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A short proof that shuffle squares are 7-avoidable

Guillaume Guégan 1 Pascal Ochem 1 
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : A shuffle square is a word that can be partitioned into two identical words. We obtain a short proof that there exist exponentially many words over the 7 letter alphabet containing no shuffle square as a factor. The method is a generalization of the so-called power series method using ideas of the entropy compression method as developped by Gonçalves et al. [Entropy compression method applied to graph colorings.
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Submitted on : Monday, September 19, 2022 - 11:43:44 AM
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Guillaume Guégan, Pascal Ochem. A short proof that shuffle squares are 7-avoidable. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), EDP Sciences, 2016, 50 (1), pp.101-103. ⟨10.1051/ita/2016007⟩. ⟨lirmm-01347424⟩



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