Circular words and applications

Benoît Rittaud
(Laboratoire Analyse, Géométrie et Applications, Institut Galilée, Université Paris-13)
Laurent Vivier
(Laboratoire de Didactique André Revuz, Université Paris Diderot)

We define the notion of circular words, then consider on such words a constraint derived from the Fibonacci condition. We give several results on the structure of these circular words, then mention possible applications to various situations: periodic expansion of numbers in numeration systems, "gcd-property" of integer sequences, partition of the prefix of the fixed point of the Fibonacci substitution, spanning trees of a wheel. Eventually, we mention some open questions.

Invited Presentation in Petr Ambrož, Štěpán Holub and Zuzana Masáková: Proceedings 8th International Conference Words 2011 (WORDS 2011), Prague, Czech Republic, 12-16th September 2011, Electronic Proceedings in Theoretical Computer Science 63, pp. 31–36.
Published: 17th August 2011.

ArXived at: http://dx.doi.org/10.4204/EPTCS.63.6 bibtex PDF
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