Identifier
Identifier
Values
[1,0] generating graphics... => 1
[1,0,1,0] generating graphics... => 2
[1,1,0,0] generating graphics... => 1
[1,0,1,0,1,0] generating graphics... => 6
[1,0,1,1,0,0] generating graphics... => 3
[1,1,0,0,1,0] generating graphics... => 3
[1,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,0] generating graphics... => 24
[1,0,1,0,1,1,0,0] generating graphics... => 12
[1,0,1,1,0,0,1,0] generating graphics... => 12
[1,0,1,1,0,1,0,0] generating graphics... => 12
[1,0,1,1,1,0,0,0] generating graphics... => 4
[1,1,0,0,1,0,1,0] generating graphics... => 12
[1,1,0,0,1,1,0,0] generating graphics... => 6
[1,1,0,1,0,0,1,0] generating graphics... => 12
[1,1,0,1,0,1,0,0] generating graphics... => 12
[1,1,0,1,1,0,0,0] generating graphics... => 6
[1,1,1,0,0,0,1,0] generating graphics... => 4
[1,1,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,0,1,0,0,0] generating graphics... => 4
[1,1,1,1,0,0,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,0,1,0] generating graphics... => 120
[1,0,1,0,1,0,1,1,0,0] generating graphics... => 60
[1,0,1,0,1,1,0,0,1,0] generating graphics... => 60
[1,0,1,0,1,1,0,1,0,0] generating graphics... => 60
[1,0,1,0,1,1,1,0,0,0] generating graphics... => 20
[1,0,1,1,0,0,1,0,1,0] generating graphics... => 60
[1,0,1,1,0,0,1,1,0,0] generating graphics... => 30
[1,0,1,1,0,1,0,0,1,0] generating graphics... => 60
[1,0,1,1,0,1,0,1,0,0] generating graphics... => 60
[1,0,1,1,0,1,1,0,0,0] generating graphics... => 30
[1,0,1,1,1,0,0,0,1,0] generating graphics... => 20
[1,0,1,1,1,0,0,1,0,0] generating graphics... => 20
[1,0,1,1,1,0,1,0,0,0] generating graphics... => 20
[1,0,1,1,1,1,0,0,0,0] generating graphics... => 5
[1,1,0,0,1,0,1,0,1,0] generating graphics... => 60
[1,1,0,0,1,0,1,1,0,0] generating graphics... => 30
[1,1,0,0,1,1,0,0,1,0] generating graphics... => 30
[1,1,0,0,1,1,0,1,0,0] generating graphics... => 30
[1,1,0,0,1,1,1,0,0,0] generating graphics... => 10
[1,1,0,1,0,0,1,0,1,0] generating graphics... => 60
[1,1,0,1,0,0,1,1,0,0] generating graphics... => 30
[1,1,0,1,0,1,0,0,1,0] generating graphics... => 60
[1,1,0,1,0,1,0,1,0,0] generating graphics... => 60
[1,1,0,1,0,1,1,0,0,0] generating graphics... => 30
[1,1,0,1,1,0,0,0,1,0] generating graphics... => 30
[1,1,0,1,1,0,0,1,0,0] generating graphics... => 30
[1,1,0,1,1,0,1,0,0,0] generating graphics... => 30
[1,1,0,1,1,1,0,0,0,0] generating graphics... => 10
[1,1,1,0,0,0,1,0,1,0] generating graphics... => 20
[1,1,1,0,0,0,1,1,0,0] generating graphics... => 10
[1,1,1,0,0,1,0,0,1,0] generating graphics... => 20
[1,1,1,0,0,1,0,1,0,0] generating graphics... => 20
[1,1,1,0,0,1,1,0,0,0] generating graphics... => 10
[1,1,1,0,1,0,0,0,1,0] generating graphics... => 20
[1,1,1,0,1,0,0,1,0,0] generating graphics... => 20
[1,1,1,0,1,0,1,0,0,0] generating graphics... => 20
[1,1,1,0,1,1,0,0,0,0] generating graphics... => 10
[1,1,1,1,0,0,0,0,1,0] generating graphics... => 5
[1,1,1,1,0,0,0,1,0,0] generating graphics... => 5
[1,1,1,1,0,0,1,0,0,0] generating graphics... => 5
[1,1,1,1,0,1,0,0,0,0] generating graphics... => 5
[1,1,1,1,1,0,0,0,0,0] generating graphics... => 1
[1,0,1,0,1,0,1,0,1,0,1,0] generating graphics... => 720
[1,0,1,0,1,0,1,0,1,1,0,0] generating graphics... => 360
[1,0,1,0,1,0,1,1,0,0,1,0] generating graphics... => 360
[1,0,1,0,1,0,1,1,0,1,0,0] generating graphics... => 360
[1,0,1,0,1,0,1,1,1,0,0,0] generating graphics... => 120
[1,0,1,0,1,1,0,0,1,0,1,0] generating graphics... => 360
[1,0,1,0,1,1,0,0,1,1,0,0] generating graphics... => 180
[1,0,1,0,1,1,0,1,0,0,1,0] generating graphics... => 360
[1,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 360
[1,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 180
[1,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 120
[1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 120
[1,0,1,0,1,1,1,0,1,0,0,0] generating graphics... => 120
[1,0,1,0,1,1,1,1,0,0,0,0] generating graphics... => 30
[1,0,1,1,0,0,1,0,1,0,1,0] generating graphics... => 360
[1,0,1,1,0,0,1,0,1,1,0,0] generating graphics... => 180
[1,0,1,1,0,0,1,1,0,0,1,0] generating graphics... => 180
[1,0,1,1,0,0,1,1,0,1,0,0] generating graphics... => 180
[1,0,1,1,0,0,1,1,1,0,0,0] generating graphics... => 60
[1,0,1,1,0,1,0,0,1,0,1,0] generating graphics... => 360
[1,0,1,1,0,1,0,0,1,1,0,0] generating graphics... => 180
[1,0,1,1,0,1,0,1,0,0,1,0] generating graphics... => 360
[1,0,1,1,0,1,0,1,0,1,0,0] generating graphics... => 360
[1,0,1,1,0,1,0,1,1,0,0,0] generating graphics... => 180
[1,0,1,1,0,1,1,0,0,0,1,0] generating graphics... => 180
[1,0,1,1,0,1,1,0,0,1,0,0] generating graphics... => 180
[1,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 180
[1,0,1,1,0,1,1,1,0,0,0,0] generating graphics... => 60
[1,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 120
[1,0,1,1,1,0,0,0,1,1,0,0] generating graphics... => 60
[1,0,1,1,1,0,0,1,0,0,1,0] generating graphics... => 120
[1,0,1,1,1,0,0,1,0,1,0,0] generating graphics... => 120
[1,0,1,1,1,0,0,1,1,0,0,0] generating graphics... => 60
[1,0,1,1,1,0,1,0,0,0,1,0] generating graphics... => 120
[1,0,1,1,1,0,1,0,0,1,0,0] generating graphics... => 120
[1,0,1,1,1,0,1,0,1,0,0,0] generating graphics... => 120
[1,0,1,1,1,0,1,1,0,0,0,0] generating graphics... => 60
[1,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 30
[1,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 30
[1,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 30
[1,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 30
[1,0,1,1,1,1,1,0,0,0,0,0] generating graphics... => 6
[1,1,0,0,1,0,1,0,1,0,1,0] generating graphics... => 360
[1,1,0,0,1,0,1,0,1,1,0,0] generating graphics... => 180
[1,1,0,0,1,0,1,1,0,0,1,0] generating graphics... => 180
[1,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 180
[1,1,0,0,1,0,1,1,1,0,0,0] generating graphics... => 60
[1,1,0,0,1,1,0,0,1,0,1,0] generating graphics... => 180
[1,1,0,0,1,1,0,0,1,1,0,0] generating graphics... => 90
[1,1,0,0,1,1,0,1,0,0,1,0] generating graphics... => 180
[1,1,0,0,1,1,0,1,0,1,0,0] generating graphics... => 180
[1,1,0,0,1,1,0,1,1,0,0,0] generating graphics... => 90
[1,1,0,0,1,1,1,0,0,0,1,0] generating graphics... => 60
[1,1,0,0,1,1,1,0,0,1,0,0] generating graphics... => 60
[1,1,0,0,1,1,1,0,1,0,0,0] generating graphics... => 60
[1,1,0,0,1,1,1,1,0,0,0,0] generating graphics... => 15
[1,1,0,1,0,0,1,0,1,0,1,0] generating graphics... => 360
[1,1,0,1,0,0,1,0,1,1,0,0] generating graphics... => 180
[1,1,0,1,0,0,1,1,0,0,1,0] generating graphics... => 180
[1,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 180
[1,1,0,1,0,0,1,1,1,0,0,0] generating graphics... => 60
[1,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 360
[1,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 180
[1,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 360
[1,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 360
[1,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 180
[1,1,0,1,0,1,1,0,0,0,1,0] generating graphics... => 180
[1,1,0,1,0,1,1,0,0,1,0,0] generating graphics... => 180
[1,1,0,1,0,1,1,0,1,0,0,0] generating graphics... => 180
[1,1,0,1,0,1,1,1,0,0,0,0] generating graphics... => 60
[1,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 180
[1,1,0,1,1,0,0,0,1,1,0,0] generating graphics... => 90
[1,1,0,1,1,0,0,1,0,0,1,0] generating graphics... => 180
[1,1,0,1,1,0,0,1,0,1,0,0] generating graphics... => 180
[1,1,0,1,1,0,0,1,1,0,0,0] generating graphics... => 90
[1,1,0,1,1,0,1,0,0,0,1,0] generating graphics... => 180
[1,1,0,1,1,0,1,0,0,1,0,0] generating graphics... => 180
[1,1,0,1,1,0,1,0,1,0,0,0] generating graphics... => 180
[1,1,0,1,1,0,1,1,0,0,0,0] generating graphics... => 90
[1,1,0,1,1,1,0,0,0,0,1,0] generating graphics... => 60
[1,1,0,1,1,1,0,0,0,1,0,0] generating graphics... => 60
[1,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 60
[1,1,0,1,1,1,0,1,0,0,0,0] generating graphics... => 60
[1,1,0,1,1,1,1,0,0,0,0,0] generating graphics... => 15
[1,1,1,0,0,0,1,0,1,0,1,0] generating graphics... => 120
[1,1,1,0,0,0,1,0,1,1,0,0] generating graphics... => 60
[1,1,1,0,0,0,1,1,0,0,1,0] generating graphics... => 60
[1,1,1,0,0,0,1,1,0,1,0,0] generating graphics... => 60
[1,1,1,0,0,0,1,1,1,0,0,0] generating graphics... => 20
[1,1,1,0,0,1,0,0,1,0,1,0] generating graphics... => 120
[1,1,1,0,0,1,0,0,1,1,0,0] generating graphics... => 60
[1,1,1,0,0,1,0,1,0,0,1,0] generating graphics... => 120
[1,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 120
[1,1,1,0,0,1,0,1,1,0,0,0] generating graphics... => 60
[1,1,1,0,0,1,1,0,0,0,1,0] generating graphics... => 60
[1,1,1,0,0,1,1,0,0,1,0,0] generating graphics... => 60
[1,1,1,0,0,1,1,0,1,0,0,0] generating graphics... => 60
[1,1,1,0,0,1,1,1,0,0,0,0] generating graphics... => 20
[1,1,1,0,1,0,0,0,1,0,1,0] generating graphics... => 120
[1,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 60
[1,1,1,0,1,0,0,1,0,0,1,0] generating graphics... => 120
[1,1,1,0,1,0,0,1,0,1,0,0] generating graphics... => 120
[1,1,1,0,1,0,0,1,1,0,0,0] generating graphics... => 60
[1,1,1,0,1,0,1,0,0,0,1,0] generating graphics... => 120
[1,1,1,0,1,0,1,0,0,1,0,0] generating graphics... => 120
[1,1,1,0,1,0,1,0,1,0,0,0] generating graphics... => 120
[1,1,1,0,1,0,1,1,0,0,0,0] generating graphics... => 60
[1,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 60
[1,1,1,0,1,1,0,0,0,1,0,0] generating graphics... => 60
[1,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 60
[1,1,1,0,1,1,0,1,0,0,0,0] generating graphics... => 60
[1,1,1,0,1,1,1,0,0,0,0,0] generating graphics... => 20
[1,1,1,1,0,0,0,0,1,0,1,0] generating graphics... => 30
[1,1,1,1,0,0,0,0,1,1,0,0] generating graphics... => 15
[1,1,1,1,0,0,0,1,0,0,1,0] generating graphics... => 30
[1,1,1,1,0,0,0,1,0,1,0,0] generating graphics... => 30
[1,1,1,1,0,0,0,1,1,0,0,0] generating graphics... => 15
[1,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 30
[1,1,1,1,0,0,1,0,0,1,0,0] generating graphics... => 30
[1,1,1,1,0,0,1,0,1,0,0,0] generating graphics... => 30
[1,1,1,1,0,0,1,1,0,0,0,0] generating graphics... => 15
[1,1,1,1,0,1,0,0,0,0,1,0] generating graphics... => 30
[1,1,1,1,0,1,0,0,0,1,0,0] generating graphics... => 30
[1,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 30
[1,1,1,1,0,1,0,1,0,0,0,0] generating graphics... => 30
[1,1,1,1,0,1,1,0,0,0,0,0] generating graphics... => 15
[1,1,1,1,1,0,0,0,0,0,1,0] generating graphics... => 6
[1,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 6
[1,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 6
[1,1,1,1,1,0,0,1,0,0,0,0] generating graphics... => 6
[1,1,1,1,1,0,1,0,0,0,0,0] generating graphics... => 6
[1,1,1,1,1,1,0,0,0,0,0,0] generating graphics... => 1
click to show generating function       
Description
The number of parking functions supported by a Dyck path.
One representation of a parking function is as a pair consisting of a Dyck path and a permutation $\pi$ such that if $[a_0, a_1, \dots, a_{n-1}]$ is the area sequence of the Dyck path then the permutation $\pi$ satisfies $pi_i < pi_{i+1}$ whenever $a_{i} < a_{i+1}$. This statistic counts the number of permutations $\pi$ which satisfy this condition.
Code
def statistic(x):
    return x.number_of_parking_functions()
Created
Sep 27, 2011 at 19:31 by Chris Berg
Updated
Dec 11, 2015 at 16:42 by Veronica Waite