# A lower bound for the partition function from Chebyshev's inequality applied to a coin flipping model for the random partition

## TL;DR

This paper establishes a lower bound for the growth rate of the partition function p(n) using a coin flipping model and Chebyshev's inequality, providing a new probabilistic approach to partition theory.

## Contribution

It introduces a novel probabilistic method employing Chebyshev's inequality to derive a lower bound for the partition function p(n).

## Key findings

- Proves that lim (log p(n))/sqrt(n) ≥ C for an explicit constant C.
- Uses a coin flipping model to analyze the random partition.
- Provides a new lower bound for the partition function growth rate.

## Abstract

We use a coin flipping model for the random partition and Chebyshev's inequality to prove the lower bound $\lim \frac{\log p(n)}{\sqrt{n}} \ge C$ for the number of partitions $p(n)$ of $n$, where $C$ is an explicit constant.