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<p>The Rogers–Ramanujan–Gordon identities generalize the classical partition identities discovered independently by Rogers and 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 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–Poincaré series of suitably constructed graded algebras.</p>

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

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • Alapan Ghosh,
  • Rupam Barman

摘要

The Rogers–Ramanujan–Gordon identities generalize the classical partition identities discovered independently by Rogers and 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 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–Poincaré series of suitably constructed graded algebras.