## Threshold functions for distinct parts: revisiting Erdős-Lehner

- Oct. 10, 2012
- 3:30 p.m.
- LeConte 312

## 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 essentially equivalent to the Erdős-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.

This is joint work with
É. Czabarka
and M. Marsili.