Identifier
-
Mp00222:
Dyck paths
—peaks-to-valleys⟶
Dyck paths
St001185: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
Cc0005;cc-rep
[1,0]=>[1,0]=>0
[1,0,1,0]=>[1,1,0,0]=>0
[1,1,0,0]=>[1,0,1,0]=>1
[1,0,1,0,1,0]=>[1,1,1,0,0,0]=>0
[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>1
[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>0
[1,1,0,1,0,0]=>[1,0,1,0,1,0]=>1
[1,1,1,0,0,0]=>[1,1,0,1,0,0]=>2
[1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>0
[1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]=>0
[1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,0]=>2
[1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0]=>0
[1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0]=>0
[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0]=>2
[1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>0
[1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>1
[1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0]=>2
[1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0]=>3
[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]=>0
[1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>2
[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0]=>0
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]=>0
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>2
[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>0
[1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>2
[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>3
[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>0
[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>0
[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>2
[1,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>0
[1,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>0
[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>0
[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>3
[1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>0
[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>1
[1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0]=>0
[1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>1
[1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0]=>0
[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>1
[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>2
[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>3
[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>0
[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>1
[1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>2
[1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>3
[1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>4
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>0
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>2
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>0
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>0
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>0
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>2
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>3
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>0
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>0
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>2
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>0
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>0
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>0
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>2
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>3
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>0
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>0
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>2
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>0
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>2
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>3
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>0
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>2
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>3
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>4
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>0
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>0
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>1
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>2
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>0
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>0
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>2
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>0
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>1
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>2
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>3
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>0
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>0
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>2
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>0
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>0
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>2
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>0
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>2
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>0
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>1
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>0
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>2
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>0
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>2
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>0
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>1
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>2
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>3
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>4
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>0
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>1
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>0
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>1
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>2
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>0
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>1
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>0
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>1
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>2
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>0
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>1
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>2
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>3
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>0
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>1
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>0
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>1
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>2
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>0
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>1
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>2
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>3
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>0
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>1
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>2
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>3
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>4
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>0
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>1
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>0
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>1
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>2
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>0
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>1
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>2
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>3
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>0
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>1
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>2
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>3
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>4
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>0
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>1
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>2
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>3
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>4
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>5
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Description
The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra.
Map
peaks-to-valleys
Description
Return the path that has a valley wherever the original path has a peak of height at least one.
More precisely, the height of a valley in the image is the height of the corresponding peak minus $2$.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.
More precisely, the height of a valley in the image is the height of the corresponding peak minus $2$.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.
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