2024/05/13 by Luca Alberto Davide Ferrari, Ferrari, Luca, Francesco Verciani +1
Engineering · Social Sciences · #05A05 #05A99 #Combinatorics (math.CO) #FOS: Mathematics #Smart Parking Systems Research #Traffic control and management #Transportation Planning and Optimization
paper · pdf · doi:10.48550/arxiv.2405.07522
openalex publication_date 2024/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Naples parking functions were introduced as a generalization of classical parking functions, in which cars are allowed to park backwards, by checking up to a fixed number of previous spots, before proceeding forward as usual. In this work we introduce the notion of a complete parking preference, through which we are able to give some information on the combinatorics of Naples parking functions. Roughly speaking, a complete parking preference is a parking preference such that, for any index j, there are more cars with preference at least j than spots available from j onward. We provide a characterization of Naples parking functions in terms of certain complete subsequences of them. As a consequence of this result we derive a characterization of permutation-invariant Naples parking functions which turns out to be equivalent to the one given by (Carvalho et al., 2021), but using a totally different approach (and language).