Theoretical Computer Science
Enumeration of irreducible binary words
Discrete Applied Mathematics
Information Processing Letters
On repetition-free binary words of minimal density
Theoretical Computer Science
Overlap-free words on two symbols
Automata on Infinite Words, Ecole de Printemps d'Informatique Théorique,
Counting Overlap-Free Binary Words
STACS '93 Proceedings of the 10th Annual Symposium on Theoretical Aspects of Computer Science
Polynomial versus exponential growth in repetition-free binary words
Journal of Combinatorial Theory Series A
Growth of repetition-free words: a review
Theoretical Computer Science - The art of theory
On the number of α-power-free binary words for 2
Theoretical Computer Science
Two-Sided Bounds for the Growth Rates of Power-Free Languages
DLT '09 Proceedings of the 13th International Conference on Developments in Language Theory
Overlap-free words and spectra of matrices
Theoretical Computer Science
Combinatorial complexity of regular languages
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Growth rates of complexity of power-free languages
Theoretical Computer Science
On the existence of minimal β-powers
DLT'10 Proceedings of the 14th international conference on Developments in language theory
Growth of power-free languages over large alphabets
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Factorial languages of low combinatorial complexity
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
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The aim of this paper is to give a short survey of the area formed by the intersection of two popular lines of investigation in formal language theory. The first line, originated by Thue in 1906, concerns about repetition-free words and languages. The second line is the study of growth functions for words and languages; it can be traced back to the classical papers by Morse and Hedlund on symbolic dynamics (1938, 1940). Growth functions of repetition-free languages are investigated since 1980's. Most of the results were obtained for power-free languages, but some ideas can be applied for languages avoiding patterns and Abelian-power-free languages as well. In this paper, we present key contributions to the area, its state-of-the-art, and conjectures that suggest answers to some natural unsolved problems. Also, we pay attention to the tools and techniques that made possible the progress in the area and suggest some technical results that would be useful to solve open problems.