A probabilistic proof of Euler's pentagonal number theorem

TL;DR

This paper introduces a probabilistic approach to proving Euler's pentagonal number theorem using a novel shuffling model, offering an alternative perspective to classical proofs.

Contribution

It provides the first probabilistic proof of Euler's pentagonal number theorem, expanding the methods available for combinatorial identities.

Findings

Probabilistic proof of Euler's pentagonal number theorem

Introduction of a shuffling model for combinatorial proofs

New insights into partition identities

Abstract

We present a probabilistic proof of Euler's pentagonal number theorem based on a shuffling model.