An Exercise on Fibonacci Representations

Jean Berstel

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 35, Issue: 6, page 491-498
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Berstel, Jean. "An Exercise on Fibonacci Representations." RAIRO - Theoretical Informatics and Applications 35.6 (2010): 491-498. <http://eudml.org/doc/222046>.

@article{Berstel2010,
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. },
author = {Berstel, Jean},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Fibonacci base},
language = {eng},
month = {3},
number = {6},
pages = {491-498},
publisher = {EDP Sciences},
title = {An Exercise on Fibonacci Representations},
url = {http://eudml.org/doc/222046},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Berstel, Jean
TI - An Exercise on Fibonacci Representations
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 6
SP - 491
EP - 498
AB - 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.
LA - eng
KW - Fibonacci base
UR - http://eudml.org/doc/222046
ER -

References

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  1. T.C. Brown, Descriptions of the characteristic sequence of an irrational. Canad. Math. Bull.36 (1993) 15-21.  Zbl0804.11021
  2. L. Carlitz, Fibonacci representations. Fibonacci Quarterly6 (1968) 193-220.  Zbl0167.03901
  3. S. Eilenberg, Automata, Languages, and Machines, Vol. A. Academic Press (1974).  Zbl0317.94045
  4. A.S. Fraenkel, Systems of numeration. Amer. Math. Monthly92 (1985) 105-114.  Zbl0568.10005
  5. C. Frougny and J. Sakarovitch, Automatic conversion from Fibonacci representation to representation in base φ and a generalization. Int. J. Algebra Comput.9 (1999) 51-384.  Zbl1040.68061
  6. A. Ostrowski, Bemerkungen zur Theorie der Diophantischen Approximation I. Abh. Math. Sem. Hamburg1 (1922) 77-98.  Zbl48.0185.01
  7. J. Sakarovitch, Éléments de théorie des automates. Vuibert (to appear).  
  8. D. Simplot and A. Terlutte, Closure under union and composition of iterated rational transductions. RAIRO: Theoret. Informatics Appl.34 (2000) 183-212.  Zbl0970.68085
  9. D. Simplot and A. Terlutte, Iteration of rational transductions. RAIRO: Theoret. Informatics Appl.34 (2000) 99-129.  Zbl0962.68090
  10. E. Zeckendorff, Représentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas. Bull. Soc. Royale Sci. Liège42 (1972) 179-182.  Zbl0252.10011

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