Geodesic
A short proof that shuffle squares are 7-avoidable
Guégan, Guillaume1 ; Ochem, Pascal2 
1 University Montpellier 2, LIRMM, France
2 CNRS, LIRMM, Montpellier, 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. 101-103

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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. arXiv:1406.4380].

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DOI : 10.1051/ita/2016007
Classification : 68R15
Keywords: Combinatorics on words, shuffle square, entropy compression

Guégan, Guillaume 1 ; Ochem, Pascal 2

1 University Montpellier 2, LIRMM, France
2 CNRS, LIRMM, Montpellier, France 
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Guégan, Guillaume; Ochem, Pascal. A short proof that shuffle squares are 7-avoidable. 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. 101-103. doi: 10.1051/ita/2016007

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