RAIRO-Theor. Inf. Appl.
Volume 44, Number 1, January-March 2010Special issue dedicated to the 12th "Journées Montoises d'Informatique Théorique"
|Page(s)||139 - 150|
|Published online||11 February 2010|
The critical exponent of the Arshon words
Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, POB 26, Rehovot 76100, Israel;
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.
Mathematics Subject Classification: 68R15.
Key words: Arshon words / critical exponent.
© EDP Sciences, 2010
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