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Journal Articles Integers : Electronic Journal of Combinatorial Number Theory Year : 2008

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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Dates and versions

lirmm-00344944 , version 1 (07-12-2008)

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  • HAL Id : lirmm-00344944 , version 1

Cite

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