Mini-course "Combinatorics on words". Lecture 1 (Guilhem Gamard)

This mini-course is an introduction to combinatorics on words, where “words” mean “strings of characters”. Of course, this relates to text algorithms, but there is much more to see! Words connect with algebra, data compression, error-correcting codes, number theory, image processing… Both theory and practice benefit from them. In order to give you a flavour of how powerful such a simple structure can be, we will survey different aspects of this theory throughout four lectures. In the first lecture, we will cover the basics (definitions, etc.) and explore the interactions with algebra: how to handle strings by doing algebra, and conversely what words can bring to algebraists. We will outline a few applications, from online text editors to image processing. The first lecture is self-contained and can be followed alone. The prerequisites are minimal (if you know how to reason by induction, you are fine). In case you are interested but cannot attend, contact me: very detailed lecture notes will