- FindStat

Identifier

St001946: Parking functions ⟶ ℤ

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
[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