Singleton mesh patterns in multidimensional permutations


题目: Singleton mesh patterns in multidimensional permutations

报告人: Sergey Kitaev

单位University of Strathclyde


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.




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 26th British Combinatorial Conference, BCC 2017

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