THE CRITICAL EXPONENT OF THE ARSHON WORDS
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.
critical exponent arshon words