Identifier
- St000014: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[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
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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.
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
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
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