Parking cars of different sizes

TL;DR

This paper generalizes parking functions to include cars of various sizes, providing a new formula for counting such parking sequences, which broadens the understanding of parking function combinatorics.

Contribution

It introduces parking sequences with different-sized cars and derives a product formula for their enumeration, extending classical parking function theory.

Findings

Derived a product formula for parking sequences with cars of different sizes.

Extended classical parking function enumeration to more general scenarios.

Provided combinatorial insights into parking sequences with variable car sizes.

Abstract

We extend the notion of parking functions to parking sequences, which include cars of different sizes, and prove a product formula for the number of such sequences.