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Identifier
Values
[1] => 0
[1,1] => 0
[1,2] => 0
[2,1] => 1
[1,1,1] => 0
[1,1,2] => 0
[1,2,1] => 1
[2,1,1] => 1
[1,1,3] => 0
[1,3,1] => 1
[3,1,1] => 1
[1,2,2] => 0
[2,1,2] => 1
[2,2,1] => 1
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 2
[1,1,1,1] => 0
[1,1,1,2] => 0
[1,1,2,1] => 1
[1,2,1,1] => 1
[2,1,1,1] => 1
[1,1,1,3] => 0
[1,1,3,1] => 1
[1,3,1,1] => 1
[3,1,1,1] => 1
[1,1,1,4] => 0
[1,1,4,1] => 1
[1,4,1,1] => 1
[4,1,1,1] => 1
[1,1,2,2] => 0
[1,2,1,2] => 1
[1,2,2,1] => 1
[2,1,1,2] => 1
[2,1,2,1] => 2
[2,2,1,1] => 1
[1,1,2,3] => 0
[1,1,3,2] => 1
[1,2,1,3] => 1
[1,2,3,1] => 1
[1,3,1,2] => 1
[1,3,2,1] => 2
[2,1,1,3] => 1
[2,1,3,1] => 2
[2,3,1,1] => 1
[3,1,1,2] => 1
[3,1,2,1] => 2
[3,2,1,1] => 2
[1,1,2,4] => 0
[1,1,4,2] => 1
[1,2,1,4] => 1
[1,2,4,1] => 1
[1,4,1,2] => 1
[1,4,2,1] => 2
[2,1,1,4] => 1
[2,1,4,1] => 2
[2,4,1,1] => 1
[4,1,1,2] => 1
[4,1,2,1] => 2
[4,2,1,1] => 2
[1,1,3,3] => 0
[1,3,1,3] => 1
[1,3,3,1] => 1
[3,1,1,3] => 1
[3,1,3,1] => 2
[3,3,1,1] => 1
[1,1,3,4] => 0
[1,1,4,3] => 1
[1,3,1,4] => 1
[1,3,4,1] => 1
[1,4,1,3] => 1
[1,4,3,1] => 2
[3,1,1,4] => 1
[3,1,4,1] => 2
[3,4,1,1] => 1
[4,1,1,3] => 1
[4,1,3,1] => 2
[4,3,1,1] => 2
[1,2,2,2] => 0
[2,1,2,2] => 1
[2,2,1,2] => 1
[2,2,2,1] => 1
[1,2,2,3] => 0
[1,2,3,2] => 1
[1,3,2,2] => 1
[2,1,2,3] => 1
[2,1,3,2] => 2
[2,2,1,3] => 1
[2,2,3,1] => 1
[2,3,1,2] => 1
[2,3,2,1] => 2
[3,1,2,2] => 1
[3,2,1,2] => 2
[3,2,2,1] => 2
[1,2,2,4] => 0
[1,2,4,2] => 1
[1,4,2,2] => 1
[2,1,2,4] => 1
>>> Load all 145 entries. <<<
[2,1,4,2] => 2
[2,2,1,4] => 1
[2,2,4,1] => 1
[2,4,1,2] => 1
[2,4,2,1] => 2
[4,1,2,2] => 1
[4,2,1,2] => 2
[4,2,2,1] => 2
[1,2,3,3] => 0
[1,3,2,3] => 1
[1,3,3,2] => 1
[2,1,3,3] => 1
[2,3,1,3] => 1
[2,3,3,1] => 1
[3,1,2,3] => 1
[3,1,3,2] => 2
[3,2,1,3] => 2
[3,2,3,1] => 2
[3,3,1,2] => 1
[3,3,2,1] => 2
[1,2,3,4] => 0
[1,2,4,3] => 1
[1,3,2,4] => 1
[1,3,4,2] => 1
[1,4,2,3] => 1
[1,4,3,2] => 2
[2,1,3,4] => 1
[2,1,4,3] => 2
[2,3,1,4] => 1
[2,3,4,1] => 1
[2,4,1,3] => 1
[2,4,3,1] => 2
[3,1,2,4] => 1
[3,1,4,2] => 2
[3,2,1,4] => 2
[3,2,4,1] => 2
[3,4,1,2] => 1
[3,4,2,1] => 2
[4,1,2,3] => 1
[4,1,3,2] => 2
[4,2,1,3] => 2
[4,2,3,1] => 2
[4,3,1,2] => 2
[4,3,2,1] => 3
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Description
The number of descents in a parking function.
This is the number of indices $i$ such that $p_i > p_{i+1}$.
References
[1] Schumacher, P.R.F. Descents in Parking Functions, Journal of Integer Sequences, Vol. 21 (2018), Article 18.2.3. https://www.emis.de/journals/JIS/VOL21/Schumacher/schu5.pdf
Code
def statistic(p):
    return sum(1 for i in range(len(p)-1) if p[i] > p[i+1])
Created
May 24, 2024 at 20:37 by Jennifer Elder
Updated
May 24, 2024 at 20:37 by Jennifer Elder