Combinatorial properties of smooth infinite words

Authors:
S. Brlek;S. Dulucq;A. Ladouceur;L. Vuillon
Affiliations:
LaCIM, Dept. Informatique, Université du Québec à Montréal, "Centre-Ville", Montréal, Qué., Canada;LABRI, Université Bordeaux I, Talence Cedex, France;LaCIM, Dept. Informatique, Université du Québec à Montréal, "Centre-Ville", Montréal, Qué., Canada;LAMA, Université de Savoie, Le Bourget du Lac, France
Venue:
Theoretical Computer Science
Year:
2006

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Abstract

We describe some combinatorial properties of an intriguing class of infinite words, called smooth, connected with the Kolakoski one, K, defined as the fixed point of the run-length encoding Δ. It is based on a bijection on the free monoid over Σ = {1, 2}, that shows some surprising mixing properties. All words contain the same finite number of square factors, and consequently they are cube-free. This suggests that they have the same complexity as confirmed by extensive computations. We further investigate the occurrences of palindromic subwords. Finally, we show that there exist smooth words obtained as fixed points of substitutions (realized by transducers) as in the case of K.