{
  "abstract": "Tamari lattices and weak Bruhat order are classical posets on the vertices of associahedra and permutohedra. These posets are particular instances of the \\emph{flip order} on the vertices of graph associahedra. We present here a generalisation of the flip order to all the faces of nestohedra, encoded in terms of hypergraphs. For right-filled hypergraphs, we characterise our order in terms of generalised inversions. As an application, we describe shuffle products on faces of suitable nestohedra as sums over intervals in this order.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.20132",
  "author_total": 3,
  "authors": [
    {
      "name": "Pierre-Louis Curien"
    },
    {
      "name": "Bérénice Delcroix-Oger"
    },
    {
      "name": "Jovana Obradović"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1h5sjypsrc6wm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.20132",
  "fulltext_url": null,
  "id": "1h5sjypsrc6wm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.20132",
  "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": "W7170152720",
  "pdf_url": "https://arxiv.org/pdf/2607.20132",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1h5sjypsrc6wm.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:13Z",
      "native_id": "2607.20132",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.20132"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Generalised flip order on the faces of nestohedra",
  "title_text": "Generalised flip order on the faces of nestohedra",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/1h5sjypsrc6wm",
  "venue": "arXiv",
  "versions": []
}