Seminar on Discrete Mathematics: New combinatorial perspectives on MVP parking functions

：Thomas Selig（西安利物浦大学）
：2024-06-24 10:00
：海韵园数理大楼686会议室

报告人：Thomas Selig（西安利物浦大学）

时  间：2024年6月24日10:00

地  点：海韵园数理大楼686会议室

内容摘要:

In parking problems, a given number of cars enter a one-way street sequentially, and try to park according to a specified preferred spot in the street. When two cars have the same preferred spot, we say that a collision occurs. Different models are possible depending on the chosen rule for handling collisions. In this talk, we will study a variant called the MVP ("Most Valuable Player") model. In this, priority is given to later cars, as follows. When a car finds its preferred spot already occupied by a previous car, it bumps that car out of the spot and parks there. The previous car then drives forward in the street, and parks in the first available spot. An MVP parking function is an allocation of a preferred spot to each car which allows all cars to park according to this model.

We will study MVP parking functions according to their outcome permutation, which described the final order of the cars once they have all successfully parked. We exhibit rich combinatorial connections to a variety of objects such as permutation inversion graphs, Motzkin paths, non-crossing matchings, and more.

个人简介：

Dr. Thomas Selig is an Assistant Professor in the Department of Computing, School of Advanced Technology, at Xi'an Jiaotong-Liverpool University, Suzhou, China. He received his PhD in Computer Science from the University of Bordeaux, France, in December 2014. He followed this with postdoctoral research positions at the University of Strathclyde, Glasgow, UK from 2015 to 2018, and at the University of Iceland, Reykjavik, Iceland, from 2018 to 2019. His research interests are in the fields of enumerative and bijective combinatorics, with some interactions with theoretical computer science and discrete probability theory. He is particularly interested in discrete time-based dynamical systems such as sandpile models and parking functions and has published papers in the Journal of Combinatorial Theory, Series A, European Journal of Combinatorics, etc.

 

联系人：靳宇