Abstract

. Axel Thue proved that overlapping factors could be avoided in arbitrarily long words on a two-letter alphabet while, on the same alphabet, square factors always occur in words longer than 3. Fran¸coise Dejean stated an analogous result for three-letter alphabets : every long enough word has a factor which is a fractional power with an exponent at least 7=4 and there exist arbitrary long words in which no factor is a fractional power with an exponent strictly greater than 7=4. The number 7=4 is called the repetition threshold of the three-letter alphabets. Thereafter, she proposed the following conjecture : the repetition threshold of the k-letter alphabets is equal to k=(k \Gamma 1) except in the particular cases k = 3, where this threshold is 7=4, and k = 4, where it is 7=5. For k = 4, this conjecture was proved by Jean Jacques Pansiot. In this paper, we give a computer-aided proof of Dejean's conjecture for several other values : 5; 6; 7; 8; 9; 10; 11. R'esum'e. Axel Thue a montr'...

Citations