Sam Armon, USC

Title: Primeness for generalized parking functions

Abstract: Classical parking functions were originally introduced by Konheim and Weiss to describe their research on computer storage, and have since been studied extensively from a combinatorial point of view. The notion of a prime parking function, due to Gessel, allows one to decompose an arbitrary parking function into “irreducible” components, and there are elegant enumerative results counting the number of (prime) parking functions. We study a generalization of the classical parking functions — the (two-dimensional) vector parking functions — and define the prime objects in this setting, also proving enumerative results which generalize the classical case.