Experimenting with the Garsia-Milne Involution Principle

TL;DR

This paper revisits the Garsia-Milne Involution Principle, a combinatorial tool used in bijective proofs like the Rogers-Ramanujan identities, analyzing its general properties and complexity.

Contribution

It provides a broad, application-independent perspective on the Involution Principle and explores its computational complexity.

Findings

Offers a general framework for the Involution Principle

Analyzes the complexity of the involution process

Provides insights into its applicability beyond specific identities

Abstract

In 1981, Adriano Garsia and Steve Milne found the first bijective proof of the celebrated Rogers-Ramanujan identities. To achieve this feat, they invented a versatile tool that they called the Involution Principle. In this note we revisit this useful principle from a very general perspective, independent of its application to specific combinatorial identities, and will explore its complexity.