研究生: |
陳怡廷 Chen, Yi-Ting |
---|---|
論文名稱: |
Enumeration and Asymptotics on Restricted Growth Functions of Order 2 Enumeration and Asymptotics on Restricted Growth Functions of Order 2 |
指導教授: |
林延輯
Lin, Yen-Chi |
學位類別: |
碩士 Master |
系所名稱: |
數學系 Department of Mathematics |
論文出版年: | 2015 |
畢業學年度: | 103 |
語文別: | 英文 |
論文頁數: | 21 |
中文關鍵詞: | 近似常態性 、Hayman admissible 函數 、機率分佈 、限制成⾧函數 、鞍點法 |
英文關鍵詞: | asymptotic normality, Hayman admissible functions, probability distribution, restricted growth functions, saddle-point method |
論文種類: | 學術論文 |
相關次數: | 點閱:123 下載:48 |
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本篇論⽂中,我們延伸限制成⾧函數到更高次,並找到二次限制成長函數和B型對稱分割的⼀對⼀對應關係。為了改善透過傳統⽅法得到的漸進結果,我們介紹⼀個類似⽜頓法的演算法。假設二次限制成長函數為均勻分佈,我們得到二次限制成長函數最大值的期望值和變異數的漸進公式。最後,我們驗證二次限制成⾧函數最大值的分佈收斂到常態分佈。
In this thesis, we extend the restricted growth functions to higher order and find a bijection between restricted growth functions of order 2 and symmetric partitions of type B. To improve the asymptotic results via traditional methods, we introduce an algorithm which is similar to Newton-Raphson method. Assuming that the restricted growth functions of order 2 are uniformly distributed, we obtain the asymptotic formulae for the expectation and variance of the maximum in a random restricted growth function of order 2. Finally, we verify that the distribution of maximum in restricted growth functions of order 2 will converge to a normal distribution.
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