Sturm numbers and substitution invariance of 3iet words
Pierre Arnoux, Valérie Berthé, Zuzana Masáková, Edita Pelantová · arXiv (Cornell University) · 2007
In this paper, we give a necessary condition for an infinite word defined by a non-degenerate interval exchange on three intervals (3iet word) to be invariant by a substitution: a natural parameter associated to this word must be a Sturm number. We deduce some algebraic consequences from this condition concerning the incidence matrix of the associated substitution. As a by-product of our proof, we give a combinatorial characterization of 3iet words.