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Zeckendorf proved that every positive integer $n$ can be written uniquely as the sum of non-adjacent Fibonacci numbers; a similar result holds for other positive linear recurrence sequences. These legal decompositions can be used to construct a game
Externí odkaz:
http://arxiv.org/abs/2211.14973
Autor:
Bołdyriew, Elżbieta, Cusenza, Anna, Dai, Linglong, Ding, Pei, Dunkelberg, Aidan, Haviland, John, Huffman, Kate, Ke, Dianhui, Kleber, Daniel, Kuretski, Jason, Lentfer, John, Luo, Tianhao, Miller, Steven J., Mizgerd, Clayton, Tiwari, Vashisth, Ye, Jingkai, Zhang, Yunhao, Zheng, Xiaoyan, Zhu, Weiduo
Zeckendorf's Theorem states that every positive integer can be uniquely represented as a sum of non-adjacent Fibonacci numbers, indexed from $1, 2, 3, 5,\ldots$. This has been generalized by many authors, in particular to constant coefficient fixed d
Externí odkaz:
http://arxiv.org/abs/2009.12475
Autor:
Cusenza, Anna, Dunkelberg, Aiden, Huffman, Kate, Ke, Dianhui, McClatchey, Micah, Miller, Steven J., Mizgerd, Clayton, Tiwari, Vashisth, Ye, Jingkai, Zheng, Xiaoyan
Zeckendorf proved that every positive integer $n$ can be written uniquely as the sum of non-adjacent Fibonacci numbers. We use this decomposition to construct a two-player game. Given a fixed integer $n$ and an initial decomposition of $n=n F_1$, the
Externí odkaz:
http://arxiv.org/abs/2009.09510
Autor:
Cusenza, Anna, Dunkelberg, Aidan, Huffman, Kate, Ke, Dianhui, Kleber, Daniel, Miller, Steven J., Mizgerd, Clayton, Tiwari, Vashisth, Ye, Jingkai, Zheng, Xiaoyan
Edouard Zeckendorf proved that every positive integer $n$ can be uniquely written \cite{Ze} as the sum of non-adjacent Fibonacci numbers, known as the Zeckendorf decomposition. Based on Zeckendorf's decomposition, we have the Zeckendorf game for mult
Externí odkaz:
http://arxiv.org/abs/2009.03708
Akademický článek
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Autor:
Cusenza, Anna, Dunkelberg, Aidan, Huffman, Kate, Ke, Dianhui, McClatchey, Micah, Miller, Steven J., Mizgerd, Clayton, Tiwari, Vashisth, Ye, Jingkai, Zheng, Xiaoyan
Publikováno v:
The Fibonacci Quarterly; February 2022, Vol. 60 Issue: 1 p57-71, 15p
Autor:
Cusenza, Anna, Dunkelberg, Aidan, Huffman, Kate, Ke, Dianhui, Kleber, Daniel, Miller, Steven J., Mizgerd, Clayton, Tiwari, Vashisth, Ye, Jingkai, Zheng, Xiaoyan
Publikováno v:
The Fibonacci Quarterly; November 2021, Vol. 59 Issue: 4 p308-318, 11p