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A Combinatorial Proof of S-adicity for Sequences with Linear Complexity

Julien Leroy 1 Gwenaël Richomme 2, 3
1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
2 UPVM - Université Paul-Valéry - Montpellier 3
3 ESCAPE - Systèmes complexes, automates et pavages
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : Using Rauzy graphs, Ferenczi proved that if a symbolic dynamical system has linear complexity then it is S-adic. Being more specific, the result can also be proved for infinite words. We provide a new proof of this latter result using the notion of return words to a set of words.
Keywords : linear complexity morphism subword complexity uniform recurrence factor complexity S-adicity S-adic conjecture
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Journal articles
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00797658
Contributor : Gwenaël Richomme <>
Submitted on : Thursday, March 7, 2013 - 8:36:01 AM
Last modification on : Thursday, May 13, 2021 - 12:10:01 PM

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  • HAL Id : lirmm-00797658, version 1

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CNRS | INSMI | LIRMM | TDS-MACS | MIPS | UNIV-MONTPELLIER | ESCAPE | UNIV-MONTP3 | LAMFA

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Julien Leroy, Gwenaël Richomme. A Combinatorial Proof of S-adicity for Sequences with Linear Complexity. Integers : Electronic Journal of Combinatorial Number Theory, State University of West Georgia, Charles University, and DIMATIA, 2013, 13, pp.article #A5. ⟨lirmm-00797658⟩

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