题目:Singleton mesh patterns in multidimensional permutations
报告人:Sergey Kitaev
单位：University of Strathclyde
Abstract:
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 several 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.
时间：2024年5月17日，10:00-11:00
About the Speaker:
·
·- Domain: Combinatorics, Graph Theory
·- 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 Permutations Patterns Conference, AMS-MAA Joint Meetings and several other events
·- Leverhulme Research Fellow (2023-24)
·- Chair of 26thBritish Combinatorial Conference, BCC 2017
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