A first investigation of Sturmian trees

Authors:
Jean Berstel;Luc Boasson;Olivier Carton;Isabelle Fagnot
Affiliations:
Institut Gaspard-Monge, Université de Marne-la-Vallée and CNRS, Marne-la-Vallée;Laboratoire d'Informatique Algorithmique: Fondements et Applications, Université Denis-Diderot Paris VII and CNRS, Paris;Laboratoire d'Informatique Algorithmique: Fondements et Applications, Université Denis-Diderot Paris VII and CNRS, Paris;Institut Gaspard-Monge, Université de Marne-la-Vallée and CNRS, Marne-la-Vallée
Venue:
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Year:
2007

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Abstract

We consider Sturmian trees as a natural generalization of Sturmian words. A Sturmian tree is a tree having n+1 distinct subtrees of height n for each n. As for the case of words, Sturmian trees are irrational trees of minimal complexity. We give various examples of Sturmian trees, and we characterize one family of Sturmian trees by means of a structural property of their automata.