Lucy Martinez, Rutgers University

Abstract

Consider a one-way street with n parking spots numbered 1 through n. A sequence of n cars enters the street one at a time, each with a preferred spot. Each car i drives to its preferred spot and follows the parking rule: car i tries to park in their preferred spot if possible, and otherwise takes the next available spot if it exists. If all cars can park under the parking rule, then the sequence of preferences is called a parking function. In a parking function, a lucky car is a car that parks in its preferred parking spot, and the parking outcome is the permutation encoding the order in which the cars park on the street. In this talk, we will present a characterization of the set of parking outcomes arising from parking functions with a fixed set of lucky cars.

Based on joint work with Pamela E. Harris.

See: https://sites.math.rutgers.edu/~kmg326/GCS/GCS.html