On Combinatorial Problems Related to Generalized Parking Functions by Kimberly Hadaway ’21, Mathematics Senior Thesis Defense, Tuesday, May 11, 1 pm, live talk can be accessed at https://williams.zoom.us/j/97617951870.
Abstract: In this thesis, we study combinatorial problems related to generalized parking functions. Our work is motivated by two different research questions posed to us by Dr. Ken Fan and Dr. Shanise Walker. First, we reframe Dr. Fan’s probabilistic question in terms of defective defective parking functions, which enumerate the number of cars unable to park in the classical parking function problem, thereby providing a partial answer to his question. Second, we answer Dr. Walker’s question establishing a bijection between unit interval parking functions and the Fubini rankings, which get their name as they are enumerated by the Fubini numbers.