Algebra and Combinatorics Seminar

Date: November 6, 2020

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Lauren Snider, Texas A&M

Title: On 2-dimensional parking functions

Abstract: A 2-dimensional U-parking function is a pair of integer sequences whose order statistics are bounded by certain weights along lattice paths in the plane. U-parking functions are natural higher-dimensional generalizations of classical parking functions. Other interesting generalizations include (p,q)-parking functions (Cori and Poulalhon) and graphical parking functions (Postnikov and Shapiro) . In this talk, we will show that (p,q)-parking functions are in fact U-parking functions for a particular node-set U, as well as explicitly describe the overlap between U-parking functions and graphical parking functions when U is affine. Along the way, we will discuss some results regarding the enumeration of increasing U-parking functions. This is based on joint work with Catherine Yan.