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Statistic identifier: St001946

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Collection: Parking functions

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Description: The number of descents in a parking function.
This is the number of indices $i$ such that $p_i > p_{i+1}$.

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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]]

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Code:


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Statistic 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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Created: May 24, 2024 at 20:37 by Jennifer Elder

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Last Updated: May 24, 2024 at 20:37 by Jennifer Elder