{
  "abstract": "The hypersimplex $Δ_{k,n}$ is the convex hull of all 0/1-vectors of length $ n $ with coordinate sum $ k $. Early conjectured, and Kim proved, a combinatorial formula for the $ h^* $-polynomial of $Δ_{k,n}$ in terms of hypersimplicial decorated ordered set partitions. In this paper, we refine the Early--Kim formula to the flag $h$-numbers of the alcove triangulation of $\\hyp$. We also give a representation-theoretic interpretation of its flag $f$-numbers in terms of Young permutation modules.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07451",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuhan Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bvxgzes9s4n82.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07451",
  "fulltext_url": null,
  "id": "bvxgzes9s4n82",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07451",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7221043188",
  "pdf_url": "https://arxiv.org/pdf/2610.07451",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bvxgzes9s4n82.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07451",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07451"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A flag refinement of the $ h^* $-formula for the hypersimplices",
  "title_text": "A flag refinement of the $ h^* $-formula for the hypersimplices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/bvxgzes9s4n82",
  "venue": "arXiv",
  "versions": []
}