{
  "abstract": "We prove that monomial coefficients in affine families of key and Schubert polynomials are eventually polynomial. These results extend to finite products. Using M.~Watanabe's Schubert duality, we deduce that stretched Schubert structure constants are eventually polynomial. This proves a conjecture stated by I.~Pak and Z.~Slonim. We also prove that the positive key expansion of every affine-code family of Schubert polynomials eventually has fixed coefficients and affine indices. The proofs combine Demazure operators and vector partition functions with P.~Magyar's orthodontic formula and the generalized Demazure character theory of V.~Lakshmibai, P.~Littelmann, and P.~Magyar.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.18746",
  "author_total": 1,
  "authors": [
    {
      "name": "Per Alexandersson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4paa49fzzfbax.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.18746",
  "fulltext_url": null,
  "id": "4paa49fzzfbax",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.18746",
  "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.AG"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7170063717",
  "pdf_url": "https://arxiv.org/pdf/2607.18746",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4paa49fzzfbax.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2607.18746",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.18746"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Polynomiality of Stretched Schubert Structure Constants and Key Coefficients",
  "title_text": "Polynomiality of Stretched Schubert Structure Constants and Key Coefficients",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/4paa49fzzfbax",
  "venue": "arXiv",
  "versions": []
}