Suppose that m drivers each choose a preferred parking space in a linear car park with n spots. In order, each driver goes to their desired spot and parks there if possible. If the spot is already occupied then the car parks in the first available spot after that; if no such spot is available then the car leaves the street without parking. When m > n, there will always be defects–cars that are not able to park. Building upon the work in Cameron et al. "Counting defective parking functions," we introduce a multi-shuffle construction to defective parking functions and investigate parking statistics of a defective parking function chosen uniformly at random.
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Mann, John T.; You, Zecheng; and Yin, Mei
"Asymptotic Behavior of Random Defective Parking Functions,"
DU Undergraduate Research Journal Archive: Vol. 4:
2, Article 2.
Available at: https://digitalcommons.du.edu/duurj/vol4/iss2/2