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Sturm Numbers and Substitution Invariance of 3iet Words

Abstract : 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 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.
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Contributor : Valerie Berthe <>
Submitted on : Sunday, December 7, 2008 - 12:03:23 PM
Last modification on : Monday, March 29, 2021 - 3:24:02 PM


  • HAL Id : lirmm-00344944, version 1



Pierre Arnoux, Valerie Berthe, Zuzana Masáková, Edita Pelantova. Sturm Numbers and Substitution Invariance of 3iet Words. Integers : Electronic Journal of Combinatorial Number Theory, State University of West Georgia, Charles University, and DIMATIA, 2008, 8 A14, pp.14. ⟨lirmm-00344944⟩



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