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Generalizing the results of Thue (for n = 2) [Norske Vid. Selsk. Skr. Mat. Nat. Kl. 1 (1912) 1-67] and of Klepinin and Sukhanov (for n = 3) [Discrete Appl. Math. 114 (2001) 155-169], we prove that for all n ≥ 2, the critical exponent of the Arshon word of order n is given by (3n-2)/(2n-2), and this exponent is attained at position 1.
@article{ITA_2010__44_1_139_0,
author = {Krieger, Dalia},
title = {The critical exponent of the {Arshon} words},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {139--150},
publisher = {EDP-Sciences},
volume = {44},
number = {1},
year = {2010},
doi = {10.1051/ita/2010009},
mrnumber = {2604939},
zbl = {1184.68375},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2010009/}
}
TY - JOUR AU - Krieger, Dalia TI - The critical exponent of the Arshon words JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2010 SP - 139 EP - 150 VL - 44 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita/2010009/ DO - 10.1051/ita/2010009 LA - en ID - ITA_2010__44_1_139_0 ER -
%0 Journal Article %A Krieger, Dalia %T The critical exponent of the Arshon words %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2010 %P 139-150 %V 44 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita/2010009/ %R 10.1051/ita/2010009 %G en %F ITA_2010__44_1_139_0
Krieger, Dalia. The critical exponent of the Arshon words. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 1, pp. 139-150. doi: 10.1051/ita/2010009
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