An exercise on Fibonacci representations

Jean Berstel

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2001)

  • 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 - Informatique Théorique et Applications 35.6 (2001): 491-498. <http://eudml.org/doc/92679>.

@article{Berstel2001,
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 - Informatique Théorique et Applications},
keywords = {Fibonacci base},
language = {eng},
number = {6},
pages = {491-498},
publisher = {EDP-Sciences},
title = {An exercise on Fibonacci representations},
url = {http://eudml.org/doc/92679},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Berstel, Jean
TI - An exercise on Fibonacci representations
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2001
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/92679
ER -

References

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  1. [1] T.C. Brown, Descriptions of the characteristic sequence of an irrational. Canad. Math. Bull. 36 (1993) 15-21. Zbl0804.11021MR1205889
  2. [2] L. Carlitz, Fibonacci representations. Fibonacci Quarterly 6 (1968) 193-220. Zbl0167.03901MR236094
  3. [3] S. Eilenberg, Automata, Languages, and Machines, Vol. A. Academic Press (1974). Zbl0317.94045MR530382
  4. [4] A.S. Fraenkel, Systems of numeration. Amer. Math. Monthly 92 (1985) 105-114. Zbl0568.10005MR777556
  5. [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. Zbl1040.68061MR1723473
  6. [6] A. Ostrowski, Bemerkungen zur Theorie der Diophantischen Approximation I. Abh. Math. Sem. Hamburg 1 (1922) 77-98. Zbl48.0185.01JFM48.0185.01
  7. [7] J. Sakarovitch, Éléments de théorie des automates. Vuibert (to appear). Zbl0743.68086
  8. [8] D. Simplot and A. Terlutte, Closure under union and composition of iterated rational transductions. RAIRO: Theoret. Informatics Appl. 34 (2000) 183-212. Zbl0970.68085MR1796268
  9. [9] D. Simplot and A. Terlutte, Iteration of rational transductions. RAIRO: Theoret. Informatics Appl. 34 (2000) 99-129. Zbl0962.68090MR1774304
  10. [10] E. Zeckendorff, 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. Zbl0252.10011MR308032

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