Parking Functions: Choose your own adventure
Science Workshop—Spring 2021
OPEN TO THE PUBLIC | For this week's Science workshop, Pamela Harris, PhD, Associate Professor of Mathematics at Williams College, will speak about parking functions.
Consider a parking lot consisting of n consecutive parking spots along a one-way street labeled 1 to n. Suppose n cars want to park one at a time in the parking lot and each car has a preferred parking spot. Each car coming into the lot initially tries to park in its preferred spot. However, if a car’s preferred spot is already occupied, then it will proceed forward in the street parking in the next available spot. Since the parking lot is along a one-way street, it is not guaranteed that every car will be able to park before driving past the parking lot. If we let ai denote the preference of car i and all of the cars are able to park under these conditions, then the preference list (a1, a2, . . . , an) is called a parking function (of length n). For example, (1, 2, 4, 2, 2) is a parking function, but (1, 2, 2, 5, 5) is not (you should convince yourself of this!). In this talk we provide an answer to the question of how many parking functions of length n there are and we consider many new avenues for research stemming from this enumerative question.
Workshop speaker, Pamela Harris, PhD is an Associate Professor of Mathematics at Williams College. she co-hosts the podcast Mathematically Uncensored and co-founded Lathisms: Latinxs and Hispanics in the Mathematical Sciences.
Dr Harris's research interests are in algebra and combinatorics, particularly as these subjects relate to the representation theory of Lie algebras.
Please note that this event is on Thursday instead of the usual Friday.