A proof of the Göllnitz-Gordon-Andrews identities via commutative algebra
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913057352974336 |
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| author | Barman, Rupam Ghosh, Alapan Singh, Gurinder |
| author_facet | Barman, Rupam Ghosh, Alapan Singh, Gurinder |
| contents | The Göllnitz-Gordon-Andrews identities generalize the partition identities discovered independently by H. Göllnitz and B. Gordon. In this article, we present a commutative algebra proof of the Göllnitz-Gordon-Andrews identities. More generally, we establish a family of identities, the special cases of which are the Göllnitz-Gordon-Andrews identities. In the proof, we relate the generating functions associated with these identities to the Hilbert-Poincaré series of suitably constructed graded algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02189 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A proof of the Göllnitz-Gordon-Andrews identities via commutative algebra Barman, Rupam Ghosh, Alapan Singh, Gurinder Combinatorics Number Theory The Göllnitz-Gordon-Andrews identities generalize the partition identities discovered independently by H. Göllnitz and B. Gordon. In this article, we present a commutative algebra proof of the Göllnitz-Gordon-Andrews identities. More generally, we establish a family of identities, the special cases of which are the Göllnitz-Gordon-Andrews identities. In the proof, we relate the generating functions associated with these identities to the Hilbert-Poincaré series of suitably constructed graded algebras. |
| title | A proof of the Göllnitz-Gordon-Andrews identities via commutative algebra |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2602.02189 |