Algebra and Combinatorics Seminar

Date: April 26, 2019

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Yue Cai, Texas A&M University

Title: Rational parking functions

Abstract: Vector parking functions are sequences of non-negative integers whose order statistics are bounded by a given integer sequence $(a_0, a_1, \dots, a_n)$. In this talk, we will generalize the notion to parking functions with a linear boundary of rational slope. Using the theory of fractional power series and the Newton-Puiseux Theorem, we convert an Appell relation of Goncarov polynomials to the exponential generating function for rational parking functions in terms of elementary symmetric functions. Time permits, we will also discuss the case of vector parking functions with periodic boundaries. This is joint work with Catherine Yan.