An Almost Accurate Location of the Maximum Stirling Number(s) of the Second Kind |
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Authors: | Horst Wegner |
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Institution: | 1. Department of Mathematics, University of Duisburg-Essen, Forsthausweg 2, 47057, Duisburg, Germany
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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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