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Société
mathématique
du Canada
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Pamela E. Harris
University of Wisconsin-Milwaukee
Le vendredi 2 juin 2023 | 17h00 - 18h00pm
John Urschel est un associé junior à Harvard. Auparavant, il était un membre du Institute for Advanced Study, et avant cela, un doctorant en mathématiques à MIT. En 2017, Urschel était nommé à liste Forbes’ “30 under 30” de jeunes scientifiques exceptionnels. Ses intérêts de recherches incluent l’analyse numérique, la théorie de graphe, et la science de données/apprentissage automatique.
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.