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arXiv · 2602.02187

$J$-generalization of the Rogers-Ramanujan-Gordon identities via commutative algebra

Alapan Ghosh·Rupam Barman
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Abstract

The Rogers-Ramanujan-Gordon identities generalize the classical partition identities discovered independently by L. J. Rogers and S. Ramanujan. In 2021, Afsharijoo provided a commutative algebra proof of the Rogers-Ramanujan-Gordon identities. Building on the Afsharijoo's approach, we present a commutative algebra proof of a broader family of identities introduced by Coulson \textit{et al.}, which includes the Rogers-Ramanujan-Gordon identities as a special case. In the proof, we relate the generating functions associated with these identities to the Hilbert-Poincar\'e series of suitably constructed graded algebras.

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Alapan Ghosh, Rupam Barman. 2026-02-02. $J$-generalization of the Rogers-Ramanujan-Gordon identities via commutative algebra. https://arxiv.org/abs/2602.02187

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