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MaximalParkingDisplacement on ParkingFunction ​

The most spots any car drives past its preferred spot.

On ParkingFunction

FindStat's St000943.

Called as CombinatorialStat(x, "MaximalParkingDisplacement"). The head's page has its examples.

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Distribution

Over ParkingFunctions at each size, tallied here in your browser; sizes past 6 are not offered.

FindStat St000943

The number of spots the most unlucky car had to go further in a parking function.

ObjectValue
[1]0
[1,1]1
[1,2]0
[2,1]0
[1,1,1]2
[1,1,2]1
[1,1,3]1
[1,2,1]2

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000943 has the rest.