The number of Prime Parking Functions

TL;DR

This paper provides a new proof that the count of prime parking functions of length n is (n-1)^{n-1}, offering a fresh interpretation closely related to the original definition.

Contribution

It introduces a direct proof for the enumeration of prime parking functions and offers a new interpretation aligned with the parking function concept.

Findings

Number of prime parking functions of length n is (n-1)^{n-1}

New direct proof method for counting prime parking functions

Provides a close-term interpretation related to the original parking function definition

Abstract

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.