  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.
