Repetition-free words

Growth of repetition-free words -- a review

This survey reviews recent results on repetitions in words, with emphasis on the estimations for the number of repetition-free words. © 2005 Published by Elsevier B.V.

Cyclically repetition-free words on small alphabets

All sufficiently long binary words contain a square but there are infinite binary words having only the short squares 00, 11 and 0101. Recently it was shown by J. Currie that there exist cyclically square-free words in a ternary alphabet except for lengths 5, 7, 9, 10, 14, and 17. We consider binary words all conjugates of which contain only short squares. We show that the number c(n) of these ...

Letter frequency in infinite repetition-free words

We estimate the extremal letter frequency in infinite words over a finite alphabet avoiding some repetitions. For ternary square-free words, we improve the bounds of Tarannikov on the minimal letter frequency, and prove that the maximal letter frequency is 255 653 . Kolpakov et al. have studied the function ρ such that ρ(x) is the minimal letter frequency in an infinite binary x-free word. In p...

Shortest Repetition-Free Words Accepted by Automata

We consider the following problem: given that a finite automaton M of N states accepts at least one k-power-free (resp., overlapfree) word, what is the length of the shortest such word accepted? We give upper and lower bounds which, unfortunately, are widely separated.

On Repetition-Free Binary Words of Minimal Density