# On a group theoretic generalization of the Morse-Hedlund theorem

15 May 2015 Charlier Emilie Puzynina Svetlana Zamboni Luca Q.

In their 1938 seminal paper on symbolic dynamics, Morse and Hedlund proved that every aperiodic infinite word $x\in A^N,$ over a non empty finite alphabet $A,$ 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. In this paper we obtain a broad generalization of the Morse-Hedlund theorem via group actions... (read more)

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