## Sturm numbers and substitution invariance of 3iet words.(English)Zbl 1202.11021

Summary: 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 with 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.

### MSC:

 11B85 Automata sequences 37B10 Symbolic dynamics 68R15 Combinatorics on words

### Keywords:

interval exchange on three intervals
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