Binary patterns in binary cube-free words: avoidability and growth
Robert Mercas
Pascal Ochem
Alexey V. Samsonov
Arseny M. Shur
2134/24602
https://repository.lboro.ac.uk/articles/Binary_patterns_in_binary_cube-free_words_avoidability_and_growth/9402065
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 growth rates of languages avoiding minimal avoidable patterns are approximated through computer-assisted upper bounds. Finally, a new example of a pattern-avoiding language of polynomial growth is given.
2017-03-31 11:59:15
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