{
  "abstract": "In this paper we first introduce the \\emph{infinite multi-row periodic pattern of shape $α$} as a geometric realization of $\\mathbf{C}_α$. We then give an explicit formula for the coefficients $b^λ_{α,β}$ appearing in the species decomposition \\[ \\mathbf{C}_α\\times \\mathbf{C}_β = \\sum_{λ\\vdash n} b^λ_{α,β}\\,\\mathbf{C}_λ. \\]",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05010",
  "author_total": 2,
  "authors": [
    {
      "name": "Josaphat Baolahy"
    },
    {
      "name": "Benjamin Randrianirina"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4qrj4w370pa3m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05010",
  "fulltext_url": null,
  "id": "4qrj4w370pa3m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05010",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7211896812",
  "pdf_url": "https://arxiv.org/pdf/2609.05010",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4qrj4w370pa3m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.05010",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05010"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Molecular Species $\\mathbf{C}_α$: Geometric Realization and a Closed Formula for Kronecker Coefficients",
  "title_text": "The Molecular Species C_α: Geometric Realization and a Closed Formula for Kronecker Coefficients",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/4qrj4w370pa3m",
  "venue": "arXiv",
  "versions": []
}