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].
Accepté le :
DOI : 10.1051/ita/2016007
Mots-clés : Combinatorics on words, shuffle square, entropy compression
@article{ITA_2016__50_1_101_0, author = {Gu\'egan, Guillaume and Ochem, Pascal}, title = {A short proof that shuffle squares are 7-avoidable}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {101--103}, publisher = {EDP-Sciences}, volume = {50}, number = {1}, year = {2016}, doi = {10.1051/ita/2016007}, zbl = {1353.68224}, mrnumber = {3518162}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ita/2016007/} }
TY - JOUR AU - Guégan, Guillaume AU - Ochem, Pascal TI - A short proof that shuffle squares are 7-avoidable JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2016 SP - 101 EP - 103 VL - 50 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita/2016007/ DO - 10.1051/ita/2016007 LA - en ID - ITA_2016__50_1_101_0 ER -
%0 Journal Article %A Guégan, Guillaume %A Ochem, Pascal %T A short proof that shuffle squares are 7-avoidable %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2016 %P 101-103 %V 50 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita/2016007/ %R 10.1051/ita/2016007 %G en %F ITA_2016__50_1_101_0
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. http://archive.numdam.org/articles/10.1051/ita/2016007/
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