A parking function of length n is prime if we obtain a parking function of length n−1 by deleting one 1 from it. In this note we give a new direct proof that the number of prime parking functions of length n is (n−1)n−1. This proof leads to a new interpretation, in close terms to the definition of parking function.
@article{arxiv.2302.04210,
title = {The number of Prime Parking Functions},
author = {Rui Duarte and António Guedes de Oliveira},
journal= {arXiv preprint arXiv:2302.04210},
year = {2023}
}