Partitions of multisets. II
[For part I see the paper of the first author, ibid. 9, 301-311 (1974; Zbl 0289.05014.] A multiset of type \(m\) is a multiset in which exactly \(m_ i\) distinct elements appear exactly \(i\) times. The number of partitions of a multiset of type \(m\) having exactly \(t\) blocks of size \(b\) is \(e^{-\gamma}\gamma^ t/t!+o(1)\) when \(M\to \infty,\), where \(M=\sum im_ i,\gamma =(\log s)^ b/b!\) and \(s \log s=M.\) This result extends an earlier result of \textit{J. Haigh} [J. Comb. Theory, Ser. A 13, 287--295 (1972; Zbl 0238.05003)].
scientific article; zbMATH DE number 3880712