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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:106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.

    1 Introduction 1 2 Definition 4 3 The Asymptotic Estimation of the Number of Restricted Growth Functions of Order 2 6 4 The Asymptotic Estimation of the Expected Value and the Variance of Restricted Growth Functions of Order 2 11 5 The Asymptotic Normality of Restricted Growth Functions of Order 2 15 6 Conclusion and Future Work 19 References 20

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