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 andSukhanov (for n = 3) [Discrete Appl. Math. 114 (2001) 155–169], weprove that for all n ≥ 2, the critical exponent of the Arshon word oforder n is given by (3n −2)/(2n − 2), and this exponent is attained atposition 1