Gentile统计与限制划分
Gentile statistics and restricted partitions
摘要：
在最近的一篇论文中（Tran等人，Ann.Phys.311（2004）204）中，利用整数的分割与多粒子系统的量子态密度的联系，导出了关于整数的分割的一些渐近数论结果。我们推广这些结果，得到一个渐近公式的限制或有色分区p_k^s（n），这是一个整数n的分区到的整数的s^{th}次幂的被加数，使得每个幂的给定整数可以出现最多k次。虽然该方法是不严格的，它重现了众所周知的渐近结果，除了产生更一般的结果，为任意值的s=1。
英文摘要：
In a recent paper (Tran et al., Ann.Phys.311(2004)204), some asymptotic number theoretical results on the partitioning of an integer were derived exploiting its connection to the quantum density of states of a many-particle system. We generalise these results to obtain an asymptotic formula for the restricted or coloured partitions p_k^s(n), which is the number of partitions of an integer n into the summand of s^{th} powers of integers such that each power of a given integer may occur utmost k times. While the method is not rigorous, it reproduces the well known asymptotic results for s=1 apart from yielding more general results for arbitrary values of s.
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