Polynomial versus exponential growth in repetition-free binary words

Polynomial versus exponential growth in repetition-free binary words

It is known that the number of overlap-free binary words of length n grows polynomially, while the number of cubefree binary words grows exponentially. We show that the dividing line between polynomial and exponential growth is 73 . More precisely, there are only polynomially many binary words of length n that avoid 7 3 -powers, but there are exponentially many binary words of length n that avo...

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.

On Repetition-Free Binary Words of Minimal Density

Binary patterns in binary cube-free words: Avoidability and growth

The avoidability of binary patterns by binary cube-free words is investigated and the exact bound between unavoidable and avoidable patterns is found. All avoidable patterns are shown to be D0L-avoidable. For avoidable patterns, the growth rates of the avoiding languages are studied. All such languages, except for the overlap-free language, are proved to have exponential growth. The exact growt...

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...