Algebra and Combinatorics Seminar

Date: September 30, 2016

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Catherine Yan, Texas A&M University

Title: Goncarov polynomials and parking functions

Abstract: This is the first part of 2 talks, in which we establish the connection between vector-parking functions and the classical univariate Goncarov polynomials. A $\mathbf{u}$-parking function is a sequence of positive integers whose order statistics are bounded by the given vector $\mathbf{u}$. The Goncarov polynomial $g_n(x; a_0, \dots, a_{n-1})$ is the polynomial of degree $n$ whose $i$th derivative, when evaluated at $a_i$, is $n! \delta_{i,n}$. We show that Goncarov polynomials provide a natural algebraic tool for working with vector parking functions and use them to enumerate parking functions. This is a joint work with Joseph Kung.