Reduction in non-($k + 1$)-power-free morphisms

Wlazinski, Francis

doi:10.1051/ita/2016006

Geodesic

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Reduction in non-(

k + 1

)-power-free morphisms

Wlazinski, Francis ¹

¹ L.A.M.F.A., UMR 7352 du CNRS, Université de Picardie Jules Verne, 33 rue Saint-Leu, 80039 Amiens cedex 1, France.

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Special issue dedicated to the 15th "Journées Montoises d'Informatique Théorique", Tome 50 (2016) no. 1, pp. 3-20

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Résumé

Under some hypotheses, if the image by a morphism of a $(k + 1)$ -power-free word contains a $(k + 1)$ -power, we can reduce this word to obtain a new word with the same scheme. These hypotheses are satisfied in the case of uniform morphisms. This allows us to state that, when $k \geq 4$ , a $k$ -power-free uniform morphism is a $(k + 1)$ -power-free morphism.

Reçu le : 2016-03-24
Accepté le : 2016-03-24

MR Zbl

DOI : 10.1051/ita/2016006

Classification : 68R15
Keywords: Word, morphism, uniform and k-power

Affiliations des auteurs :

Wlazinski, Francis ¹

¹ L.A.M.F.A., UMR 7352 du CNRS, Université de Picardie Jules Verne, 33 rue Saint-Leu, 80039 Amiens cedex 1, France.

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     title = {Reduction in non-($k + 1$)-power-free morphisms},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
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     publisher = {EDP-Sciences},
     volume = {50},
     number = {1},
     year = {2016},
     doi = {10.1051/ita/2016006},
     mrnumber = {3518156},
     zbl = {1362.68243},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2016006/}
}

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Wlazinski, Francis. Reduction in non-($k + 1$)-power-free morphisms. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Special issue dedicated to the 15th "Journées Montoises d'Informatique Théorique", Tome 50 (2016) no. 1, pp. 3-20. doi: 10.1051/ita/2016006

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