Date(s) - 01/12/2015
11 h 00 min - 12 h 00 min
In their 1938 seminal paper on symbolic dynamics, Morse and Hedlund proved that every aperiodic infinite word x contains at least n+1 distinct factors of each length n. They further showed that an infinite word x has exactly n+1 distinct factors of each length n if and only if x is binary, aperiodic and balanced, i.e., x is a Sturmian word. We obtain a broad generalization of the Morse-Hedlund theorem via group actions. This is a joint work with Émilie Charlier and Luca. Q. Zamboni.