Abstract

A bijection is a one-to-one correspondence between two sets. Often, there is more than one way to construct a bijection between equinumerous sets - and if the sets are not very small and we do not require the bijections to be intelligible, there can be many. But what makes a bijection "good"? Should it be easy to describe? Or should it reveal deeper structural similarities between the sets? While the answer “it depends” is valid, much more can be said under certain assumptions in specific contexts.In this talk, I will explore this idea through a remarkable story in the theory of permutation patterns. The talk will be accessible to a general audience.

Biography

Sergey Kitaev is a Professor of Mathematics in the Department of Mathematics and Statistics and the Associate Dean (Research) in the Faculty of Science. He also serves as the Head of the Mathematical and Stochastic Analysis Group, the co-Head of the Applied and Discrete Analysis Group, and the Head of the Strathclyde Combinatorics Group. He is an editor of Journal of Combinatorial Theory, Series A (JCTA), Proceedings of the Edinburgh Mathematical Society (PEMS), and Enumerative Combinatorics and Applications (ECA). Professor Kitaev’s research interests include, but are not limited to, Combinatorics, Graph Theory, Discrete Analysis, Formal Languages and Optimisation. He is the author of more than 175 research papers and he is in the list of the most cited mathematicians by graduation year. Recent research has included studies in the theory of patterns in combinatorial structures and the theory of word-representable graphs. Professor Kitaev’s book Patterns in Permutations and Words, published by Springer (EATCS monographs in Theoretical Computer Science book series) in 2011, is the first comprehensive source over results and trends in the fast-growing field of patterns in permutations and words. His other book Words and Graphs, published by Springer (EATCS monographs in Theoretical Computer Science book series) in 2015, is a comprehansive introduction to the theory of word-representable graphs that he pioneered alone.