论文标题
整数分区的中心限制定理
A Central Limit Theorem for Integer Partitions into Small Powers
论文作者
论文摘要
对$ n = a_ {1} + \ dots + a _ {\ ell} $的解决方案数量的研究$ p（n）$，带有integers $ 1 \ leq a_ {1} \ leq \ leq \ leq \ dots \ leq a _ {\ ell} $ a _ {\ ell} $具有长期历史。在本文中，我们研究了整数的变体，即整数分区\ begin {equation*} n = \ lfloor a_1^α\ rfloor + \ cdots + \ lfloor a_ \ ell^al^α\ rfloor \ end end {equart {equation*}，$ 1 \ leq a_1 <\ cdots <a_ \ ell $和一些已固定的$ 0 <α<α<1 $。特别是，我们使用鞍点方法证明了此类分区中汇总数的中心限制定理。
The study of the well-known partition function $p(n)$ counting the number of solutions to $n = a_{1} + \dots + a_{\ell}$ with integers $1 \leq a_{1} \leq \dots \leq a_{\ell}$ has a long history in combinatorics. In this paper, we study a variant, namely partitions of integers into \begin{equation*} n=\lfloor a_1^α\rfloor + \cdots + \lfloor a_\ell^α\rfloor \end{equation*} with $1\leq a_1 < \cdots < a_\ell$ and some fixed $0 < α< 1$. In particular, we prove a central limit theorem for the number of summands in such partitions, using the saddle point method.
