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-----------------------------------------------------------------------------
Statistic identifier: St000014
-----------------------------------------------------------------------------
Collection: Dyck paths
-----------------------------------------------------------------------------
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.
-----------------------------------------------------------------------------
References: [1] [[http://www.findstat.org/ParkingFunctions]]
-----------------------------------------------------------------------------
Code:
def statistic(x):
return x.number_of_parking_functions()
-----------------------------------------------------------------------------
Statistic values:
[1,0] => 1
[1,0,1,0] => 2
[1,1,0,0] => 1
[1,0,1,0,1,0] => 6
[1,0,1,1,0,0] => 3
[1,1,0,0,1,0] => 3
[1,1,0,1,0,0] => 3
[1,1,1,0,0,0] => 1
[1,0,1,0,1,0,1,0] => 24
[1,0,1,0,1,1,0,0] => 12
[1,0,1,1,0,0,1,0] => 12
[1,0,1,1,0,1,0,0] => 12
[1,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,0,1,0] => 12
[1,1,0,0,1,1,0,0] => 6
[1,1,0,1,0,0,1,0] => 12
[1,1,0,1,0,1,0,0] => 12
[1,1,0,1,1,0,0,0] => 6
[1,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0] => 120
[1,0,1,0,1,0,1,1,0,0] => 60
[1,0,1,0,1,1,0,0,1,0] => 60
[1,0,1,0,1,1,0,1,0,0] => 60
[1,0,1,0,1,1,1,0,0,0] => 20
[1,0,1,1,0,0,1,0,1,0] => 60
[1,0,1,1,0,0,1,1,0,0] => 30
[1,0,1,1,0,1,0,0,1,0] => 60
[1,0,1,1,0,1,0,1,0,0] => 60
[1,0,1,1,0,1,1,0,0,0] => 30
[1,0,1,1,1,0,0,0,1,0] => 20
[1,0,1,1,1,0,0,1,0,0] => 20
[1,0,1,1,1,0,1,0,0,0] => 20
[1,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,0,1,0,1,0,1,0] => 60
[1,1,0,0,1,0,1,1,0,0] => 30
[1,1,0,0,1,1,0,0,1,0] => 30
[1,1,0,0,1,1,0,1,0,0] => 30
[1,1,0,0,1,1,1,0,0,0] => 10
[1,1,0,1,0,0,1,0,1,0] => 60
[1,1,0,1,0,0,1,1,0,0] => 30
[1,1,0,1,0,1,0,0,1,0] => 60
[1,1,0,1,0,1,0,1,0,0] => 60
[1,1,0,1,0,1,1,0,0,0] => 30
[1,1,0,1,1,0,0,0,1,0] => 30
[1,1,0,1,1,0,0,1,0,0] => 30
[1,1,0,1,1,0,1,0,0,0] => 30
[1,1,0,1,1,1,0,0,0,0] => 10
[1,1,1,0,0,0,1,0,1,0] => 20
[1,1,1,0,0,0,1,1,0,0] => 10
[1,1,1,0,0,1,0,0,1,0] => 20
[1,1,1,0,0,1,0,1,0,0] => 20
[1,1,1,0,0,1,1,0,0,0] => 10
[1,1,1,0,1,0,0,0,1,0] => 20
[1,1,1,0,1,0,0,1,0,0] => 20
[1,1,1,0,1,0,1,0,0,0] => 20
[1,1,1,0,1,1,0,0,0,0] => 10
[1,1,1,1,0,0,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,0] => 5
[1,1,1,1,0,0,1,0,0,0] => 5
[1,1,1,1,0,1,0,0,0,0] => 5
[1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => 720
[1,0,1,0,1,0,1,0,1,1,0,0] => 360
[1,0,1,0,1,0,1,1,0,0,1,0] => 360
[1,0,1,0,1,0,1,1,0,1,0,0] => 360
[1,0,1,0,1,0,1,1,1,0,0,0] => 120
[1,0,1,0,1,1,0,0,1,0,1,0] => 360
[1,0,1,0,1,1,0,0,1,1,0,0] => 180
[1,0,1,0,1,1,0,1,0,0,1,0] => 360
[1,0,1,0,1,1,0,1,0,1,0,0] => 360
[1,0,1,0,1,1,0,1,1,0,0,0] => 180
[1,0,1,0,1,1,1,0,0,0,1,0] => 120
[1,0,1,0,1,1,1,0,0,1,0,0] => 120
[1,0,1,0,1,1,1,0,1,0,0,0] => 120
[1,0,1,0,1,1,1,1,0,0,0,0] => 30
[1,0,1,1,0,0,1,0,1,0,1,0] => 360
[1,0,1,1,0,0,1,0,1,1,0,0] => 180
[1,0,1,1,0,0,1,1,0,0,1,0] => 180
[1,0,1,1,0,0,1,1,0,1,0,0] => 180
[1,0,1,1,0,0,1,1,1,0,0,0] => 60
[1,0,1,1,0,1,0,0,1,0,1,0] => 360
[1,0,1,1,0,1,0,0,1,1,0,0] => 180
[1,0,1,1,0,1,0,1,0,0,1,0] => 360
[1,0,1,1,0,1,0,1,0,1,0,0] => 360
[1,0,1,1,0,1,0,1,1,0,0,0] => 180
[1,0,1,1,0,1,1,0,0,0,1,0] => 180
[1,0,1,1,0,1,1,0,0,1,0,0] => 180
[1,0,1,1,0,1,1,0,1,0,0,0] => 180
[1,0,1,1,0,1,1,1,0,0,0,0] => 60
[1,0,1,1,1,0,0,0,1,0,1,0] => 120
[1,0,1,1,1,0,0,0,1,1,0,0] => 60
[1,0,1,1,1,0,0,1,0,0,1,0] => 120
[1,0,1,1,1,0,0,1,0,1,0,0] => 120
[1,0,1,1,1,0,0,1,1,0,0,0] => 60
[1,0,1,1,1,0,1,0,0,0,1,0] => 120
[1,0,1,1,1,0,1,0,0,1,0,0] => 120
[1,0,1,1,1,0,1,0,1,0,0,0] => 120
[1,0,1,1,1,0,1,1,0,0,0,0] => 60
[1,0,1,1,1,1,0,0,0,0,1,0] => 30
[1,0,1,1,1,1,0,0,0,1,0,0] => 30
[1,0,1,1,1,1,0,0,1,0,0,0] => 30
[1,0,1,1,1,1,0,1,0,0,0,0] => 30
[1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,0] => 360
[1,1,0,0,1,0,1,0,1,1,0,0] => 180
[1,1,0,0,1,0,1,1,0,0,1,0] => 180
[1,1,0,0,1,0,1,1,0,1,0,0] => 180
[1,1,0,0,1,0,1,1,1,0,0,0] => 60
[1,1,0,0,1,1,0,0,1,0,1,0] => 180
[1,1,0,0,1,1,0,0,1,1,0,0] => 90
[1,1,0,0,1,1,0,1,0,0,1,0] => 180
[1,1,0,0,1,1,0,1,0,1,0,0] => 180
[1,1,0,0,1,1,0,1,1,0,0,0] => 90
[1,1,0,0,1,1,1,0,0,0,1,0] => 60
[1,1,0,0,1,1,1,0,0,1,0,0] => 60
[1,1,0,0,1,1,1,0,1,0,0,0] => 60
[1,1,0,0,1,1,1,1,0,0,0,0] => 15
[1,1,0,1,0,0,1,0,1,0,1,0] => 360
[1,1,0,1,0,0,1,0,1,1,0,0] => 180
[1,1,0,1,0,0,1,1,0,0,1,0] => 180
[1,1,0,1,0,0,1,1,0,1,0,0] => 180
[1,1,0,1,0,0,1,1,1,0,0,0] => 60
[1,1,0,1,0,1,0,0,1,0,1,0] => 360
[1,1,0,1,0,1,0,0,1,1,0,0] => 180
[1,1,0,1,0,1,0,1,0,0,1,0] => 360
[1,1,0,1,0,1,0,1,0,1,0,0] => 360
[1,1,0,1,0,1,0,1,1,0,0,0] => 180
[1,1,0,1,0,1,1,0,0,0,1,0] => 180
[1,1,0,1,0,1,1,0,0,1,0,0] => 180
[1,1,0,1,0,1,1,0,1,0,0,0] => 180
[1,1,0,1,0,1,1,1,0,0,0,0] => 60
[1,1,0,1,1,0,0,0,1,0,1,0] => 180
[1,1,0,1,1,0,0,0,1,1,0,0] => 90
[1,1,0,1,1,0,0,1,0,0,1,0] => 180
[1,1,0,1,1,0,0,1,0,1,0,0] => 180
[1,1,0,1,1,0,0,1,1,0,0,0] => 90
[1,1,0,1,1,0,1,0,0,0,1,0] => 180
[1,1,0,1,1,0,1,0,0,1,0,0] => 180
[1,1,0,1,1,0,1,0,1,0,0,0] => 180
[1,1,0,1,1,0,1,1,0,0,0,0] => 90
[1,1,0,1,1,1,0,0,0,0,1,0] => 60
[1,1,0,1,1,1,0,0,0,1,0,0] => 60
[1,1,0,1,1,1,0,0,1,0,0,0] => 60
[1,1,0,1,1,1,0,1,0,0,0,0] => 60
[1,1,0,1,1,1,1,0,0,0,0,0] => 15
[1,1,1,0,0,0,1,0,1,0,1,0] => 120
[1,1,1,0,0,0,1,0,1,1,0,0] => 60
[1,1,1,0,0,0,1,1,0,0,1,0] => 60
[1,1,1,0,0,0,1,1,0,1,0,0] => 60
[1,1,1,0,0,0,1,1,1,0,0,0] => 20
[1,1,1,0,0,1,0,0,1,0,1,0] => 120
[1,1,1,0,0,1,0,0,1,1,0,0] => 60
[1,1,1,0,0,1,0,1,0,0,1,0] => 120
[1,1,1,0,0,1,0,1,0,1,0,0] => 120
[1,1,1,0,0,1,0,1,1,0,0,0] => 60
[1,1,1,0,0,1,1,0,0,0,1,0] => 60
[1,1,1,0,0,1,1,0,0,1,0,0] => 60
[1,1,1,0,0,1,1,0,1,0,0,0] => 60
[1,1,1,0,0,1,1,1,0,0,0,0] => 20
[1,1,1,0,1,0,0,0,1,0,1,0] => 120
[1,1,1,0,1,0,0,0,1,1,0,0] => 60
[1,1,1,0,1,0,0,1,0,0,1,0] => 120
[1,1,1,0,1,0,0,1,0,1,0,0] => 120
[1,1,1,0,1,0,0,1,1,0,0,0] => 60
[1,1,1,0,1,0,1,0,0,0,1,0] => 120
[1,1,1,0,1,0,1,0,0,1,0,0] => 120
[1,1,1,0,1,0,1,0,1,0,0,0] => 120
[1,1,1,0,1,0,1,1,0,0,0,0] => 60
[1,1,1,0,1,1,0,0,0,0,1,0] => 60
[1,1,1,0,1,1,0,0,0,1,0,0] => 60
[1,1,1,0,1,1,0,0,1,0,0,0] => 60
[1,1,1,0,1,1,0,1,0,0,0,0] => 60
[1,1,1,0,1,1,1,0,0,0,0,0] => 20
[1,1,1,1,0,0,0,0,1,0,1,0] => 30
[1,1,1,1,0,0,0,0,1,1,0,0] => 15
[1,1,1,1,0,0,0,1,0,0,1,0] => 30
[1,1,1,1,0,0,0,1,0,1,0,0] => 30
[1,1,1,1,0,0,0,1,1,0,0,0] => 15
[1,1,1,1,0,0,1,0,0,0,1,0] => 30
[1,1,1,1,0,0,1,0,0,1,0,0] => 30
[1,1,1,1,0,0,1,0,1,0,0,0] => 30
[1,1,1,1,0,0,1,1,0,0,0,0] => 15
[1,1,1,1,0,1,0,0,0,0,1,0] => 30
[1,1,1,1,0,1,0,0,0,1,0,0] => 30
[1,1,1,1,0,1,0,0,1,0,0,0] => 30
[1,1,1,1,0,1,0,1,0,0,0,0] => 30
[1,1,1,1,0,1,1,0,0,0,0,0] => 15
[1,1,1,1,1,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,0,0,0,0,1,0,0] => 6
[1,1,1,1,1,0,0,0,1,0,0,0] => 6
[1,1,1,1,1,0,0,1,0,0,0,0] => 6
[1,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,0] => 1
-----------------------------------------------------------------------------
Created: Sep 27, 2011 at 19:31 by Chris Berg
-----------------------------------------------------------------------------
Last Updated: Dec 11, 2015 at 16:42 by Veronica Waite