We introduce parking assortments, a generalization of parking functions with cars of assorted lengths. In this setting, there are n cars of varying lengths y entering a one-way street with m parking spots. The cars have parking preferences and enter the street in order. Each car follows a natural extension of the classical parking rule: it begins looking for parking at its preferred spot and parks in the first spot available thereafter, if there are any. If all cars are able to park under the preference list x, we say x is a parking assortment for y. Parking assortments also generalize parking sequences, since each car seeks for the first contiguously available spots it fits in past its preference. Given a parking assortment x for y, we say it is permutation invariant if all rearrangements of x are also parking assortments for y.

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• Pamela E. Harris

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