{
  "abstract": "Skew divided difference operators \\(\\partial_{w/v}\\), introduced by Macdonald, play an important role in the study of Schubert polynomials and their structure constants. For permutations \\(u,v,w\\in S_n\\), we show that the coefficient of each monomial \\(\\xx^α\\) in \\(\\partial_{w/v}\\SSch_u(\\xx;\\yy)\\), where \\(\\SSch_u(\\xx;\\yy)\\) is the double Schubert polynomial, is a single triple Schubert coefficient evaluated at \\(\\tb=0\\), whose indices form an explicit lift of \\((u,v,w)\\) to \\(S_{n+\\absα}\\). As an application, we show that every coefficient of \\(\\partial_{w/v}\\SSch_u(\\xx)\\) is a single Schubert structure constant. This gives a new proof of Kirillov's conjecture that these coefficients are nonnegative.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21053",
  "author_total": 1,
  "authors": [
    {
      "name": "Byung-Hak Hwang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3j68h9exynvw1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21053",
  "fulltext_url": null,
  "id": "3j68h9exynvw1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21053",
  "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"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7222741959",
  "pdf_url": "https://arxiv.org/pdf/2610.21053",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3j68h9exynvw1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21053",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21053"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Coefficient lifting for skew divided differences and triple Schubert coefficients",
  "title_text": "Coefficient lifting for skew divided differences and triple Schubert coefficients",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/3j68h9exynvw1",
  "venue": "arXiv",
  "versions": []
}