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Texas A&M University

Algebra and Combinatorics Seminar

Date: February 22, 2019

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Westin King, TAMU


Title: Decompositions of Parking Functions on Trees

Abstract: Parking functions describe a sequence of drivers attempting to find a place to park in a one-way linear parking lot. We can introduce a more complicated "parking lot" by considering directed trees and again ask if all the drivers can park. In this talk, I will give enumerative results concerning certain types of these generalized parking functions by considering decompositions based on the movement of drivers while they attempt to park. Additionally, I will discuss the number of "lucky drivers," those who park in the first parking space they encounter, and will find they are related to the Narayana numbers, which refine the ubiquitous Catalan numbers.