Canadian
Mathematical
Society
Pamela E. Harris
University of Wisconsin-Milwaukee
Friday May 31, 2024 | 5pm - 6pm
Dr. Pamela E. Harris is a Mexican-American mathematician and serves as Associate Professor of Mathematics at the University of Wisconsin-Milwaukee. She received her B.S. from Marquette University, and M.S. and Ph.D. in mathematics from the University of Wisconsin-Milwaukee. Dr. Pamela E. Harris's research is in algebraic combinatorics and she is the author of over 70 peer-reviewed research articles in internationally recognized journals. She is a Fellow of the American Mathematical Society and of the Association for Women in Mathematics. Dr. Harris is an award winning mathematical educator, receiving the 2022 MAA Deborah and Franklin Tepper Haimo Award for Excellence in Mathematical Education, the 2020 recipient of the MAA Northeast Section Award for Distinguished College or University Teaching, the 2019 MAA Henry L. Alder Award for Distinguished Teaching by a Beginning College or University Mathematics Faculty Member, and the 2019 Council on Undergraduate Research Mathematics and Computer Sciences Division Early Career Faculty Mentor Award. She is the President and co-founder of Lathisms: Latinxs and Hispanics in the Mathematical Sciences and cohosts the podcast Mathematically Uncensored.
ABSTRACT
Parking Functions: Choose your own adventure
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, (4,2,1,2,2) is a parking function, but (5,1,2,5,2) 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. This talk will be in the style of a “Choose Your Own Adventure” book and the audience will make choices to dictate the routes we take.