Identifier
-
Mp00199:
Dyck paths
—prime Dyck path⟶
Dyck paths
St001230: Dyck paths ⟶ ℤ
Values
[1,0] => [1,1,0,0] => 0
[1,0,1,0] => [1,1,0,1,0,0] => 0
[1,1,0,0] => [1,1,1,0,0,0] => 0
[1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 0
[1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 0
[1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 0
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[] => [1,0] => 0
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Description
The number of simple modules with injective dimension equal to the dominant dimension equal to one and the dual property.
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
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