姓名 |
鍾明珈(Ming-chia Chung)
查詢紙本館藏 |
畢業系所 |
數學系 |
論文名稱 |
機率方法再組合學中的探討 (The probabilistic method in additive combinatorics)
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相關論文 | |
檔案 |
[Endnote RIS 格式]
[Bibtex 格式]
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摘要(中) |
機率方法又稱為Erdős 機率方法,用機率方法去建構一個合理性質的集合
對組合學來說是很有用而且強大的,像是thin bases 。在這篇論文裡,我們探
討和機率方法有關的內容,包含sum-free set, prime divisors, thin bases 還有 complementary bases。讓我們透過探討過程,了解論文中的內容以及定理間的關係。 |
摘要(英) |
The probabilistic method is also called Erdős probabilistic method. In combinatorics, the probabilistic method is powerful and useful for constructing sets with certain desirable properties (Example. thin bases of the integers). In this thesis we use probabilistic method to study sum-free set, prime divisors, thin bases and complementary bases to probing the probabilistic method. |
關鍵字(中) |
★ 機率方法 |
關鍵字(英) |
★ The probabilistic method |
論文目次 |
中文摘要 i
英文摘要 ii
目錄 iii
符號 v
1 Introduction 1
2 The first moment method 2
2.1 Sum-free sets 3
3 The second moment method 4
3.1 The number of prime divisors 5
4 The exponential moment method 9
4.1 Sidon′s problem on thin bases 11
4.2 Complementary bases 14
參考資料 16 |
參考文獻 |
[1] CSAIL. Randomness and Computation. Ronitt Rubinfeld, MIT Computer
Science And Intelligence Laboratory. Available at: http:// people.
csail.mit.edu/ ronitt/ COURSE/ S08/ download/ notes02.pdf. (2012)Accessed
24 May 2015.
[2] CMU. Chernoff Bounds. Shuchi Chawla, Carnegie Mellon University. Available
at: http:// www.cs.cmu.edu/ afs/ cs/ academic/ class/ 15859-f04/ www/
scribes/lec9.pdf. (2004)Accessed 16 March 2015.
[3] J.Spencer and N.Alon, The Probabilistic Method, 3rd(2007),1-4.
[4] P.Tuan, On a theorem of Hardy and Ramanujan, J.London Math. Soc. 9
(1934), 274–276.
[5] T.Tao and V.Vu, Additive-Combinatorics, 1st (2006), 1-18.
[6] WMD. Base. Wolfram Math World. Available at: http:// mathworld.
wolfram.com/Base.html. Accessed 21 April 2015. |
指導教授 |
沈俊嚴(Chun-Yen Shen)
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審核日期 |
2015-7-31 |
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