We show that the minimal proportion of one letter in an n-th power-free binary word is asymptotically 1=n. We also consider a generalization of n-th power-free words deened through the notion of exponent: a word is x-th power-free for a real x, if it does not contain subwords of exponent x or more. We study the minimal proportion of one letter in an x-th power-free binary word as a function of ...

We review the recent progress in the investigation of powerfree words, with particular emphasis on binary cubefree and ternary squarefree words. Besides various bounds on the entropy, we provide bounds on letter frequencies and consider their empirical distribution obtained by an enumeration of binary cubefree words up to length 80.

letter to the editor

letter to the editor

letter to the editor

letter to the editor

letter to the editor

letter to the editor