{
  "abstract": "We develop a few calculus rules to compute or lower bound the facial distance of a polytope. We illustrate our calculus rules on various popular polytopes. In particular, we provide a provide a lower bound on the facial distance of the Birkhoff polytope.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28971",
  "author_total": 2,
  "authors": [
    {
      "name": "Javier Pena"
    },
    {
      "name": "Elias Wirth"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a8fvss424zk6x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28971",
  "fulltext_url": null,
  "id": "a8fvss424zk6x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28971",
  "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"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7204909108",
  "pdf_url": "https://arxiv.org/pdf/2608.28971",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a8fvss424zk6x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.28971",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28971"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Calculus of the Facial Distance",
  "title_text": "Calculus of the Facial Distance",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/a8fvss424zk6x",
  "venue": "arXiv",
  "versions": []
}