Integers with a maximal number of Fibonacci representations
Petra Kocábová; Zuzana Masáková; Edita Pelantová
RAIRO - Theoretical Informatics and Applications (2010)
- Volume: 39, Issue: 2, page 343-359
- ISSN: 0988-3754
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topKocábová, Petra, Masáková, Zuzana, and Pelantová, Edita. "Integers with a maximal number of Fibonacci representations." RAIRO - Theoretical Informatics and Applications 39.2 (2010): 343-359. <http://eudml.org/doc/92770>.
@article{Kocábová2010,
abstract = {
We study the properties of the function R(n) which determines the number of representations
of an integer n as a sum of distinct Fibonacci numbers Fk. We determine the maximum and
mean values of R(n) for Fk ≤ n < Fk+1.
},
author = {Kocábová, Petra, Masáková, Zuzana, Pelantová, Edita},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Fibonacci numbers; Zeckendorf representation.; Zeckendorf representation},
language = {eng},
month = {3},
number = {2},
pages = {343-359},
publisher = {EDP Sciences},
title = {Integers with a maximal number of Fibonacci representations},
url = {http://eudml.org/doc/92770},
volume = {39},
year = {2010},
}
TY - JOUR
AU - Kocábová, Petra
AU - Masáková, Zuzana
AU - Pelantová, Edita
TI - Integers with a maximal number of Fibonacci representations
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 39
IS - 2
SP - 343
EP - 359
AB -
We study the properties of the function R(n) which determines the number of representations
of an integer n as a sum of distinct Fibonacci numbers Fk. We determine the maximum and
mean values of R(n) for Fk ≤ n < Fk+1.
LA - eng
KW - Fibonacci numbers; Zeckendorf representation.; Zeckendorf representation
UR - http://eudml.org/doc/92770
ER -
References
top- J. Berstel, An exercise on Fibonacci representations. RAIRO-Inf. Theor. Appl.35 (2001) 491–498.
- M. Bicknell-Johnson, The smallest positive integer having Fk representations as sums of distinct Fibonacci numbers, in Applications of Fibonacci numbers. Vol. 8, Kluwer Acad. Publ., Dordrecht (1999) 47–52.
- M. Bicknell-Johnson and D.C. Fielder, The number of representations of N using distinct Fibonacci numbers, counted by recursive formulas. Fibonacci Quart.37 (1999) 47–60.
- M. Edson and L. Zamboni, On representations of positive integers in the Fibonacci base. Preprint University of North Texas (2003).
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