Balanced words and related concepts: applications and complexity issues

In this talk, I present a few results and several questions about "regular" sequences of integers
and related concepts, such as balanced words, partitions and covers of the integers by
arithmetic sequences. Such concepts have been investigated in pure mathematics, but also
naturally arise in a variety of application fields such as production planning, political science, or
queueing theory. I briefly present some of these applications and explain how they motivate
seemingly new questions relating, for instance, to the algorithmic complexity of regular partitions, or to the structure of balanced words.
The presentation is based on joint work with Nadia Brauner and Vincent Jost (Grenoble).