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On a paper by Castelli, Mignosi, Restivo

Published online by Cambridge University Press:  15 April 2002

Jacques Justin
Jacques Justin*
Affiliation:
LIAFA, Université Paris VII, Case 7014, 2 place Jussieu, 75251 Paris Cedex 05, France; (justin@liafa.jussieu.fr) Mailing address: 19 rue de Bagneux, 92330 Sceaux, France
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Abstract

Fine and Wilf's theorem has recently been extended to words having three periods. Following the method of the authors we extend it to an arbitrary number of periods and deduce from that a characterization of generalized Arnoux-Rauzy sequences or episturmian infinite words.

Keywords

Fine and Wilf theoremArnoux-Rauzy sequenceepisturmian word.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 34 , Issue 5 , September 2000 , pp. 373 - 377
Copyright
© EDP Sciences, 2000

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References

Arnoux, P. and Rauzy, G., Représentation géométrique de suites de complexité 2n+1. Bull. Soc. Math. France 119 (1991) 199-215. CrossRef
Castelli, M.G., Mignosi, F. and Restivo, A., Fine and Wilf's theorem for three periods and a generalization of Sturmian words. Theoret. Comput. Sci. 218 (1999) 83-94. CrossRef
de Luca, A., Sturmian words, structure, combinatorics and their arithmetics. Theoret. Comput. Sci. 183 (1997) 45-82. CrossRef
X. Droubay, J. Justin and G. Pirillo, Episturmian words and some constructions of de Luca and Rauzy. Theoret. Comput. Sci. (to appear).
Fine, N.J. and Wilf, H.S., Uniqueness Theorem for Periodic Functions. Proc. Am. Math. Soc. 16 (1965) 109-114. CrossRef
J. Justin and G. Pirillo, Episturmian words and episturmian morphisms. Preprint.
M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA (1983).