Permutation Invariant Parking Assortments
Douglas M. Chen, Pamela E. Harris, J. Carlos Mart\'inez Mori, Eric J., Pab\'on-Cancel, and Gabriel Sargent

TL;DR
This paper generalizes parking functions to parking assortments with cars of various lengths, characterizes permutation invariance properties, and provides results for small cases and minimally invariant lengths.
Contribution
It introduces parking assortments, explores permutation invariance, and characterizes minimally invariant car lengths for any number of cars.
Findings
All parking functions are permutation invariant.
Characterization of permutation invariance for n=2,3.
Identification of minimally invariant car lengths.
Abstract
We introduce parking assortments, a generalization of parking functions with cars of assorted lengths. In this setting, there are cars of lengths entering a one-way street with parking spots. The cars have parking preferences , where , and enter the street in order. Each car , with length and preference , follows a natural extension of the classical parking rule: it begins looking for parking at its preferred spot and parks in the first contiguously available spots thereafter, if there are any. If all cars are able to park under the preference list , we say is a parking assortment for . Parking assortments also generalize parking sequences, introduced by Ehrenborg and…
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Taxonomy
TopicsSmart Parking Systems Research
