学术期刊
切换导航
首 页
文 章
期 刊
投 稿
预 印
会 议
书 籍
新 闻
合 作
我 们
按学科分类
Journals by Subject
按期刊分类
Journals by Title
核心OA期刊
Core OA Journal
数学与物理
Math & Physics
化学与材料
Chemistry & Materials
生命科学
Life Sciences
医药卫生
Medicine & Health
信息通讯
Information & Communication
工程技术
Engineering & Technology
地球与环境
Earth & Environment
经济与管理
Economics & Management
人文社科
Humanities & Social Sciences
合作期刊
Cooperation Journals
首页
数学与物理
应用数学进展
Vol. 5 No. 2 (May 2016)
期刊菜单
最新文章
历史文章
检索
领域
编委
投稿须知
文章处理费
最新文章
历史文章
检索
领域
编委
投稿须知
文章处理费
Fibonacci数列及其推广形式的正整数表示
Representation of Natural Numbers Using Generalized Fibonacci Sequence
DOI:
10.12677/AAM.2016.52029
,
PDF
,
HTML
,
XML
,
被引量
下载: 2,218
浏览: 5,229
国家自然科学基金支持
作者:
郭婷婷
,
晁福刚
:华东师范大学数学系,上海;
任韩
:华东师范大学数学系,上海;上海市核心数学与实践重点实验室,上海
关键词:
正整数表示
;
Fibonacci数列
;
计数多项式
;
二项编码
;
Representation of Natural Numbers
;
Fibonacci Sequence
;
Enumerating Polynomial
;
Binomial Code
摘要:
正整数表示问题前人多有研究,而基于Fibonacci数列及其推广形式的分析并不多见。本文的主要工作是探讨了该类整数表示的可行性,发现了表示的多样性,从而从最少表示及最多表示的角度来展开分析,分别引入了它们的计数多项式以及0与1的编码形式。起初是只针对Fibonacci数列,之后研究Lucas数列的情况,再接着对一类推广:n代的Fibonacci数列做了猜测。
Abstract:
Previously, there were many studies about the problem of representation of natural numbers. But it’s comparatively rare to study the problem based on Fibonacci sequence and its extension. This thesis mainly discussed the feasibility and diversity of this kind of representation. Utilizing enu-merating polynomials and binomial codes, we focused on minimal and maximal representations of natural numbers. In addition to Fibonacci sequence, we also studied the situation of Lucas sequence and offered some hypotheses in the case of n-step Fibonacci sequence.
文章引用:
郭婷婷, 晁福刚, 任韩. Fibonacci数列及其推广形式的正整数表示[J]. 应用数学进展, 2016, 5(2): 225-231.
http://dx.doi.org/10.12677/AAM.2016.52029
参考文献
[
1
]
Hoggatt Jr., V.E. and Chow, B. (1972) Some Theorems on Completeness. Fibonacci Quarterly, 10, 551-554.
[
2
]
Ferns, H.H. (1965) On the Representation of Integers as Sums of Distinct Fibonacci Numbers. Fibonacci Quarterly, 3, 21-30.
[
3
]
Brown Jr., J.L. (1964) Zeckendorf’s Theorem and Some Applications. Fibonacci Quarterly, 2, 163-168.
[
4
]
Bicknell-Johnson, M. and Fielder, D.C. (1999) The Number of Representations of n Using Distinct Fibonacci Numbers, Counted by Recursive Formulas. Fibonacci Quarterly, 37, 47-60.
[
5
]
Brown Jr., J.L. (1969) Unique Representations of Integers as Sums of Distinct Lucas Numbers. Fibonacci Quarterly, 7, 243-252.
[
6
]
Daykin, D.E. (1969) Representations of Natural Numbers as Sums of Generalized Fibonacci Numbers. Fibonacci Quarterly, 7, 494-510.
投稿
为你推荐
友情链接
科研出版社
开放图书馆