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arXiv · 1209.5764

Threshold functions for distinct parts: revisiting Erdos-Lehner

Éva Czabarka·Matteo Marsili·László Székely
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Abstract

We study four problems: put $n$ distinguishable/non-distinguishable balls into $k$ non-empty distinguishable/non-distinguishable boxes randomly. What is the threshold function $k=k(n) $ to make almost sure that no two boxes contain the same number of balls? The non-distinguishable ball problems are very close to the Erd\H os--Lehner asymptotic formula for the number of partitions of the integer $n$ into $k$ parts with $k=o(n^{1/3})$. The problem is motivated by the statistics of an experiment, where we only can tell whether outcomes are identical or different.

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Éva Czabarka, Matteo Marsili, László Székely. 2012-10-11. Threshold functions for distinct parts: revisiting Erdos-Lehner. https://arxiv.org/abs/1209.5764

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