{
  "abstract": "A classical result by Kreweras (1965) allows one to compute the number of plane partitions of a given skew shape and bounded parts as certain determinants. We prove that these determinants expand as polynomials with nonnegative coefficients. This result can be reformulated in terms of order polynomials of cell posets of skew shapes and explains important positivity phenomena about the Ehrhart polynomials of shard polytopes, matroids, and order polytopes. Among other applications, we generalize a positivity statement from Schubert calculus by Fomin and Kirillov (1997) from straight shapes to skew shapes. We show that all shard polytopes are Ehrhart positive and, stronger, that all fence posets, including the zig‐zag poset, and all circular fence posets have order polynomials with nonnegative coefficients. We discuss a general method for proving positivity that reduces to showing positivity of the linear terms of the order polynomials. We propose positivity conjectures on other relevant classes of posets.",
  "abstract_shown": true,
  "affiliations": [
    "Università di Pisa Pisa Italy",
    "Université du Québec à Montréal Montréal Québec Canada",
    "University of Southern California Los Angeles, California USA"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Luis Ferroni",
      "orcid": "0000-0001-5181-7932"
    },
    {
      "affs": [
        1
      ],
      "name": "Alejandro H. Morales",
      "orcid": "0000-0002-2848-3230"
    },
    {
      "affs": [
        2
      ],
      "name": "Greta Panova",
      "orcid": "0000-0003-0785-1580"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/711qwm75tyzbz.bib",
  "cited_by": 13,
  "doi": "10.1112/plms.70204",
  "fulltext_url": null,
  "id": "711qwm75tyzbz",
  "issns": [
    "0024-6115",
    "1460-244X"
  ],
  "landing_url": "https://doi.org/10.1112/plms.70204",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W4415289328",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-01",
  "publisher": "Wiley",
  "ris": "https://research.draconitic.com/paper/711qwm75tyzbz.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T13:20:42Z",
      "native_id": "W4415289328",
      "source": "openalex",
      "url": "https://doi.org/10.1112/plms.70204"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2607|Advanced Combinatorial Mathematics",
      "subfield": "combinatorics"
    }
  ],
  "title": "Skew shapes, Ehrhart positivity, and beyond",
  "title_text": "Skew shapes, Ehrhart positivity, and beyond",
  "type": "peer-reviewed",
  "updated_at": "2026-11-09T13:21:00Z",
  "url": "https://research.draconitic.com/paper/711qwm75tyzbz",
  "venue": "Proceedings of the London Mathematical Society",
  "versions": []
}