We prove two cases of a strong version of Dejean’s conjecture involving extremal letter frequencies. The results are that there exist an infinite -free word over a 5 letter alphabet with letter frequency and an infinite -free word over a 6 letter alphabet with letter frequency .
@article{ITA_2008__42_3_477_0, author = {Chalopin, J\'er\'emie and Ochem, Pascal}, title = {Dejean's conjecture and letter frequency}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {477--480}, publisher = {EDP-Sciences}, volume = {42}, number = {3}, year = {2008}, doi = {10.1051/ita:2008013}, mrnumber = {2434030}, zbl = {1147.68612}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ita:2008013/} }
TY - JOUR AU - Chalopin, Jérémie AU - Ochem, Pascal TI - Dejean's conjecture and letter frequency JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2008 SP - 477 EP - 480 VL - 42 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita:2008013/ DO - 10.1051/ita:2008013 LA - en ID - ITA_2008__42_3_477_0 ER -
%0 Journal Article %A Chalopin, Jérémie %A Ochem, Pascal %T Dejean's conjecture and letter frequency %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2008 %P 477-480 %V 42 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita:2008013/ %R 10.1051/ita:2008013 %G en %F ITA_2008__42_3_477_0
Chalopin, Jérémie; Ochem, Pascal. Dejean's conjecture and letter frequency. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 3, pp. 477-480. doi : 10.1051/ita:2008013. http://archive.numdam.org/articles/10.1051/ita:2008013/
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