Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 015, 6 pages      arXiv:2501.18061      https://doi.org/10.3842/SIGMA.2025.015
Contribution to the Special Issue on Basic Hypergeometric Series Associated with Root Systems and Applications in honor of Stephen C. Milne

Experimenting with the Garsia-Milne Involution Principle

Shalosh B. Ekhad and Doron Zeilberger
Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen Rd., Piscataway, NJ 08854-8019, USA

Received January 31, 2025, in final form February 26, 2025; Published online March 04, 2025

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.

Key words: Garsia-Milne involution principle.

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