报 告 人：Yan Catherine 教授（美国得克萨斯农工大学）
报告题目：Vector Parking Functions
报告时间：2021年6月 8日上午9:00--10:00
报告地点：Join Zoom Meetinghttps://tamu.zoom.us/j/95083649588?pwd=TGFuSFdnSmFhcXVCRjFWdzJ4M0dTQT09
Meeting ID: 950 8364 9588
Passcode: 800927
主办单位：数学与统计学院、科学技术研究院
报告人简介：
Catherine Yan is a Professor in the Department of Mathematics at Texas A&M University. Her mathematical interest lies in Algebraic and Enumerative Combinatorics. She received a Bachelor degree at Peking University and a Phd in Mathematics at MIT under the supervision of Gian-Carlo Rota. She was a Sloan Research Fellow and a Fellow of American Mathematics Society, and serves on the editorial boards of several research journals, including being a co-Editor-in-Chief for Advances in Applied Mathematics.
报告摘要：
Vector parking functions are sequences of non-negative integers whose order statistics are bounded by a given integer sequence $u = (u_0, u_1, u_2, . . .)$. The classical parking function corresponds to the integer $u=(1,2,3, ... )$. In this talk we discuss how to compute the number of vector parking functions. When $u$ is an integer sequence, we show that there is a set of interpolation polynomials that offer a natural algebraic tool to study vector parking functions. Then we extend this theory to the case when $u$ is a periodic sequence, in particular, when $u$ is given by a linear function with rational slope. This leads to an explicit formula of the exponential generating function for rational parking functions. Our techniques include the theory of fractional power series, an analog of Newton Puiseux Theorem, and the theory of Goncarov polynomials. This talk is based on joint work with Joseph Kung and Yue Cai.
邀请人：祝宝宣