The Rogers-Ramanujan Identities and Cauchy's Identity

TL;DR

This paper explores the Rogers-Ramanujan identities through the lens of the Cauchy identity for Schur functions, providing new insights into their combinatorial and algebraic structures.

Contribution

It introduces a novel approach linking Rogers-Ramanujan identities with Schur function identities, enhancing understanding of their underlying combinatorics.

Findings

Established connections between Rogers-Ramanujan and Schur identities

Derived new algebraic relations involving Schur functions

Provided a framework for further combinatorial interpretations

Abstract

The Rogers-Ramanujan identities are investigated using the Cauchy identity for Schur functions.