报告人：Sergey Kitaev（University of Strathclyde）

时间：2024年06月25日 09:00-

地址：数统学院LD302

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.

简介：Sergey Kitaev. Professor of Mathematics, University of Strathclyde.Associate Dean (Research), Faculty of Science.Head of the Strathclyde Combinatorics Group.Editor of Journal of Combinatorial Theory, Series A and Proceedings of Edinburgh Mathematical Society.Author of 165+ publications including two Springer books.In the list of most cited mathematicians by graduation year.Invited Speaker at Algorithms and Software for Discrete Computational Mathematics, International Conference on Riordan Arrays and Related Topics, International Conference on Developments in Language Theory, International Permutation Patterns Conference, AMSMAA Joint Meetings and several other events.Leverhulme Research Fellow (2023-24).Chair of 26th British Combinatorial Conference, BCC 2017.

邀请人：数学研究中心

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