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An Exercise on Fibonacci Representations

Published online by Cambridge University Press:  15 July 2002

Jean Berstel
Jean Berstel*
Affiliation:
Institut Gaspard Monge (IGM), Université de Marne-la-Vallée, 5 boulevard Descartes, 77454 Marne-la-Vallée Cedex 2, France; (Jean.Berstel@univ-mlv.fr)
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Abstract

We give a partial answer to a question of Carlitz asking for a closed formula for the number of distinct representations of an integer in the Fibonacci base.

Keywords

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 35 , Issue 6: A tribute to Aldo de Luca , November 2001 , pp. 491 - 498
Copyright
© EDP Sciences, 2001

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References

Brown, T.C., Descriptions of the characteristic sequence of an irrational. Canad. Math. Bull. 36 (1993) 15-21. CrossRef
Carlitz, L., Fibonacci representations. Fibonacci Quarterly 6 (1968) 193-220.
S. Eilenberg, Automata, Languages, and Machines, Vol. A. Academic Press (1974).
Fraenkel, A.S., Systems of numeration. Amer. Math. Monthly 92 (1985) 105-114. CrossRef
Frougny, C. and Sakarovitch, J., Automatic conversion from Fibonacci representation to representation in base φ and a generalization. Int. J. Algebra Comput. 9 (1999) 51-384.
Ostrowski, A., Bemerkungen zur Theorie der Diophantischen Approximation I. Abh. Math. Sem. Hamburg 1 (1922) 77-98. CrossRef
J. Sakarovitch, Éléments de théorie des automates. Vuibert (to appear).
Simplot, D. and Terlutte, A., Closure under union and composition of iterated rational transductions. RAIRO: Theoret. Informatics Appl. 34 (2000) 183-212.
Simplot, D. and Terlutte, A., Iteration of rational transductions. RAIRO: Theoret. Informatics Appl. 34 (2000) 99-129.
Zeckendorff, E., Représentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas. Bull. Soc. Royale Sci. Liège 42 (1972) 179-182.