{
  "abstract": "We introduce a transformation on partially ordered sets, termed the \\emph{stellahedral transform}, with notable features. It preserves the properties of being Eulerian, Cohen--Macaulay, and of being the face poset of a polytope. Furthermore, it admits an explicit geometric realization for convex polytopes and specializes to the construction that takes a simplex to the stellahedron. One motivation for this definition comes from the theory of toric $h$-polynomials and (augmented) Chow polynomials of Eulerian posets. We show that the right augmented Chow polynomial of an Eulerian poset $P$ agrees with the toric $h$-polynomial of the stellahedral transform of $P$. We use this perspective, together with $\\mathbf{cd}$-index results due to Ehrenborg (2005) and Karu (2006), to prove two positivity results for augmented Chow polynomials: for Gorenstein* posets they are unimodal, and for face posets of polytopes they are $γ$-positive. Along the way we provide negative answers to two open questions concerning Eulerian and Gorenstein* posets. First, the question on the nonnegativity of Eulerian Chow polynomials, posed by Ferroni, Matherne, and Vecchi (2024). Second, the question posed by Athanasiadis and Kalampogia-Evangelinou (2023) on the real-rootedness of chain and Chow polynomials of Gorenstein* posets: these examples provide a novel application of a technique introduced by Murai and Nevo (2014).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22078",
  "author_total": 3,
  "authors": [
    {
      "name": "Tommaso Faustini"
    },
    {
      "name": "Luis Ferroni"
    },
    {
      "name": "Ludovico Piazza"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e40k5hcpv87e9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22078",
  "fulltext_url": null,
  "id": "e40k5hcpv87e9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22078",
  "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": "W7213896350",
  "pdf_url": "https://arxiv.org/pdf/2609.22078",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e40k5hcpv87e9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.22078",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22078"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Stellahedral geometry of partially ordered sets",
  "title_text": "Stellahedral geometry of partially ordered sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/e40k5hcpv87e9",
  "venue": "arXiv",
  "versions": []
}