{
  "abstract": "In this paper, we revisit the work of Berkovich and Paule on variants of the Andrews-Gordon identities. We find a generalization of their principal polynomial identity and, as a consequence, obtain new $\\vec M$ versions of the Andrews-Gordon identities. More precisely, for non-negative integers $M_1\\ge M_2\\ge M_3\\ge\\ldots\\ge M_ν$, we show that a broad class of multi-sums of the form $$ \\sum\\limits_{\\mathbf n} \\frac{ q^{ N_1^2+\\cdots+N_ν^2 - M_1N_1 - M_2N_2 - \\cdots - M_νN_ν} }{ (q)_{n_1}(q)_{n_2}\\cdots(q)_{n_ν} } $$ can be expressed as a sum of products. Above, we use standard notations for $q$-Pochhammer symbols and $N_i = \\sum\\limits_{k=i}^νn_k$ for $1\\le i\\le ν$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07490",
  "author_total": 2,
  "authors": [
    {
      "name": "Alexander Berkovich"
    },
    {
      "name": "Aritram Dhar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1a56vy5978vhv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07490",
  "fulltext_url": null,
  "id": "1a56vy5978vhv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07490",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7212053915",
  "pdf_url": "https://arxiv.org/pdf/2609.07490",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1a56vy5978vhv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.07490",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07490"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "$\\vec M$ Versions of Andrews-Gordon Identities Revisited",
  "title_text": "M⃗ Versions of Andrews-Gordon Identities Revisited",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/1a56vy5978vhv",
  "venue": "arXiv",
  "versions": []
}