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arXiv · 0902.2964

Bounds on the Location of the Maximum Stirling Numbers of the Second Kind

Yaming Yu
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Abstract

Let K_n denote the smaller mode of the nth row of Stirling numbers of the second kind S(n, k). Using a probablistic argument, it is shown that for all n>=2, [exp(w(n))]-2<=K_n<=[exp(w(n))]+1, where [x] denotes the integer part of x, and w(n) is Lambert's W-function.

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Yaming Yu. 2009-02-17. Bounds on the Location of the Maximum Stirling Numbers of the Second Kind. https://doi.org/10.1016/j.disc.2009.02.022

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