Identifier
Identifier
St000120 : Dyck paths ⟶ ℤ
Values
[1,0]
generating graphics...
=> 0
[1,0,1,0]
generating graphics...
=> 1
[1,1,0,0]
generating graphics...
=> 0
[1,0,1,0,1,0]
generating graphics...
=> 1
[1,0,1,1,0,0]
generating graphics...
=> 1
[1,1,0,0,1,0]
generating graphics...
=> 2
[1,1,0,1,0,0]
generating graphics...
=> 1
[1,1,1,0,0,0]
generating graphics...
=> 0
[1,0,1,0,1,0,1,0]
generating graphics...
=> 2
[1,0,1,0,1,1,0,0]
generating graphics...
=> 2
[1,0,1,1,0,0,1,0]
generating graphics...
=> 1
[1,0,1,1,0,1,0,0]
generating graphics...
=> 1
[1,0,1,1,1,0,0,0]
generating graphics...
=> 1
[1,1,0,0,1,0,1,0]
generating graphics...
=> 2
[1,1,0,0,1,1,0,0]
generating graphics...
=> 2
[1,1,0,1,0,0,1,0]
generating graphics...
=> 2
[1,1,0,1,0,1,0,0]
generating graphics...
=> 1
[1,1,0,1,1,0,0,0]
generating graphics...
=> 1
[1,1,1,0,0,0,1,0]
generating graphics...
=> 3
[1,1,1,0,0,1,0,0]
generating graphics...
=> 2
[1,1,1,0,1,0,0,0]
generating graphics...
=> 1
[1,1,1,1,0,0,0,0]
generating graphics...
=> 0
[1,0,1,0,1,0,1,0,1,0]
generating graphics...
=> 2
[1,0,1,0,1,0,1,1,0,0]
generating graphics...
=> 2
[1,0,1,0,1,1,0,0,1,0]
generating graphics...
=> 2
[1,0,1,0,1,1,0,1,0,0]
generating graphics...
=> 2
[1,0,1,0,1,1,1,0,0,0]
generating graphics...
=> 2
[1,0,1,1,0,0,1,0,1,0]
generating graphics...
=> 3
[1,0,1,1,0,0,1,1,0,0]
generating graphics...
=> 3
[1,0,1,1,0,1,0,0,1,0]
generating graphics...
=> 2
[1,0,1,1,0,1,0,1,0,0]
generating graphics...
=> 2
[1,0,1,1,0,1,1,0,0,0]
generating graphics...
=> 2
[1,0,1,1,1,0,0,0,1,0]
generating graphics...
=> 1
[1,0,1,1,1,0,0,1,0,0]
generating graphics...
=> 1
[1,0,1,1,1,0,1,0,0,0]
generating graphics...
=> 1
[1,0,1,1,1,1,0,0,0,0]
generating graphics...
=> 1
[1,1,0,0,1,0,1,0,1,0]
generating graphics...
=> 2
[1,1,0,0,1,0,1,1,0,0]
generating graphics...
=> 2
[1,1,0,0,1,1,0,0,1,0]
generating graphics...
=> 2
[1,1,0,0,1,1,0,1,0,0]
generating graphics...
=> 2
[1,1,0,0,1,1,1,0,0,0]
generating graphics...
=> 2
[1,1,0,1,0,0,1,0,1,0]
generating graphics...
=> 3
[1,1,0,1,0,0,1,1,0,0]
generating graphics...
=> 3
[1,1,0,1,0,1,0,0,1,0]
generating graphics...
=> 3
[1,1,0,1,0,1,0,1,0,0]
generating graphics...
=> 2
[1,1,0,1,0,1,1,0,0,0]
generating graphics...
=> 2
[1,1,0,1,1,0,0,0,1,0]
generating graphics...
=> 2
[1,1,0,1,1,0,0,1,0,0]
generating graphics...
=> 1
[1,1,0,1,1,0,1,0,0,0]
generating graphics...
=> 1
[1,1,0,1,1,1,0,0,0,0]
generating graphics...
=> 1
[1,1,1,0,0,0,1,0,1,0]
generating graphics...
=> 3
[1,1,1,0,0,0,1,1,0,0]
generating graphics...
=> 3
[1,1,1,0,0,1,0,0,1,0]
generating graphics...
=> 3
[1,1,1,0,0,1,0,1,0,0]
generating graphics...
=> 2
[1,1,1,0,0,1,1,0,0,0]
generating graphics...
=> 2
[1,1,1,0,1,0,0,0,1,0]
generating graphics...
=> 3
[1,1,1,0,1,0,0,1,0,0]
generating graphics...
=> 2
[1,1,1,0,1,0,1,0,0,0]
generating graphics...
=> 1
[1,1,1,0,1,1,0,0,0,0]
generating graphics...
=> 1
[1,1,1,1,0,0,0,0,1,0]
generating graphics...
=> 4
[1,1,1,1,0,0,0,1,0,0]
generating graphics...
=> 3
[1,1,1,1,0,0,1,0,0,0]
generating graphics...
=> 2
[1,1,1,1,0,1,0,0,0,0]
generating graphics...
=> 1
[1,1,1,1,1,0,0,0,0,0]
generating graphics...
=> 0
[1,0,1,0,1,0,1,0,1,0,1,0]
generating graphics...
=> 3
[1,0,1,0,1,0,1,0,1,1,0,0]
generating graphics...
=> 3
[1,0,1,0,1,0,1,1,0,0,1,0]
generating graphics...
=> 3
[1,0,1,0,1,0,1,1,0,1,0,0]
generating graphics...
=> 3
[1,0,1,0,1,0,1,1,1,0,0,0]
generating graphics...
=> 3
[1,0,1,0,1,1,0,0,1,0,1,0]
generating graphics...
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
generating graphics...
=> 2
[1,0,1,0,1,1,0,1,0,0,1,0]
generating graphics...
=> 2
[1,0,1,0,1,1,0,1,0,1,0,0]
generating graphics...
=> 2
[1,0,1,0,1,1,0,1,1,0,0,0]
generating graphics...
=> 2
[1,0,1,0,1,1,1,0,0,0,1,0]
generating graphics...
=> 2
[1,0,1,0,1,1,1,0,0,1,0,0]
generating graphics...
=> 2
[1,0,1,0,1,1,1,0,1,0,0,0]
generating graphics...
=> 2
[1,0,1,0,1,1,1,1,0,0,0,0]
generating graphics...
=> 2
[1,0,1,1,0,0,1,0,1,0,1,0]
generating graphics...
=> 3
[1,0,1,1,0,0,1,0,1,1,0,0]
generating graphics...
=> 3
[1,0,1,1,0,0,1,1,0,0,1,0]
generating graphics...
=> 3
[1,0,1,1,0,0,1,1,0,1,0,0]
generating graphics...
=> 3
[1,0,1,1,0,0,1,1,1,0,0,0]
generating graphics...
=> 3
[1,0,1,1,0,1,0,0,1,0,1,0]
generating graphics...
=> 3
[1,0,1,1,0,1,0,0,1,1,0,0]
generating graphics...
=> 3
[1,0,1,1,0,1,0,1,0,0,1,0]
generating graphics...
=> 2
[1,0,1,1,0,1,0,1,0,1,0,0]
generating graphics...
=> 2
[1,0,1,1,0,1,0,1,1,0,0,0]
generating graphics...
=> 2
[1,0,1,1,0,1,1,0,0,0,1,0]
generating graphics...
=> 2
[1,0,1,1,0,1,1,0,0,1,0,0]
generating graphics...
=> 2
[1,0,1,1,0,1,1,0,1,0,0,0]
generating graphics...
=> 2
[1,0,1,1,0,1,1,1,0,0,0,0]
generating graphics...
=> 2
[1,0,1,1,1,0,0,0,1,0,1,0]
generating graphics...
=> 4
[1,0,1,1,1,0,0,0,1,1,0,0]
generating graphics...
=> 4
[1,0,1,1,1,0,0,1,0,0,1,0]
generating graphics...
=> 3
[1,0,1,1,1,0,0,1,0,1,0,0]
generating graphics...
=> 3
[1,0,1,1,1,0,0,1,1,0,0,0]
generating graphics...
=> 3
[1,0,1,1,1,0,1,0,0,0,1,0]
generating graphics...
=> 2
[1,0,1,1,1,0,1,0,0,1,0,0]
generating graphics...
=> 2
[1,0,1,1,1,0,1,0,1,0,0,0]
generating graphics...
=> 2
[1,0,1,1,1,0,1,1,0,0,0,0]
generating graphics...
=> 2
[1,0,1,1,1,1,0,0,0,0,1,0]
generating graphics...
=> 1
[1,0,1,1,1,1,0,0,0,1,0,0]
generating graphics...
=> 1
[1,0,1,1,1,1,0,0,1,0,0,0]
generating graphics...
=> 1
[1,0,1,1,1,1,0,1,0,0,0,0]
generating graphics...
=> 1
[1,0,1,1,1,1,1,0,0,0,0,0]
generating graphics...
=> 1
[1,1,0,0,1,0,1,0,1,0,1,0]
generating graphics...
=> 3
[1,1,0,0,1,0,1,0,1,1,0,0]
generating graphics...
=> 3
[1,1,0,0,1,0,1,1,0,0,1,0]
generating graphics...
=> 3
[1,1,0,0,1,0,1,1,0,1,0,0]
generating graphics...
=> 3
[1,1,0,0,1,0,1,1,1,0,0,0]
generating graphics...
=> 3
[1,1,0,0,1,1,0,0,1,0,1,0]
generating graphics...
=> 2
[1,1,0,0,1,1,0,0,1,1,0,0]
generating graphics...
=> 2
[1,1,0,0,1,1,0,1,0,0,1,0]
generating graphics...
=> 2
[1,1,0,0,1,1,0,1,0,1,0,0]
generating graphics...
=> 2
[1,1,0,0,1,1,0,1,1,0,0,0]
generating graphics...
=> 2
[1,1,0,0,1,1,1,0,0,0,1,0]
generating graphics...
=> 2
[1,1,0,0,1,1,1,0,0,1,0,0]
generating graphics...
=> 2
[1,1,0,0,1,1,1,0,1,0,0,0]
generating graphics...
=> 2
[1,1,0,0,1,1,1,1,0,0,0,0]
generating graphics...
=> 2
[1,1,0,1,0,0,1,0,1,0,1,0]
generating graphics...
=> 3
[1,1,0,1,0,0,1,0,1,1,0,0]
generating graphics...
=> 3
[1,1,0,1,0,0,1,1,0,0,1,0]
generating graphics...
=> 3
[1,1,0,1,0,0,1,1,0,1,0,0]
generating graphics...
=> 3
[1,1,0,1,0,0,1,1,1,0,0,0]
generating graphics...
=> 3
[1,1,0,1,0,1,0,0,1,0,1,0]
generating graphics...
=> 3
[1,1,0,1,0,1,0,0,1,1,0,0]
generating graphics...
=> 3
[1,1,0,1,0,1,0,1,0,0,1,0]
generating graphics...
=> 3
[1,1,0,1,0,1,0,1,0,1,0,0]
generating graphics...
=> 2
[1,1,0,1,0,1,0,1,1,0,0,0]
generating graphics...
=> 2
[1,1,0,1,0,1,1,0,0,0,1,0]
generating graphics...
=> 3
[1,1,0,1,0,1,1,0,0,1,0,0]
generating graphics...
=> 2
[1,1,0,1,0,1,1,0,1,0,0,0]
generating graphics...
=> 2
[1,1,0,1,0,1,1,1,0,0,0,0]
generating graphics...
=> 2
[1,1,0,1,1,0,0,0,1,0,1,0]
generating graphics...
=> 4
[1,1,0,1,1,0,0,0,1,1,0,0]
generating graphics...
=> 4
[1,1,0,1,1,0,0,1,0,0,1,0]
generating graphics...
=> 4
[1,1,0,1,1,0,0,1,0,1,0,0]
generating graphics...
=> 3
[1,1,0,1,1,0,0,1,1,0,0,0]
generating graphics...
=> 3
[1,1,0,1,1,0,1,0,0,0,1,0]
generating graphics...
=> 3
[1,1,0,1,1,0,1,0,0,1,0,0]
generating graphics...
=> 2
[1,1,0,1,1,0,1,0,1,0,0,0]
generating graphics...
=> 2
[1,1,0,1,1,0,1,1,0,0,0,0]
generating graphics...
=> 2
[1,1,0,1,1,1,0,0,0,0,1,0]
generating graphics...
=> 2
[1,1,0,1,1,1,0,0,0,1,0,0]
generating graphics...
=> 1
[1,1,0,1,1,1,0,0,1,0,0,0]
generating graphics...
=> 1
[1,1,0,1,1,1,0,1,0,0,0,0]
generating graphics...
=> 1
[1,1,0,1,1,1,1,0,0,0,0,0]
generating graphics...
=> 1
[1,1,1,0,0,0,1,0,1,0,1,0]
generating graphics...
=> 3
[1,1,1,0,0,0,1,0,1,1,0,0]
generating graphics...
=> 3
[1,1,1,0,0,0,1,1,0,0,1,0]
generating graphics...
=> 3
[1,1,1,0,0,0,1,1,0,1,0,0]
generating graphics...
=> 3
[1,1,1,0,0,0,1,1,1,0,0,0]
generating graphics...
=> 3
[1,1,1,0,0,1,0,0,1,0,1,0]
generating graphics...
=> 3
[1,1,1,0,0,1,0,0,1,1,0,0]
generating graphics...
=> 3
[1,1,1,0,0,1,0,1,0,0,1,0]
generating graphics...
=> 3
[1,1,1,0,0,1,0,1,0,1,0,0]
generating graphics...
=> 2
[1,1,1,0,0,1,0,1,1,0,0,0]
generating graphics...
=> 2
[1,1,1,0,0,1,1,0,0,0,1,0]
generating graphics...
=> 3
[1,1,1,0,0,1,1,0,0,1,0,0]
generating graphics...
=> 2
[1,1,1,0,0,1,1,0,1,0,0,0]
generating graphics...
=> 2
[1,1,1,0,0,1,1,1,0,0,0,0]
generating graphics...
=> 2
[1,1,1,0,1,0,0,0,1,0,1,0]
generating graphics...
=> 4
[1,1,1,0,1,0,0,0,1,1,0,0]
generating graphics...
=> 4
[1,1,1,0,1,0,0,1,0,0,1,0]
generating graphics...
=> 4
[1,1,1,0,1,0,0,1,0,1,0,0]
generating graphics...
=> 3
[1,1,1,0,1,0,0,1,1,0,0,0]
generating graphics...
=> 3
[1,1,1,0,1,0,1,0,0,0,1,0]
generating graphics...
=> 4
[1,1,1,0,1,0,1,0,0,1,0,0]
generating graphics...
=> 3
[1,1,1,0,1,0,1,0,1,0,0,0]
generating graphics...
=> 2
[1,1,1,0,1,0,1,1,0,0,0,0]
generating graphics...
=> 2
[1,1,1,0,1,1,0,0,0,0,1,0]
generating graphics...
=> 3
[1,1,1,0,1,1,0,0,0,1,0,0]
generating graphics...
=> 2
[1,1,1,0,1,1,0,0,1,0,0,0]
generating graphics...
=> 1
[1,1,1,0,1,1,0,1,0,0,0,0]
generating graphics...
=> 1
[1,1,1,0,1,1,1,0,0,0,0,0]
generating graphics...
=> 1
[1,1,1,1,0,0,0,0,1,0,1,0]
generating graphics...
=> 4
[1,1,1,1,0,0,0,0,1,1,0,0]
generating graphics...
=> 4
[1,1,1,1,0,0,0,1,0,0,1,0]
generating graphics...
=> 4
[1,1,1,1,0,0,0,1,0,1,0,0]
generating graphics...
=> 3
[1,1,1,1,0,0,0,1,1,0,0,0]
generating graphics...
=> 3
[1,1,1,1,0,0,1,0,0,0,1,0]
generating graphics...
=> 4
[1,1,1,1,0,0,1,0,0,1,0,0]
generating graphics...
=> 3
[1,1,1,1,0,0,1,0,1,0,0,0]
generating graphics...
=> 2
[1,1,1,1,0,0,1,1,0,0,0,0]
generating graphics...
=> 2
[1,1,1,1,0,1,0,0,0,0,1,0]
generating graphics...
=> 4
[1,1,1,1,0,1,0,0,0,1,0,0]
generating graphics...
=> 3
[1,1,1,1,0,1,0,0,1,0,0,0]
generating graphics...
=> 2
[1,1,1,1,0,1,0,1,0,0,0,0]
generating graphics...
=> 1
[1,1,1,1,0,1,1,0,0,0,0,0]
generating graphics...
=> 1
[1,1,1,1,1,0,0,0,0,0,1,0]
generating graphics...
=> 5
[1,1,1,1,1,0,0,0,0,1,0,0]
generating graphics...
=> 4
[1,1,1,1,1,0,0,0,1,0,0,0]
generating graphics...
=> 3
[1,1,1,1,1,0,0,1,0,0,0,0]
generating graphics...
=> 2
[1,1,1,1,1,0,1,0,0,0,0,0]
generating graphics...
=> 1
[1,1,1,1,1,1,0,0,0,0,0,0]
generating graphics...
=> 0
Description
The number of left tunnels of a Dyck path.
A tunnel is a pair (a,b) where a is the position of an open parenthesis and b is the position of the matching close parenthesis. If a+b<n then the tunnel is called left.
References
[1] Elizalde, S. Fixed points and excedances in restricted permutations MathSciNet:2880679 arXiv:math/0212221
Code
def statistic(x):
    return x.number_of_tunnels("left")

Created
Jun 18, 2013 at 17:45 by Viviane Pons
Updated
May 20, 2016 at 20:52 by Martin Rubey