Identifier
-
Mp00103:
Dyck paths
—peeling map⟶
Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00028: Dyck paths —reverse⟶ Dyck paths
St001201: Dyck paths ⟶ ℤ
Values
[1,0] => [1,0] => [1,0] => [1,0] => 1
[1,0,1,0] => [1,0,1,0] => [1,0,1,0] => [1,0,1,0] => 2
[1,1,0,0] => [1,0,1,0] => [1,0,1,0] => [1,0,1,0] => 2
[1,0,1,0,1,0] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 3
[1,0,1,1,0,0] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 3
[1,1,0,0,1,0] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 3
[1,1,0,1,0,0] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 3
[1,1,1,0,0,0] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => [1,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [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] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 4
[1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [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] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 5
[1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => [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
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => 4
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Description
The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path.
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.
Map
bounce path
Description
Sends a Dyck path $D$ of length $2n$ to its bounce path.
This path is formed by starting at the endpoint $(n,n)$ of $D$ and travelling west until encountering the first vertical step of $D$, then south until hitting the diagonal, then west again to hit $D$, etc. until the point $(0,0)$ is reached.
This map is the first part of the zeta map Mp00030zeta map.
This path is formed by starting at the endpoint $(n,n)$ of $D$ and travelling west until encountering the first vertical step of $D$, then south until hitting the diagonal, then west again to hit $D$, etc. until the point $(0,0)$ is reached.
This map is the first part of the zeta map Mp00030zeta map.
Map
peeling map
Description
Send a Dyck path to its peeled Dyck path.
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