Abstract
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.
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Wegner, H. An Almost Accurate Location of the Maximum Stirling Number(s) of the Second Kind. Results. Math. 61, 231–243 (2012). https://doi.org/10.1007/s00025-011-0093-1
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DOI: https://doi.org/10.1007/s00025-011-0093-1