An Exercise on Fibonacci Representations
RAIRO - Theoretical Informatics and Applications (2010)
- Volume: 35, Issue: 6, page 491-498
- ISSN: 0988-3754
Access Full Article
top
Abstract
topHow to cite
topBerstel, 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
top- T.C. Brown, Descriptions of the characteristic sequence of an irrational. Canad. Math. Bull.36 (1993) 15-21.
- L. Carlitz, Fibonacci representations. Fibonacci Quarterly6 (1968) 193-220.
- S. Eilenberg, Automata, Languages, and Machines, Vol. A. Academic Press (1974).
- A.S. Fraenkel, Systems of numeration. Amer. Math. Monthly92 (1985) 105-114.
- 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.
- A. Ostrowski, Bemerkungen zur Theorie der Diophantischen Approximation I. Abh. Math. Sem. Hamburg1 (1922) 77-98.
- J. Sakarovitch, Éléments de théorie des automates. Vuibert (to appear).
- D. Simplot and A. Terlutte, Closure under union and composition of iterated rational transductions. RAIRO: Theoret. Informatics Appl.34 (2000) 183-212.
- D. Simplot and A. Terlutte, Iteration of rational transductions. RAIRO: Theoret. Informatics Appl.34 (2000) 99-129.
- 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.
Citations in EuDML Documents
top- Petra Kocábová, Zuzana Masáková, Edita Pelantová, Integers with a maximal number of Fibonacci representations
- Petra Kocábová, Zuzana Masáková, Edita Pelantová, Integers with a maximal number of Fibonacci representations
- Marcia Edson, Luca Q. Zamboni, On the Number of Partitions of an Integer in the -bonacci Base
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.