{
  "abstract": "Let $\\Bbbk$ be an algebraically closed field of characteristic zero, let $V=\\Bbbk^\\ell$ and $W=\\Bbbk^m$, and set \\[ \\mathcal R_{\\ell,m}=\\operatorname{Sym}(\\operatorname{Sym}^2V\\otimes W)^{U_V}. \\] We construct an explicit skew-symmetrizable seed $Σ_{\\ell,m}$ by restricting and folding the determinantal seed for the flagged $m$-arrow Kronecker quiver. For every $\\ell,m\\ge2$, we have \\[ \\mathcal R_{\\ell,m}=\\mathcal U(Σ_{\\ell,m}), \\] with polynomial frozen coefficients, and $Σ_{\\ell,m}$ admits a reddening sequence. The theta basis extends across the frozen boundary exactly for parameters in a rational polyhedral cone $\\mathscr C_{\\ell,m}$. Its weight fibers count the multigraded highest-weight multiplicities of $\\mathcal R_{\\ell,m}$, and the Jacobi--Trudi identity expresses symmetric-square plethysm coefficients as finite alternating sums of these counts. Optimized frozens give an explicit finite system of inequalities for $\\mathscr C_{\\ell,m}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.00963",
  "author_total": 2,
  "authors": [
    {
      "name": "Yelin Fan"
    },
    {
      "name": "Jiarui Fei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/arrtprtfqshzm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.00963",
  "fulltext_url": null,
  "id": "arrtprtfqshzm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.00963",
  "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.AC"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7172414416",
  "pdf_url": "https://arxiv.org/pdf/2608.00963",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/arrtprtfqshzm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2608.00963",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.00963"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Cluster Algebras for Bosonic Plethysm",
  "title_text": "Cluster Algebras for Bosonic Plethysm",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/arrtprtfqshzm",
  "venue": "arXiv",
  "versions": []
}