The Method of Combinatorial Telescoping

TL;DR

This paper introduces a combinatorial telescoping method for proving q-series identities, transforming bijections of combinatorial objects into telescoping relations, demonstrated through Watson's identity related to Rogers-Ramanujan identities.

Contribution

The paper presents a novel combinatorial telescoping technique that simplifies proofs of q-series identities by linking combinatorial classifications to telescoping relations.

Findings

Provided a combinatorial proof of Watson's identity

Connected combinatorial objects to telescoping relations

Enhanced understanding of Rogers-Ramanujan identities

Abstract

We present a method for proving q-series identities by combinatorial telescoping, in the sense that one can transform a bijection or a classification of combinatorial objects into a telescoping relation. We shall illustrate this method by giving a combinatorial proof of Watson's identity which implies the Rogers-Ramanujan identities.