Gentile statistics and restricted partitions

Abstract

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.

13 Pages, 3 Postscript figures, title changed and minor corrections

References in corpus (1)

• On the Quantum Density of States and Partitioning an Integer

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• Enumeration of plane partitions with a restricted number of parts