ColinGeniet

This talk will first introduce combinatorics on permutations and patterns, presenting the basic notions and some fundamental results: the Marcus-Tardos theorem which bounds the density of matrices avoiding a given pattern, and the Guillemot-Marx algorithm for pattern detection using the notion now known as twin-width. I will then present a decomposition result: permutations avoiding a …

This talk is an introduction to the recent notion of merge-width, proposed by Jan Dreier and Szymon Torúnczyk. I will give an overview of the context and motivations for merge-width, namely the first-order model checking problem, and present the definition, some examples, and some basic proof techniques with the example of χ-boundedness. This is based …