科研之友
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摘要
The Stirling number of the second kind S(n, k) is the number of ways of partitioning a set of n elements into k nonempty subsets. It is well known that the numbers S(n, k) are unimodal in k, and there are at most two consecutive values K (n) such that (for fixed n) S(n, K (n) ) is maximal. We determine asymptotic bounds for K (n) , which are unexpectedly good and improve earlier results. The method used here shows a possible strategy for obtaining numerical bounds such that in almost all cases K (n) can be uniquely determined.
- 出版日期2012-6
