{
  "abstract": "We prove four conjectures of Takigiku and Tsuchioka consisting of eight Rogers--Ramanujan type identities. Two conjectures involve triple sums and a third involves quadruple sums, and their product sides are certain level $2$ principal characters of $A_{13}^{(2)}$. The fourth conjecture gives multisum representations of certain level $2$ principal characters of $A_{2\\ell-1}^{(2)}$. The proofs rely on the Bailey pair method, finite sum identities involving Gaussian polynomials, and the quintuple product identity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18666",
  "author_total": 1,
  "authors": [
    {
      "name": "Liuquan Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f51hd51bpn1y2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18666",
  "fulltext_url": null,
  "id": "f51hd51bpn1y2",
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  "landing_url": "https://arxiv.org/abs/2610.18666",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
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  "openalex": "W7221774372",
  "pdf_url": "https://arxiv.org/pdf/2610.18666",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f51hd51bpn1y2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18666",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18666"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Proofs of four Takigiku--Tsuchioka conjectures on level $2$ principal characters of $A_{2\\ell-1}^{(2)}$",
  "title_text": "Proofs of four Takigiku--Tsuchioka conjectures on level $2$ principal characters of A_2ℓ−1^(2)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/f51hd51bpn1y2",
  "venue": "arXiv",
  "versions": []
}