报告题目：Singleton mesh patterns in multidimensional permutations

报 告 人：Sergey Kitaev 教授（University of Strathclyde）

报告时间：2025年3月16日（星期日）10:00—11:00

报告地点：数学科学学院114（小报告厅）      

校内联系人：陈曦 副教授         联系方式：84708351-8604

报告摘要：Permutation patterns is a popular area of research introduced in 1968, but with roots going to the 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.

报告人简介：Sergey Kitaev，英国思克莱德大学理学院副院长、数学与统计学系教授，现任《Journal of Combinatorial Theory, Series A》、《Proceedings of the Edinburgh Mathematical Society》、《Enumerative Combinatorics and Applications》期刊编委。2003年博士毕业于瑞典哥德堡大学，主要研究组合计数问题，已在《J. Combin. Theory Ser. A》、《Adv. in Appl. Math.》、《European J. Combin.》等期刊发表论文160余篇，著有专著《Patterns in Permutations and Words》和《Words and Graphs》。先后主持冰岛和英国国家基金委的项目，并多次应邀在重要组合数学会议上做大会报告。