Lucy Martinez, Rutgers University

Abstract

Classical parking functions are a central subject in combinatorics. There are three natural sub-families of parking functions: the increasing ones, the prime ones, and the prime increasing ones. In this talk, we consider the vector parking functions for a non-decreasing sequence of positive integers $boldsymbol{u}=(u_0, u_1, ldots, u_{n-1})$. We say that a sequence $boldsymbol{a} = (a_0, a_1, ldots, a_{n-1})$ is a $boldsymbol{u}$-parking function of length $n$ if the order statistics of $boldsymbol{a}$ satisfy $a_{(i)}< u_i$ for each $i$. We propose the proper definition of prime vector parking functions and then investigate combinatorial statistics for the arithmetic vector $boldsymbol{u}$ given by $u_i=a+bi$. Joint work with Joanne Beckford, Dillon Hanson, Naomi Krawzik, Olya Mandelshtam, and Catherine Yan.

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