Corpus ID: 162168623

A Short Note on the Average Maximal Number of Balls in a Bin

@article{Michelen2020ASN,
  title={A Short Note on the Average Maximal Number of Balls in a Bin},
  author={M. Michelen},
  journal={J. Integer Seq.},
  year={2020},
  volume={23},
  pages={20.1.7}
}

• M. Michelen
• Published 2020
• Mathematics, Computer Science
• J. Integer Seq.

We analyze the asymptotic behavior of the average maximal number of balls in a bin obtained by throwing uniformly at random $r$ balls without replacement into $n$ bins, $T$ times. Writing the expected maximum as $\frac{r}{n}T+ C_{n,r}\sqrt{T} + o(\sqrt{T})$, a recent preprint of Behrouzi-Far and Zeilberger asks for an explicit expression for $C_{n,r}$ in terms of $n,r$ and $\pi$. In this short note, we find an expression for $C_{n,r}$ in terms of $n, r$ and the expected maximum of $n… Expand

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