Identifier
-
Mp00201:
Dyck paths
—Ringel⟶
Permutations
St000058: Permutations ⟶ ℤ
Values
[1,0] => [2,1] => 2
[1,0,1,0] => [3,1,2] => 3
[1,1,0,0] => [2,3,1] => 3
[1,0,1,0,1,0] => [4,1,2,3] => 4
[1,0,1,1,0,0] => [3,1,4,2] => 4
[1,1,0,0,1,0] => [2,4,1,3] => 4
[1,1,0,1,0,0] => [4,3,1,2] => 4
[1,1,1,0,0,0] => [2,3,4,1] => 4
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 5
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => 5
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => 5
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => 5
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => 5
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => 5
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => 5
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => 5
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 6
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => 5
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => 5
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 5
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 5
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 5
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => 6
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => 6
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => 6
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => 6
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => 6
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => 6
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => 6
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => 6
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => 4
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => 6
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => 6
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => 6
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => 6
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => 6
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => 6
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => 6
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => 6
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => 6
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => 6
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => 6
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => 6
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => 4
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => 3
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => 4
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => 6
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => 6
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => 3
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => 6
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => 6
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => 6
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => 6
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => 4
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => 6
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => 6
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => 3
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => 4
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => 6
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => 6
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => 6
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => 6
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => 6
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 6
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => 7
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => 7
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => 7
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => 7
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => 7
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => 7
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => 7
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => 7
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => 10
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => 7
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => 7
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => 7
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => 7
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => 7
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => 7
[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => 7
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => 7
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => 7
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => 7
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => 7
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => 7
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => 10
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => 12
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => 10
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => 7
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => 7
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => 12
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => 7
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => 7
[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => 7
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => 7
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => 10
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => 7
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => 7
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => 12
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => 10
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => 7
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Description
The order of a permutation.
$\operatorname{ord}(\pi)$ is given by the minimial $k$ for which $\pi^k$ is the identity permutation.
$\operatorname{ord}(\pi)$ is given by the minimial $k$ for which $\pi^k$ is the identity permutation.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
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