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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}
}

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