{
  "abstract": "Backman and Liu proved that every integral generalized permutohedron of type $A$, and in particular every matroid base polytope, admits a regular unimodular triangulation. The analogous statement fails in type $B$: the delta-matroid simplex \\[\\operatorname*{conv}\\{\\mathbf{0},\\ e_1+e_2,\\ e_1+e_3,\\ e_2+e_3\\}\\] has normalized volume $2$ and no lattice points other than its vertices, so it has no unimodular triangulation. We show moreover that, up to the natural symmetries of the $0/1$ cube and deletion of constant coordinates, it is the unique non-unimodular delta-matroid polytope that is a simplex. We prove instead that every delta-matroid polytope admits a regular dyadic triangulation, meaning a lattice triangulation whose maximal simplices have normalized volumes that are powers of two. More generally, every integral type $B$ generalized permutohedron admits such a triangulation. The main lattice-theoretic ingredient is that the type $B$ root configuration forms a totally dyadic system, a $2$-local analogue of total unimodularity. As a consequence, these polytopes satisfy a dyadic version of the integer decomposition property. In each dimension the corresponding exponent can be chosen uniformly, even though ordinary integer decomposition can fail for delta-matroid polytopes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18331",
  "author_total": 1,
  "authors": [
    {
      "name": "Mathieu Vallée"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ftcnnpzrvdwny.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18331",
  "fulltext_url": null,
  "id": "ftcnnpzrvdwny",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18331",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213529220",
  "pdf_url": "https://arxiv.org/pdf/2609.18331",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ftcnnpzrvdwny.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18331",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18331"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Regular dyadic triangulations of delta-matroid polytopes",
  "title_text": "Regular dyadic triangulations of delta-matroid polytopes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/ftcnnpzrvdwny",
  "venue": "arXiv",
  "versions": []
}