Date of Submission

Spring 2023

Academic Program

Mathematics

Project Advisor 1

Lauren Rose

Abstract/Artist's Statement

Senior Project submitted to The Division of Science, Mathematics and Computing of Bard College.

This project is about a generalization of parking functions called parking garage functions. Parking functions have been well studied, but the concept of parking garage functions is new and introduced in the project. Parking garage functions are sequences that represent the parking garage level preferences of cars which lead to all cars parking on a level after a systematic placement. We found a recursive formula for the number of sequences that are a parking garage function. We also found a closed formula for a subset of parking garage functions, descending parking garage functions, via a bijection between descending parking garage functions and Dyck paths which are paths on a rectangular grid which only take right and upward steps starting at the origin and remain under a positively sloped diagonal that goes through the origin.

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Open Access

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