Résumé : A braid can be seen as an equivalence class of words, and choosing a unique word representing each braid helps computing braids, motivating the study of normal forms. In the standard braid monoid, two such normal forms are the Garside normal form, which cuts a braid into a sequence of small simple braids, and the alternating normal form, which consists of recursively splitting a braid into a sequence of braids using less strands. The Garside normal form has many useful properties, in particular forming a regular and automatic language, as well as having a simple local characterization. On the other hand, only the regularity of the alternating normal was known. I will describe a new local characterization of the alternating normal form, explicitly construct its minimal automaton, and give some intuitions regarding its automaticity.

Dernière modification : Tuesday 11 February 2025

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