Philip Hall's 'rather curious' formula and the Rogers-Ramanujan identities

TL;DR

This paper demonstrates that a peculiar group-theoretical formula by Philip Hall can be derived from the Rogers-Ramanujan identities, linking group theory with partition identities.

Contribution

It establishes a novel connection between Hall's group formula and the Rogers-Ramanujan identities, providing new insights into their relationship.

Findings

Hall's formula follows from Rogers-Ramanujan identities

Links group theory with partition identities

Provides a new perspective on Hall's formula

Abstract

We show that a strange group theoretical formula of Hall follows from the Rogers-Ramanujan identities.