Algebra and Combinatorics Seminar

Date: April 14, 2023

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Lauren Snider, Texas A&M University

Title: (S_p x S_q)-Invariant G-Parking Functions

Abstract: G-parking functions are generalizations of classical parking functions which depend on a connected multigraph G having a distinct root vertex. Gaydarov and Hopkins classified all such graphs G whose G-parking functions are invariant under action by the symmetric group S_n (where n+1 is the order of G), through which they clarified the relationship between G-parking functions and vector parking functions. In this talk, I will present a classification of all graphs G whose G-parking functions are (S_p x S_q)-invariant, with p+q+1 the order of G. Seeking a 2-dimensional analogue of Gaydarov and Hopkins' results, I will then characterize the overlap between G-parking functions and 2-dimensional U-parking functions, i.e., pairs of integer sequences whose order statistics are bounded by certain weights along lattice paths in the plane. This talk is based on joint work with Catherine Yan.