{
  "abstract": "We use the partition functions of a five-vertex exactly solvable lattice model from statistical mechanics to give new combinatorial formulae for the Schubert structure constants of torus-equivariant quantum K-theory rings of Grassmannians. The proofs build on our earlier results where we identified the transfer matrices of these lattice models geometrically as multiplications by the Hirzebruch $λ_y$ classes of the tautological subbundle and the (dual) quotient bundle. The structure constants are solutions of a system of linear equations with coefficients given by the partition function. This system may be solved explicitly by specializing the Hirzebruch parameter $y$ to an equivariant parameter, leading to explicit formulae using Cramer's rule. Furthermore, we give an alternative combinatorial construction of the partition functions in terms of sums over cylindric set-valued tableaux, which we call cylindric Grothendieck polynomials. The latter generalise McNamara's factorial skew Grothendieck and Yeliussizov's modified Grothendieck polynomials and can be thought of as an equivariant K-theoretic version of Postnikov's toric Schur function. We also provide new polynomial representatives for equivariant K-theory classes of Richardson varieties and their variants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31607",
  "author_total": 3,
  "authors": [
    {
      "name": "Vassily Gorbounov"
    },
    {
      "name": "Christian Korff"
    },
    {
      "name": "Leonardo C. Mihalcea"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/27f3tpqkmm11h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31607",
  "fulltext_url": null,
  "id": "27f3tpqkmm11h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31607",
  "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",
      "nlin.SI"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7223333609",
  "pdf_url": "https://arxiv.org/pdf/2610.31607",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/27f3tpqkmm11h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2610.31607",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31607"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.SI",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Quantum K-structure constants and cylindric Grothendieck polynomials for Grassmannians",
  "title_text": "Quantum K-structure constants and cylindric Grothendieck polynomials for Grassmannians",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/27f3tpqkmm11h",
  "venue": "arXiv",
  "versions": []
}