License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FUN.2021.16
URN: urn:nbn:de:0030-drops-127770
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12777/
Idziaszek, Tomasz
Efficient Algorithm for Multiplication of Numbers in Zeckendorf Representation
Abstract
In the Zeckendorf representation an integer is expressed as a sum of Fibonacci numbers in which no two are consecutive. We show O(n log n) algorithm for multiplication of two n-digit numbers in Zeckendorf representation.
For this purpose we investigate a relationship between the numeral system using Zeckendorf representations and the golden ratio numeral system. We also show O(n) algorithms for converting numbers between these systems.
BibTeX - Entry
@InProceedings{idziaszek:LIPIcs:2020:12777,
author = {Tomasz Idziaszek},
title = {{Efficient Algorithm for Multiplication of Numbers in Zeckendorf Representation}},
booktitle = {10th International Conference on Fun with Algorithms (FUN 2021)},
pages = {16:1--16:9},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-145-0},
ISSN = {1868-8969},
year = {2020},
volume = {157},
editor = {Martin Farach-Colton and Giuseppe Prencipe and Ryuhei Uehara},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12777},
URN = {urn:nbn:de:0030-drops-127770},
doi = {10.4230/LIPIcs.FUN.2021.16},
annote = {Keywords: Fibonacci numbers, Zeckendorf representation, multiplication algorithm, Fast Fourier Transform, golden ratio numeral system, Lucas numbers}
}
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Keywords: |
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Fibonacci numbers, Zeckendorf representation, multiplication algorithm, Fast Fourier Transform, golden ratio numeral system, Lucas numbers |
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Collection: |
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10th International Conference on Fun with Algorithms (FUN 2021) |
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Issue Date: |
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2020 |
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Date of publication: |
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16.09.2020 |
