Seminars on Discrete Mathematics：Singleton mesh patterns in multidimensional permutations

：Sergey Kitaev（英国思克莱德大学）
：2023-03-21 14:30
：厦大海韵园数理大楼686会议室

报告人：Sergey Kitaev（英国思克莱德大学）

时  间：2023年3月21日下午14:30-16:00

地  点：厦大海韵园数理大楼686会议室

内容摘要:

Permutation patterns is a popular area of research introduced in 1968, but with roots going to work of Leonhard Euler in 1749.

In this talk, I will present a brand-new notion of a singleton mesh pattern (SMP), which is a multidimensional mesh pattern of length 1. It turns out that avoidance of this pattern in arbitrary large multi-dimensional permutations can be characterised using an invariant of a pattern called its rank. This allows to determine avoidability for an SMP P efficiently, even though determining rank of P is an NP-complete problem. Moreover, using the notion of a minus-antipodal pattern, one can characterise SMPs which occur at most once in any d-dimensional permutation.

I will also discuss a number of enumerative results regarding the distributions of certain general projective, plus-antipodal, minus-antipodal and hyperplane SMPs.

This is joint work with Sergey Avgustinovich, Jeffrey Liese, Vladimir Potapov and Anna Taranenko.

个人简介：

Sergey Kitaev，英国思克莱德大学理学院副院长、教授。2003年博士毕业于瑞典哥德堡大学。主要研究组合计数问题，完成了置换与词和图的两本著作，在J. Combin. Theory Ser. A，Adv in Appl. Math., European J. Combin.等杂志上发表多篇文章。先后主持过冰岛和英国国家基金委的项目，并多次被邀请在重要组合数学会议上做大会报告。

 

联系人：靳宇