{
  "abstract": "We prove the (signed) Grothendieck join--meet positivity $$ G_{λ\\veeμ}G_{λ\\wedgeμ} -G_λG_μ\\in \\sum_ν \\mathbb{N}\\cdot (-1)^{|ν|-|λ|-|μ|}G_ν$$ for stable Grothendieck polynomials using geometric Satake equivalence, thereby resolving a conjecture posed by Thomas and Yong.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34607",
  "author_total": 4,
  "authors": [
    {
      "name": "Peter L. Guo"
    },
    {
      "name": "Mingyang Kang"
    },
    {
      "name": "Jiaji Liu"
    },
    {
      "name": "Rui Xiong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bnfsd1ycy6d3y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34607",
  "fulltext_url": null,
  "id": "bnfsd1ycy6d3y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34607",
  "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": "W7223781226",
  "pdf_url": "https://arxiv.org/pdf/2610.34607",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bnfsd1ycy6d3y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34607",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34607"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A proof of the Grothendieck join-meet positivity",
  "title_text": "A proof of the Grothendieck join-meet positivity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/bnfsd1ycy6d3y",
  "venue": "arXiv",
  "versions": []
}