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

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

2009-02-17

arxiv.org/abs/0902.2964v1

Discrete Mathematics 309 (2009) 4624-4627

Mathematics

Combinatorics

accepted by Discrete Mathematics

Scientific paper

10.1016/j.disc.2009.02.022

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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