{
  "abstract": "The forest polynomials $\\mathfrak{P}_a$ of Nadeau-Tewari form a $\\mathbb{Z}$-basis of $\\mathbb{Z}[x_1,x_2,\\ldots]$ whose role for the cohomology of the quasisymmetric flag variety parallels that of Schubert polynomials for the classical flag variety. Nonnegativity of the structure constants $β_{a,b}^c$ in $\\mathfrak{P}_a \\mathfrak{P}_b = \\sum_c β_{a,b}^c \\mathfrak{P}_c$ is known, but no Littlewood-Richardson-style enumerative rule has been available. We give such a rule: $β_{a,b}^c$ counts pairs of forest RC graphs of forest-codes $a$ and $b$ whose lift product lands on a forest RC graph of forest-code and weight both equal to $c$. The same rule descends to the cup product on $H^\\bullet(\\mathrm{QFl}_n)$. The proof introduces a squash product $\\boxtimes$ on RC graphs, which on full Grassmannian RC graphs of a fixed height recovers the plactic monoid, a multiplactic algebra $\\mathcal{M}_n$ that models Schubert polynomial multiplication, and a lift product $*$ on RC graphs whose quasi-crystal structure, in the framework of Cain-Guilherme-Malheiro, transports the Nadeau-Tewari forest equivalence through the computation. The row-decomposition machinery on RC graphs that underlies these constructions is developed in a companion paper.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.23876",
  "author_total": 1,
  "authors": [
    {
      "name": "Matthew J. Samuel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aacs2fe06m2k1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.23876",
  "fulltext_url": null,
  "id": "aacs2fe06m2k1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.23876",
  "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": "W7165759527",
  "pdf_url": "https://arxiv.org/pdf/2606.23876",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aacs2fe06m2k1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2606.23876",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.23876"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Littlewood-Richardson Rule for Forest Polynomials",
  "title_text": "A Littlewood-Richardson Rule for Forest Polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/aacs2fe06m2k1",
  "venue": "arXiv",
  "versions": []
}