1,0,0,1,0] => [1,0,1,1,0,0] => 2
[1,1,0,1,0,0] => [1,1,0,1,0,0] => 2
[1,1,1,0,0,0] => [1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0] => 3
[1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0] => 2
[1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0] => 5
[1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0] => 5
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0] => 5
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 4
[1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0] => 3
[1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 3
[1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
[1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,0,0,0,0] => 2
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => 2
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 2
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [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] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,0] => [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] => [1,1,0,0,1,1,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
[1,0,1,1,0,0,1,1,0,0,1,0] => [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] => [1,1,0,1,0,0,1,1,0,0,1,0] => 6
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,0,1,1,0,0,1,0] => 6
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,0,0,1,0] => [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] => [1,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 6
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,1,0,0,1,0] => 6
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,1,0,0,0,1,0] => [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] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,0,1,0,0,0,1,0] => 6
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Description
The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path.
Let $A$ be the Nakayama algebra associated to a Dyck path as given in DyckPaths/NakayamaAlgebras. This statistics is the number of indecomposable summands of $D(A) \otimes D(A)$, where $D(A)$ is the natural dual of $A$.
Let $A$ be the Nakayama algebra associated to a Dyck path as given in DyckPaths/NakayamaAlgebras. This statistics is the number of indecomposable summands of $D(A) \otimes D(A)$, where $D(A)$ is the natural dual of $A$.
Map
reverse
Description
The reversal of a Dyck path.
This is the Dyck path obtained by reading the path backwards.
This is the Dyck path obtained by reading the path backwards.
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